Functions of ManagementManagement has been described as a social process involving responsibility for economical and effective planning & regulation of operation of an enterprise in the fulfillment of given purposes. It is a dynamic process consisting of various elements and activities. These activities are different from operative functions like marketing, finance, purchase etc. Rather these activities are common to each and every manger irrespective of his level or status.

Different experts have classified functions of management. According to Jerry, “There are four fundamental functions of management i.e. planning, organizing, actuating and controlling”.

According to Henry Fayol, “To manage is to forecast and plan, to organize, to command, & to control”. Whereas Luther Gullick has given a keyword ’POSDCORB’ where P stands for Planning, O for Organizing, S for Staffing, D for Directing, Co for Co-ordination, R for reporting & B for Budgeting. But the most widely accepted are functions of management given by KOONTZ and O’DONNEL i.e. Planning, Organizing, Staffing, Directing and Controlling.

For theoretical purposes, it may be convenient to separate the function of management but practically these functions are overlapping in nature i.e. they are highly inseparable. Each function blends into the other & each affects the performance of others.

1. Planning

It is the basic function of management. It deals with chalking out a future course of action & deciding in advance the most appropriate course of actions for achievement of pre-determined goals. According to KOONTZ, “Planning is deciding in advance - what to do, when to do & how to do. It bridges the gap from where we are & where we want to be”. A plan is a future course of actions. It is an exercise in problem solving & decision making. Planning is determination of courses of action to achieve desired goals. Thus, planning is a systematic thinking about ways & means for accomplishment of pre-determined goals. Planning is necessary to ensure proper utilization of human & non-human resources. It is all pervasive, it is an intellectual activity and it also helps in avoiding confusion, uncertainties, risks, wastages etc.

2. Organizing

It is the process of bringing together physical, financial and human resources and developing productive relationship amongst them for achievement of organizational goals. According to Henry Fayol, “To organize a business is to provide it with everything useful or its functioning i.e. raw material, tools, capital and personnel’s”. To organize a business involves determining & providing human and non-human resources to the organizational structure. Organizing as a process involves:

Identification of activities. Classification of grouping of activities.

Assignment of duties. Delegation of authority and creation of responsibility. Coordinating authority and responsibility relationships.

3. Staffing

It is the function of manning the organization structure and keeping it manned. Staffing has assumed greater importance in the recent years due to advancement of technology, increase in size of business, complexity of human behavior etc. The main purpose of staffing is to put right man on right job i.e. square pegs in square holes and round pegs in round holes. According to Koontz & O’Donell, “Managerial function of staffing involves manning the organization structure through proper and effective selection, appraisal & development of personnel to fill the roles designed in the structure”. Staffing involves:

Manpower Planning (estimating man power in terms of searching, choose the person and giving the right place).

Recruitment, Selection & Placement. Training & Development. Remuneration. Performance Appraisal. Promotions & Transfer.

4. Directing

It is that part of managerial function which actuates the organizational methods to work efficiently for achievement of organizational purposes. It is considered life-spark of the enterprise which sets it in motion the action of people because planning, organizing and staffing are the mere preparations for doing the work. Direction is that inert-personnel aspect of management which deals directly with influencing, guiding, supervising, motivating sub-ordinate for the achievement of organizational goals. Direction has following elements:

Supervision Motivation Leadership Communication

Supervision- implies overseeing the work of subordinates by their superiors. It is the act of watching & directing work & workers.

Motivation- means inspiring, stimulating or encouraging the sub-ordinates with zeal to work. Positive, negative, monetary, non-monetary incentives may be used for this purpose.

Leadership- may be defined as a process by which manager guides and influences the work of subordinates in desired direction.

Communications- is the process of passing information, experience, opinion etc from one person to another. It is a bridge of understanding.

5. Controlling

It implies measurement of accomplishment against the standards and correction of deviation if any to ensure achievement of organizational goals. The purpose of controlling is to ensure that everything occurs in conformities with the standards. An efficient system of control helps to predict deviations before they actually occur. According to Theo Haimann, “Controlling is the process of checking whether or not proper progress is being made towards the objectives and goals and acting if necessary, to correct any deviation”. According to Koontz & O’Donell “Controlling is the measurement & correction of performance activities of subordinates in order to make sure that the enterprise objectives and plans desired to obtain them as being accomplished”. Therefore controlling has following steps:

a. Establishment of standard performance.

b. Measurement of actual performance.c. Comparison of actual performance with the standards and finding out deviation if any.d. Corrective action.

Labor Productivity

Productivity in construction is often broadly defined as output per labor hour. Since labor constitutes a large part of the construction cost and the quantity of labor hours in performing a task in construction is more susceptible to the influence of management than are materials or capital, this productivity measure is often referred to as labor productivity. However, it is important to note that labor productivity is a measure of the overall effectiveness of an operating system in utilizing labor, equipment and capital to convert labor efforts into useful output, and is not a measure of the capabilities of labor alone. For example, by investing in a piece of new equipment to perform certain tasks in construction, output may be increased for the same number of labor hours, thus resulting in higher labor productivity.

Construction output may be expressed in terms of functional units or constant dollars. In the former case, labor productivity is associated with units of product per labor hour, such as cubic yards of concrete placed per hour or miles of highway paved per hour. In the latter case, labor productivity is identified with value of construction (in constant dollars) per labor hour. The value of construction in this regard is not measured by the benefit of constructed facilities, but by construction cost. Labor productivity measured in this way requires considerable care in interpretation. For example, wage rates in construction have been declining in the US during the period 1970 to 1990, and since wages are an important component in construction costs, the value of construction put in place per hour of work will decline as a result, suggesting lower productivity.

Productivity at the Job Site

Contractors and owners are often concerned with the labor activity at job sites. For this purpose, it is convenient to express labor productivity as functional units per labor hour for each type of construction task. However, even for such specific purposes, different levels of measure may be used. For example, cubic yards of concrete placed per hour is a lower level of measure than miles of highway paved per hour. Lower-level measures are more useful for monitoring individual activities, while higher-level measures may be more convenient for developing industry-wide standards of performance.

While each contractor or owner is free to use its own system to measure labor productivity at a site, it is a good practice to set up a system which can be used to track productivity trends over time and in varied locations. Considerable efforts are required to collect information regionally or nationally over a number of years to produce such results. The productivity indices compiled from statistical data should include parameters such as the performance of major crafts, effects of project size, type and location, and other major project influences.

In order to develop industry-wide standards of performance, there must be a general agreement on the measures to be useful for compiling data. Then, the job site productivity data collected by various contractors and owners can be correlated and analyzed to develop certain measures for each of the major segment of the construction industry. Thus, a contractor or owner can compare its performance with that of the industry average.

Productivity in the Construction Industry

Because of the diversity of the construction industry, a single index for the entire industry is neither meaningful nor reliable. Productivity indices may be developed for major segments of the construction industry nationwide if reliable statistical data can be obtained for separate industrial segments. For this general type of productivity measure, it is more convenient to express labor productivity as constant dollars per labor hours since dollar values are more easily aggregated from a large amount of data collected from different sources. The use of constant dollars allows meaningful approximations of the changes in construction output from one year to another when price deflators are applied to current dollars to obtain the corresponding values in constant dollars. However, since most construction price deflators are obtained from a combination of price indices for material and labor inputs, they reflect only

the change of price levels and do not capture any savings arising from improved labor productivity. Such deflators tend to overstate increases in construction costs over a long period of time, and consequently understate the physical volume or value of construction work in years subsequent to the base year for the indices.

Factors Affecting Job-Site Productivity

Job-site productivity is influenced by many factors which can be characterized either as labor characteristics, project work conditions or as non-productive activities. The labor characteristics include:

age, skill and experience of workforce leadership and motivation of workforce

The project work conditions include among other factors:

Job size and complexity. Job site accessibility. Labor availability. Equipment utilization. Contractual agreements. Local climate. Local cultural characteristics, particularly in foreign operations.

The non-productive activities associated with a project may or may not be paid by the owner, but they nevertheless take up potential labor resources which can otherwise be directed to the project. The non-productive activities include among other factors:

Indirect labor required to maintain the progress of the project Rework for correcting unsatisfactory work Temporary work stoppage due to inclement weather or material shortage Time off for union activities Absentee time, including late start and early quits Non-working holidays Strikes

Each category of factors affects the productive labor available to a project as well as the on-site labor efficiency.

Labor Characteristics

Performance analysis is a common tool for assessing worker quality and contribution. Factors that might be evaluated include:

Quality of Work - caliber of work produced or accomplished. Quantity of Work - volume of acceptable work Job Knowledge - demonstrated knowledge of requirements, methods, techniques and skills

involved in doing the job and in applying these to increase productivity. Related Work Knowledge - knowledge of effects of work upon other areas and knowledge of

related areas which have influence on assigned work. Judgment - soundness of conclusions, decisions and actions. Initiative - ability to take effective action without being told. Resource Utilization - ability to delineate project needs and locate, plan and effectively use all

resources available. Dependability - reliability in assuming and carrying out commitments and obligations. Analytical Ability - effectiveness in thinking through a problem and reaching sound conclusions. Communicative Ability - effectiveness in using orgal and written communications and in keeping

subordinates, associates, superiors and others adequately informed. Interpersonal Skills - effectiveness in relating in an appropriate and productive manner to others.

Ability to Work Under Pressure - ability to meet tight deadlines and adapt to changes. Security Sensitivity - ability to handle confidential information appropriately and to exercise care in

safeguarding sensitive information. Safety Consciousness - has knowledge of good safety practices and demonstrates awareness of

own personal safety and the safety of others. Profit and Cost Sensitivity - ability to seek out, generate and implement profit-making ideas. Planning Effectiveness - ability to anticipate needs, forecast conditions, set goals and standards,

plan and schedule work and measure results. Leadership - ability to develop in others the willingness and desire to work towards common

objectives. Delegating - effectiveness in delegating work appropriately. Development People - ability to select, train and appraise personnel, set standards of performance,

and provide motivation to grow in their capacity. < li>Diversity (Equal Employment Opportunity) - ability to be sensitive to the needs of minorities, females and other protected groups and to demonstrate affirmative action in responding to these needs.

Duties & Responsibilities of Personnel Manager

Personnel ManagementIt is attracting and developing competent employees and creating the organizational conditions which result in their full utilization and encourages them to put forth their best efforts.

Duties & Responsibilities of Personnel ManagerHuman resource (HR) department deals with wide range of activities from strategic planning level to the day to day operations level. Therefore defining roles and responsibilities of HR manager is a quite complex task but some of the functions carried are summarized below. Involvement in the strategic planning processHR manager gets involved in the strategic planning process of the organization and identifies HR as a core competency of the organization. When HR is assumed as a core competency HR becomes a competitive advantage for the organization and HR manager is responsible of developing the HR of organizations to bring the stated competitive advantage to the organization. Forecasting the labour requirementThe HR manager holds the responsibility of forecasting the labour requirement of the organization in the future based on the future level of sales/production level of the organization. The labour forecast may identify the need for need for hiring or firing employees. RecruitmentOnce the labour forecast is done organization can identify the need for more labour in the organization if the existing workforce is not sufficient to handle the future workload. In such a situation HR manager has to recruit new potential candidates to fill the vacancies. Recruitment is the process of creating a pool of potential candidates who can be employed to fill the vacancies. SelectionSelection is the process by which the most suitable candidate is selected from the recruited pool of candidates. Selection is done by carrying out various types of tests and interviews. HR department/manager is responsible of selecting the most suitable employees to fill existing vacancies. InductionInduction is the process by which new employees are made familiarized with the organizational environment. Once the employees are selected they need to be introduced to other staff of the organization and they should be given necessary guidelines about the organizational culture and the procedures. TrainingOnce the employees are done with the induction they become an employee of the organization but the skills they possess may not be adequate to carry out required tasks. The need for training arises when the there is a gap between expected level of skills and the current level of skills of an employee. If a there is a training need HR department has to design training programs and execute them.

Motivation

HR manager is responsible of motivating employees to carry out their duties of a timely and accurate basis. Performance AppraisalThis is where the employees performance are evaluated based on expected level and the actual level of the performance. HR department needs to design performance appraisal systems to appraise the employee performance on a fairly manner. Rewarding employeesOnce the employee performance evaluation is done HR department needs to design good employee rewarding packages to reward well performing employees. These rewards could be of monetary or non monetary in nature. Managing Carrier Growth of employees/PromotionsHR department is responsible of managing the carrier growth of employees where they needs to promoted in the carrier ladder if they are suitable to fill existing vacancies in high ranks of the organizational structure. Managing redundancyWhen the organization decides that they no longer need the service of certain employee they need to be sent to be given the redundancy notices and have to be paid the redundancy charges. HR department has to manage this process. Managing employee grievanceHR department needs to accept the grievance and complaints submitted by the employees about their problems. HR department need to listen to grievance and should come up with solutions to solve problems. Managing complains about employeesThere can be complaints about employees regarding poor performance, bribery, misbehavior and so on. HR department needs to hear those complains and make necessary steps (advising/punishing employees) to solve those issue

Materials ManagementMaterials management is an important element in project planning and control. Materials represent a major expense in construction, so minimizing procurement or purchase costs presents important opportunities for reducing costs. Poor materials management can also result in large and avoidable costs during construction. First, if materials are purchased early, capital may be tied up and interest charges incurred on the excess inventory of materials. Even worse, materials may deteriorate during storage or be stolen unless special care is taken. For example, electrical equipment often must be stored in waterproof locations. Second, delays and extra expenses may be incurred if materials required for particular activities are not available. Accordingly, insuring a timely flow of material is an important concern of project managers.

Materials management is not just a concern during the monitoring stage in which construction is taking place. Decisions about material procurement may also be required during the initial planning and scheduling stages. For example, activities can be inserted in the project schedule to represent purchasing of major items such as elevators for buildings. The availability of materials may greatly influence the schedule in projects with a fast track or very tight time schedule: sufficient time for obtaining the necessary materials must be allowed. In some case, more expensive suppliers or shippers may be employed to save time.

Materials management is also a problem at the organization level if central purchasing and inventory control is used for standard items. In this case, the various projects undertaken by the organization would present requests to the central purchasing group. In turn, this group would maintain inventories of standard items to reduce the delay in providing material or to obtain lower costs due to bulk purchasing. This organizational materials management problem is analogous to inventory control in any organization facing continuing demand for particular items.

Materials ordering problems lend themselves particularly well to computer based systems to insure the consistency and completeness of the purchasing process. In the manufacturing realm, the use of automated materials requirements planning systems is common. In these systems, the master production schedule, inventory records and product component lists are merged to determine what items must be ordered, when they should be ordered, and how much of each item should be ordered in each time period. The heart of these calculations is simple arithmetic: the projected demand for each material item in each period is subtracted from the available inventory. When the inventory becomes too low, a new order is recommended. For items that are non-standard or not kept in inventory, the calculation is even simpler since no inventory must be considered. With a materials requirement system, much of the detailed record keeping is automated and project managers are alerted to purchasing requirements.

Examples of benefits for materials management systems

From a study of twenty heavy construction sites, the following benefits from the introduction of materials management systems were noted:

In one project, a 6% reduction in craft labor costs occurred due to the improved availability of materials as needed on site. On other projects, an 8% savings due to reduced delay for materials was estimated.

A comparison of two projects with and without a materials management system revealed a change in productivity from 1.92 man-hours per unit without a system to 1.14 man-hours per unit with a new system. Again, much of this difference can be attributed to the timely availability of materials.

Warehouse costs were found to decrease 50% on one project with the introduction of improved inventory management, representing a savings of $ 92,000. Interest charges for inventory also declined, with one project reporting a cash flow savings of $ 85,000 from improved materials management.

Against these various benefits, the costs of acquiring and maintaining a materials management system has to be compared. However, management studies suggest that investment in such systems can be quite beneficial.

Material Procurement and Delivery

The main sources of information for feedback and control of material procurement are requisitions, bids and quotations, purchase orders and subcontracts, shipping and receiving documents, and invoices. For projects involving the large scale use of critical resources, the owner may initiate the procurement procedure even before the selection of a constructor in order to avoid shortages and delays. Under ordinary circumstances, the constructor will handle the procurement to shop for materials with the best price/performance characteristics specified by the designer. Some overlapping and rehandling in the procurement process is unavoidable, but it should be minimized to insure timely delivery of the materials in good condition.

The materials for delivery to and from a construction site may be broadly classified as : (1) bulk materials, (2) standard off-the-shelf materials, and (3) fabricated members or units. The process of delivery, including transportation, field storage and installation will be different for these classes of materials. The equipment needed to handle and haul these classes of materials will also be different.

Bulk materials refer to materials in their natural or semi-processed state, such as earthwork to be excavated, wet concrete mix, etc. which are usually encountered in large quantities in construction. Some bulk materials such as earthwork or gravels may be measured in bank (solid in situ) volume. Obviously, the quantities of materials for delivery may be substantially different when expressed in different measures of volume, depending on the characteristics of such materials.

Standard piping and valves are typical examples of standard off-the-shelf materials which are used extensively in the chemical processing industry. Since standard off-the-shelf materials can easily be stockpiled, the delivery process is relatively simple.

Fabricated members such as steel beams and columns for buildings are pre-processed in a shop to simplify the field erection procedures. Welded or bolted connections are attached partially to the members which are cut to precise dimensions for adequate fit. Similarly, steel tanks and pressure vessels are often partly or fully fabricated before shipping to the field. In general, if the work can be done in the shop where working conditions can better be controlled, it is advisable to do so, provided that the fabricated members or units can be shipped to the construction site in a satisfactory manner at a reasonable cost.

As a further step to simplify field assembly, an entire wall panel including plumbing and wiring or even an entire room may be prefabricated and shipped to the site. While the field labor is greatly reduced in such cases, "materials" for delivery are in fact manufactured products with value added by another type of labor. With modern means of transporting construction materials and fabricated units, the percentages of costs on direct labor and materials for a project may change if more prefabricated units are introduced in the construction process.

In the construction industry, materials used by a specific craft are generally handled by craftsmen, not by general labor. Thus, electricians handle electrical materials, pipefitters handle pipe materials, etc. This multiple handling diverts scarce skilled craftsmen and contractor supervision into activities which do not directly contribute to construction. Since contractors are not normally in the freight business, they do not perform the tasks of freight delivery efficiently. All these factors tend to exacerbate the problems of freight delivery for very large projects.

These different factors could each be assessed on a three point scale: (1) recognized strength, (2) meets expectations, (3) area needing improvement. Examples of work performance in these areas might also be provided.

Project Work Conditions

Job-site labor productivity can be estimated either for each craft (carpenter, bricklayer, etc.) or each type of construction (residential housing, processing plant, etc.) under a specific set of work conditions. A base labor productivity may be defined for a set of work conditions specified by the owner or contractor who wishes to observe and measure the labor performance over a period of time under such conditions. A labor productivity index may then be defined as the ratio of the job-site labor productivity under a different set of work conditions to the base labor productivity, and is a measure of the relative labor efficiency of a project under this new set of work conditions.

The effects of various factors related to work conditions on a new project can be estimated in advance, some more accurately than others. For example, for very large construction projects, the labor productivity index tends to decrease as the project size and/or complexity increase because of logistic problems and the "learning" that the work force must undergo before adjusting to the new environment. Job-site accessibility often may reduce the labor productivity index if the workers must perform their jobs in round about ways, such as avoiding traffic in repaving the highway surface or maintaining the operation of a plant during renovation. Labor availability in the local market is another factor. Shortage of local labor will force the contractor to bring in non-local labor or schedule overtime work or both. In either case, the labor efficiency will be reduced in addition to incurring additional expenses. The degree of equipment utilization and mechanization of a construction project clearly will have direct bearing on job-site labor productivity. The contractual agreements play an important role in the utilization of union or non-union labor, the use of subcontractors and the degree of field supervision, all of which will impact job-site labor productivity. Since on-site construction essentially involves outdoor activities, the local climate will influence the efficiency of workers directly. In foreign operations, the cultural characteristics of the host country should be observed in assessing the labor efficiency.

Non-Productive Activities

The non-productive activities associated with a project should also be examined in order to examine the productive labor yield, which is defined as the ratio of direct labor hours devoted to the completion of a project to the potential labor hours. The direct labor hours are estimated on the basis of the best possible conditions at a job site by excluding all factors which may reduce the productive labor yield. For example, in the repaving of highway surface, the flagmen required to divert traffic represent indirect labor which does not contribute to the labor efficiency of the paving crew if the highway is closed to the traffic. Similarly, for large projects in remote areas, indirect labor may be used to provide housing and infrastructure for the workers hired to supply the direct labor for a project. The labor hours spent on rework to correct unsatisfactory original work represent extra time taken away from potential labor hours. The labor hours related to such activities must be deducted from the potential labor hours in order to obtain the actual productive labor yield.

Inventory Control

Once goods are purchased, they represent an inventory used during the construction process. The general objective of inventory control is to minimize the total cost of keeping the inventory while making tradeoffs among the major categories of costs: (1) purchase costs, (2) order cost, (3) holding costs, and (4) unavailable cost. These cost categories are interrelated since reducing cost in one category may increase cost in others. The costs in all categories generally are subject to considerable uncertainty.

Purchase Costs

The purchase cost of an item is the unit purchase price from an external source including transportation and freight costs. For construction materials, it is common to receive discounts for bulk purchases, so the unit purchase cost declines as quantity increases. These reductions may reflect manufacturers' marketing policies, economies of scale in the material production, or scale economies in transportation. There are also advantages in having homogeneous materials. For example, a bulk order to insure the same color or size of items such as bricks may be desirable. Accordingly, it is usually desirable to make a limited number of large purchases for materials. In some cases, organizations may consolidate small orders from a number of different projects to capture such bulk discounts; this is a basic saving to be derived from a central purchasing office.

The cost of materials is based on prices obtained through effective bargaining. Unit prices of materials depend on bargaining leverage, quantities and delivery time. Organizations with potential for long-term purchase volume can command better bargaining leverage. While orders in large quantities may result in lower unit prices, they may also increase holding costs and thus cause problems in cash flow. Requirements of short delivery time can also adversely affect unit prices. Furthermore, design characteristics which include items of odd sizes or shapes should be avoided. Since such items normally are not available in the standard stockpile, purchasing them causes higher prices.

The transportation costs are affected by shipment sizes and other factors. Shipment by the full load of a carrier often reduces prices and assures quicker delivery, as the carrier can travel from the origin to the destination of the full load without having to stop for delivering part of the cargo at other stations. Avoiding transshipment is another consideration in reducing shipping cost. While the reduction in shipping costs is a major objective, the requirements of delicate handling of some items may favor a more expensive mode of transportation to avoid breakage and replacement costs.

Order Cost

The order cost reflects the administrative expense of issuing a purchase order to an outside supplier. Order costs include expenses of making requisitions, analyzing alternative vendors, writing purchase orders, receiving materials, inspecting materials, checking on orders, and maintaining records of the entire process. Order costs are usually only a small portion of total costs for material management in construction projects, although ordering may require substantial time.

Holding Costs

The holding costs or carrying costs are primarily the result of capital costs, handling, storage, obsolescence, shrinkage and deterioration. Capital cost results from the opportunity cost or financial expense of capital tied up in inventory. Once payment for goods is made, borrowing costs are incurred or capital must be diverted from other productive uses. Consequently, a capital carrying cost is incurred equal to the value of the inventory during a period multiplied by the interest rate obtainable or paid during that period. Note that capital costs only accumulate when payment for materials actually occurs; many organizations attempt to delay payments as long as possible to minimize such costs. Handling and storage represent the movement and protection charges incurred for materials. Storage costs also include the disruption caused to other project activities by large inventories of materials that get in the way. Obsolescence is the risk that an item will lose value because of changes in specifications. Shrinkage is the decrease in inventory over time due to theft or loss. Deterioration reflects a change in material quality due to age or environmental degradation. Many of these holding cost components are difficult to predict in advance; a project manager knows only that there is some chance that specific categories of cost will occur. In addition to these major categories of cost, there may be ancillary costs of additional insurance, taxes (many states treat inventories as taxable property), or additional fire hazards. As a general rule, holding costs will typically represent 20 to 40% of the average inventory value over the course of a year; thus if the average material inventory on a project is $ 1 million over a year, the holding cost might be expected to be $200,000 to $400,000.

Unavailability Cost

The unavailability cost is incurred when a desired material is not available at the desired time. In manufacturing industries, this cost is often called the stockout or depletion cost. Shortages may delay work, thereby wasting labor resources or delaying the completion of the entire project. Again, it may be difficult to forecast in advance exactly when an item may be required or when an shipment will be received. While the project schedule gives one estimate, deviations from the schedule may occur during construction. Moreover, the cost associated with a shortage may also be difficult to assess; if the material used for one activity is not available, it may be possible to assign workers to other activities and, depending upon which activities are critical, the project may not be delayed.

Tradeoffs of Costs in Materials Management.

To illustrate the type of trade-offs encountered in materials management, suppose that a particular item is to be ordered for a project. The amount of time required for processing the order and shipping the item is uncertain. Consequently, the project manager must decide how much lead time to provide in ordering the item. Ordering early and thereby providing a long lead time will increase the chance that the item is available when needed, but it increases the costs of inventory and the chance of spoilage on site.

Let T be the time for the delivery of a particular item, R be the time required for process the order, and S be the shipping time. Then, the minimum amount of time for the delivery of the item is T = R + S. In general, both R and S are random variables; hence T is also a random variable. For the sake of simplicity, we shall consider only the case of instant processing for an order, i.e. R = 0. Then, the delivery time T equals the shipping time S.

Since T is a random variable, the chance that an item will be delivered on day t is represented by the probability p(t). Then, the probability that the item will be delivered on or before t day is given by:

If a and b are the lower and upper bounds of possible delivery dates, the expected delivery time is then given by:

The lead time L for ordering an item is the time period ahead of the delivery time, and will depend on the tradeoff between holding costs and unavailability costs. A project manager may want to avoid the unavailable cost by requiring delivery on the scheduled date of use, or may be to lower the holding cost by adopting a more flexible lead time based on the expected delivery time. For example, the manager may make the tradeoff by specifying the lead time to be D days more than the expected delivery time, i.e.,

where D may vary from 0 to the number of additional days required to produce certain delivery on the desired date.

In a more realistic situation, the project manager would also contend with the uncertainty of exactly when the item might be required. Even if the item is scheduled for use on a particular date, the work progress might vary so that the desired date would differ. In many cases, greater than expected work progress may result in no savings because materials for future activities are unavailable.

Construction Waste Generation and Management

Waste generation and management is a set of activities that include the following:

1. collection, transport, treatment and disposal of waste;2. control, monitoring and regulation of the production, collection, transport, treatment and disposal

of waste; and3. prevention of waste production through in-process modification, reuse and recycling.

The term usually relates to all kinds of waste, whether generated during the extraction of raw materials, the processing of raw materials into intermediate and final products, the consumption of final products, or other human activities, including municipal (residential, institutional, commercial), agricultural, and special (health care, household hazardous wastes, sewage sludge). Waste management is intended to reduce the effect of waste on health, the environment or aesthetics.Issues relating to waste management include:

Generation of waste Waste minimization Waste removal Waste transportation Waste treatment Recycling and reuse Storage, collection, transport, and transfer Treatment Landfill disposal Environmental considerations Financial and marketing aspects Policy and regulation Education and training

Planning and implementation.Waste management practices are not uniform among countries (developed and developing nations); regions (urban and rural area), and sectors (residential and industrial)

HistoryThroughout most of history, the amount of waste generated by humans was insignificant due to low population density and low societal levels of the exploitation of natural resources. Common waste produced during pre-modern times was mainly ashes and human biodegradable waste, and these were released back into the ground locally, with minimum environmental impact. Tools made out of wood or metal were generally reused or passed down through the generations.

SolutionsLandfill

Disposal of waste in a landfill involves burying the waste and this remains a common practice in most countries. Landfills were often established in abandoned or unused quarries, mining voids or borrow pits. A properly designed and well-managed landfill can be a hygienic and relatively inexpensive method of disposing of waste materials. Older, poorly designed or poorly managed landfills and open dumps can create a number of adverse environmental impacts such as wind-blown litter, attraction of vermin, and generation of liquid leachate. Another common product of landfills is gas (mostly composed of methane and carbon dioxide), which is produced from anaerobic breakdown of organic waste. This gas can create odor problems, kill surface vegetation and is a greenhouse gas.Design characteristics of a modern landfill include methods to contain leachate such as clay or plastic lining material. Deposited waste is normally compacted to increase its density and stability and covered to prevent attracting vermin (such as mice or rats). Many landfills also have landfill gas extraction systems installed to extract the landfill gas. Gas is pumped out of the landfill using perforated pipes and flared off or burnt in a gas engine to generate electricity.Incineration

Incineration is a disposal method in which solid organic wastes are subjected to combustion so as to convert them into residue and gaseous products. This method is useful for disposal of residue of both solid waste management and solid residue from waste water management. This process reduces the volumes of solid waste to 20 to 30 percent of the original volume. Incineration and other high temperature waste treatment systems are sometimes described as "thermal treatment". Incinerators convert waste materials into heat, gas, steam, and ash.Incineration is carried out both on a small scale by individuals and on a large scale by industry. It is used to dispose of solid, liquid and gaseous waste. It is recognized as a practical method of disposing of certain hazardous waste materials (such as biological medical waste). Incineration is a controversial method of waste disposal, due to issues such as emission of gaseous pollutants.Incineration is common in countries such as Japan where land is more scarce, as these facilities generally do not require as much area as landfills. Waste-to-energy (WtE) or energy-from-waste (EfW) are broad terms for facilities that burn waste in a furnace or boiler to generate heat, steam or electricity. Combustion in an incinerator is not always perfect and there have been concerns about pollutants in gaseous emissions from incinerator stacks. Particular concern has focused on some very persistent organic compounds such as dioxins, furans, and PAHs, which may be created and which may have serious environmental consequences.

Recycling

Recycling is a resource recovery practice that refers to the collection and reuse of waste materials such as empty beverage containers. The materials from which the items are made can be reprocessed into new products. Material for recycling may be collected separately from general waste using dedicated bins and collection vehicles, a procedure called kerbside collection. In some communities, the owner of the waste is required to separate the materials into various different bins (e.g. for paper, plastics, metals) prior to its collection. In other communities, all recyclable materials are placed in a single bin for collection, and the sorting is handled later at a central facility. The latter method is known as "single-stream recycling."The most common consumer products recycled include aluminium such as beverage cans, copper such as wire, steel from food and aerosol cans, old steel furnishings or equipment, polyethylene and PET bottles, glass bottles and jars, paper board cartons, newspapers, magazines and light paper, and corrugated fiberboard boxes.PVC, LDPE, PP, and PS (see resin identification code) are also recyclable. These items are usually composed of a single type of material, making them relatively easy to recycle into new products. The recycling of complex products (such as computers and electronic equipment) is more difficult, due to the additional dismantling and separation required.The type of material accepted for recycling varies by city and country. Each city and country has different recycling programs in place that can handle the various types of recyclable materials. However, certain variation in acceptance is reflected in the resale value of the material once it is reprocessed.Sustainability

The management of waste is a key component in a business' ability to maintaining ISO14001 accreditation. Companies are encouraged to improve their environmental efficiencies each year by eliminating waste through resource recovery practices, which are sustainability-related activities. One way to do this is by shifting away from waste management to resource recovery practices like recycling materials such as glass, food scraps, paper and cardboard, plastic bottles and metal.Biological reprocessing

Recoverable materials that are organic in nature, such as plant material, food scraps, and paper products, can be recovered through composting and digestion processes to decompose the organic matter. The resulting organic material is then recycled as much or compost for agricultural or landscaping purposes. In addition, waste gas from the process (such as methane) can be captured and used for generating electricity and heat (CHP/cogeneration) maximising efficiencies. The intention of biological processing in waste management is to control and accelerate the natural process of decomposition of organic matter.Energy recovery

Energy recovery from waste is the conversion of non-recyclable waste materials into usable heat, electricity, or fuel through a variety of processes, including combustion, gasification, pyrolyzation, anaerobic digestion, and landfill gas recovery. This process is often called waste-to-energy. Energy recovery from waste is part of the non-hazardous waste management hierarchy. Using energy recovery to convert non-recyclable waste materials into electricity and heat, generates a renewable energy source and can reduce carbon emissions by offsetting the need for energy from fossil sources as well as reduce methane generation from landfills. Globally, waste-to-energy accounts for 16% of waste management.The energy content of waste products can be harnessed directly by using them as a direct combustion fuel, or indirectly by processing them into another type of fuel. Thermal treatment ranges from using waste as a fuel source for cooking or heating and the use of the gas fuel (see above), to fuel for  boilers to generate steam and electricity in a turbine. Pyrolysis and gasification are two related forms of thermal treatment where waste materials are heated to high temperatures with limited oxygen availability. The

process usually occurs in a sealed vessel under high pressure. Pyrolysis of solid waste converts the material into solid, liquid and gas products. The liquid and gas can be burnt to produce energy or refined into other chemical products (chemical refinery). The solid residue (char) can be further refined into products such as activated carbon. Gasification and advanced Plasma arc gasification are used to convert organic materials directly into a synthetic gas (syngas) composed of carbon monoxideand hydrogen. The gas is then burnt to produce electricity and steam. An alternative to pyrolysis is high temperature and pressure supercritical water decomposition (hydrothermal monophasic oxidation).Resource recovery

Resource recovery is the systematic diversion of waste, which was intended for disposal, for a specific next use. It is the processing of recyclables to extract or recover materials and resources, or convert to energy. These activities are performed at a resource recovery facility. Resource recovery is not only environmentally important, but it is also cost effective. It decreases the amount of waste for disposal, saves space in landfills, and conserves natural resources.Resource recovery (as opposed to waste management) uses LCA (life cycle analysis) attempts to offer alternatives to waste management. For mixed MSW (Municipal Solid Waste) a number of broad studies have indicated that administration, source separation and collection followed by reuse and recycling of the non-organic fraction and energy and compost/fertilizer production of the organic material via anaerobic digestion to be the favoured path.As an example of how resource recycling can be beneficial, many of the items thrown away contain precious metals which can be recycled to create a profit, such as the silver in X rays and the components in circuit boards. Other industries can also benefit from resource recycling with the wood chippings in pallets and other packaging materials being passed onto sectors such as the horticultural profession. In this instance, workers can use the recycled chips to create paths, walkways, or arena surfaces.Avoidance and reduction methods

An important method of waste management is the prevention of waste material being created, also known as waste reduction. Methods of avoidance include reuse of second-hand products, repairing broken items instead of buying new, designing products to be refillable or reusable (such as cotton instead of plastic shopping bags), encouraging consumers to avoid using disposable products (such as disposable cutlery), removing any food/liquid remains from cans and packaging, and designing products that use less material to achieve the same purpose (for example, lightweighting of beverage cans).Pyrolysis

Pyrolysis is a process of thermo-chemically decomposition of organic materials by heat in the absence of oxygen which produces various hydrocarbon gases. During pyrolysis, the molecules of object are subjected to very high temperatures leading to very high vibrations. Therefore every molecule in the object is stretched and shaken to an extent that molecules starts breaking down. The rate of pyrolysis increases with temperature. In industrial applications, temperatures are above 430 °C (800 °F). Fast pyrolysis produces liquid fuel for feedstocks like wood. Slow pyrolysis produces gases and solid charcoal. Pyrolysis hold promise for conversion of waste biomass into useful liquid fuel. Pyrolysis of waste plastics can produce millions of litres of fuel. Solid products of this process contain metals, glass, sand and pyrolysis coke which cannot be converted to gas in the process.Vacuum pyrolysis is a process in which organic material is heated in vacuum to lower its boiling point and to avoid adverse chemical reactions. It is used in bio chemistry as synthetic tool. Pyrolysis also has an important role in combustion of wood and sawdust.

Waste handling and transport

Waste collection methods vary widely among different countries and regions. Domestic waste collection services are often provided by local government authorities, or by private companies for industrial and commercial waste. Some areas, especially those in less developed countries, do not have a formal waste-collection system.

Waste handling systems

Vacuum collection in which waste is transported from the home or commercial premises by vacuum along small bore tubes. Systems are in use in Europe and North America

Curbside collection is the most common method of disposal in most European countries, Canada, New Zealand and many other parts of the developed world in which waste is collected at regular intervals by specialised trucks. This is often associated with curb-side waste segregation. In rural areas waste may need to be taken to a transfer station. Waste collected is then transported to a regional landfill.

In many areas, pyrolysis is used to dispose of some wastes including tires, a process that can produce recovered fuels, steel and heat. In some cases tires can provide the feedstock for cement manufacture. Such systems are used in USA, California, Australia, Greece, Mexico, the United Kingdom and in Israel. The RESEM pyrolysis plant that has been operational at Texas USA since December 2011, and processes up to 60 tons per day.

In some areas such as Taipei, the city government charges its households and industries for the volume of rubbish they produce. Waste will only be collected by the city council if waste is disposed in government issued rubbish bags. This policy has successfully reduced the amount of waste the city produces and increased the recycling rate. A similar system operates in New Zealand where waste must be packed in specially identified bags.

In some jurisdictions unsegregated waste is collected at the curb-side or from waste transfer stations and then sorted into recyclables and unusable waste. Such systems are capable of sorting large volumes of solid waste, salvaging recyclables, and turning the rest into bio-gas and soil conditioner.

In San Francisco, the local government established its Mandatory Recycling and Composting Ordinance in support of its goal of zero waste by 2020, requiring everyone in the city to keep recyclables and compostables out of the landfill. The three streams are collected with the curbside "Fantastic 3" bin system - blue for recyclables, green for compostables, and black for landfill-bound materials - provided to residents and businesses and serviced by San Francisco's sole refuse hauler, Recology. The City's "Pay-As-You-Throw" system charges customers by the volume of landfill-bound materials, which provides a financial incentive to separate recyclables and compostables from other discards. The City's Department of the Environment's Zero Waste Program has led the City to achieve 80% diversion, the highest diversion rate in North America.

International waste movement

While waste transport within a given country falls under national regulations, trans-boundary movement of waste is often subject to international treaties. A major concern to many countries in the world has been hazardous waste. The Basel Convention, ratified by 172 countries, deprecates movement of hazardous waste from developed to less developed countries. The provisions of the Basel convention have been integrated into the EU waste shipment regulation. Nuclear waste, although considered hazardous, does not fall under the jurisdiction of the Basel Convention.

Benefits

Waste is not something that should be discarded or disposed of with no regard for future use. It can be a valuable resource if addressed correctly, through policy and practice. With rational and consistent waste management practices there is an opportunity to reap a range of benefits. Those benefits include:

1. Economic - Improving economic efficiency through the means of resource use, treatment and disposal and creating markets for recycles can lead to efficient practices in the production and consumption of products and materials resulting in valuable materials being recovered for reuse and the potential for new jobs and new business opportunities.

2. Social - By reducing adverse impacts on health by proper waste management practices, the resulting consequences are more appealing settlements. Better social advantages can lead to new sources of employment and potentially lifting communities out of poverty especially in some of the developing poorer countries and cities.

3. Environmental - Reducing or eliminating adverse impacts on the environmental through reducing, reusing and recycling, and minimizing resource extraction can provide improved air and water quality and help in the reduction of greenhouse emissions.

4. Inter-generational Equity - Following effective waste management practices can provide subsequent generations a more robust economy, a fairer and more inclusive society and a cleaner environment.

Challenges in developing countries

Waste management in cities with developing economies and economies in transition experience exhausted waste collection services, inadequately managed and uncontrolled dumpsites and the problems are worsening. Problems with governance also complicate the situation. Waste management, in these countries and cities, is an ongoing challenge and many struggle due to weak institutions, chronic under-resourcing and rapid urbanization. All of these challenges along with the lack of understanding of different factors that contribute to the hierarchy of waste management, affect the treatment of waste.

Technologies

Traditionally the waste management industry has been slow to adopt new technologies such as RFID (Radio Frequency Identification) tags, GPS and integrated software packages which enable better quality data to be collected without the use of estimation or manual data entry.

Technologies like RFID tags are now being used to collect data on presentation rates for curb-side pick-ups.

Benefits of GPS tracking is particularly evident when considering the efficiency of ad hoc pick-ups (like skip bins or dumpsters) where the collection is done on a consumer request basis.

Integrated software packages are useful in aggregating this data for use in optimisation of operations for waste collection operations.

Rear vision cameras are commonly used for OH&S (Occupational Health & Safety) reasons and video recording devices are becoming more widely used, particularly concerning residential services.

Central principles of waste management

Diagram of the waste hierarchy

There are a number of concepts about waste management which vary in their usage between countries or regions. Some of the most general, widely used concepts include:1. Waste hierarchy - The waste hierarchy refers to the "3 Rs" reduce, reuse and recycle, which classify waste management strategies according to their desirability in terms of waste minimization. The waste hierarchy remains the cornerstone of most waste minimization strategies. The aim of the waste hierarchy is to extract the maximum practical benefits from products and to generate the minimum amount of waste; see: resource recovery. The waste hierarchy is represented as a pyramid because the basic premise is for policy to take action first and prevent the generation of waste. The next step or preferred action is to reduce the generation of waste i.e. by re-use. The next is recycling which would include composting. Following this step is material recovery and waste-to-energy. Energy can be recovered from processes i.e. landfill and combustion, at this level of the hierarchy. The final action is disposal, in landfills or through incineration without energy recovery. This last step is the final resort for waste which has not been prevented, diverted or recovered. The waste hierarchy represents the progression of a product or material through the sequential stages of the pyramid of waste management. The hierarchy represents the latter parts of the life-cycle for each product. 2. Life-cycle of a Product - The life-cycle begins with design, then proceeds through manufacture, distribution, use and then follows through the waste hierarchy's stages of reuse, recovery, recycling and disposal. Each of the above stages of the life-cycle offers opportunities for policy intervention, to rethink the need for the product, to redesign to minimize waste potential, to extend its use. The key behind the life-cycle of a product is to optimize the use of the world's limited resources by avoiding the unnecessary generation of waste.3. Resource efficiency - the current, global, economic growth and development cannot be sustained with the current production and consumption patterns. Globally, we are extracting more resources to produce goods than the planet can replenish. Resource efficiency is the reduction of the environmental impact from the production and consumption of these goods, from final raw material extraction to last use and disposal. This process of resource efficiency can address sustainability.

Polluter pays principle - the Polluter Pays Principle is a principle where the polluting party pays for the impact caused to the environment. With respect to waste management, this generally refers to the requirement for a waste generator to pay for appropriate disposal of the unrecoverable material.

Construction Equipment

The selection of the appropriate type and size of construction equipment often affects the required amount of time and effort and thus the job-site productivity of a project. It is therefore important for site managers and construction planners to be familiar with the characteristics of the major types of equipment most commonly used in construction.

Excavation and Loading

One family of construction machines used for excavation is broadly classified as a crane-shovel as indicated by the variety of machines in Figure below. The crane-shovel consists of three major components:

a carrier or mounting which provides mobility and stability for the machine. a revolving deck or turntable which contains the power and control units. a front end attachment which serves the special functions in an operation.

The type of mounting for all machines in Figure below is referred to as crawler mounting, which is particularly suitable for crawling over relatively rugged surfaces at a job site. Other types of mounting include truck mounting and wheel mounting which provide greater mobility between job sites, but require better surfaces for their operation. The revolving deck includes a cab to house the person operating the mounting and/or the revolving deck. The types of front end attachments in Figure below might include a crane with hook, claim shell, dragline, backhoe, shovel and pile driver.

Typical Machines in the Crane-Shovel Family

A tractor consists of a crawler mounting and a non-revolving cab. When an earth moving blade is attached to the front end of a tractor, the assembly is called a bulldozer. When a bucket is attached to its front end, the assembly is known as a loader or bucket loader. There are different types of loaders designed to handle most efficiently materials of different weights and moisture contents.

Scrapers are multiple-units of tractor-truck and blade-bucket assemblies with various combinations to facilitate the loading and hauling of earthwork. Major types of scrapers include single engine two-axle or three axle scrapers, twin-engine all-wheel-drive scrapers, elevating scrapers, and push-pull scrapers. Each type has different characteristics of rolling resistance, maneuverability stability, and speed in operation.

Compaction and Grading

The function of compaction equipment is to produce higher density in soil mechanically. The basic forces used in compaction are static weight, kneading, impact and vibration. The degree of compaction that may be achieved depends on the properties of soil, its moisture content, the thickness of the soil layer for compaction and the method of compaction. Some major types of compaction equipment are shown in Figure below, which includes rollers with different operating characteristics.

The function of grading equipment is to bring the earthwork to the desired shape and elevation. Major types of grading equipment include motor graders and grade trimmers. The former is an all-purpose machine for grading and surface finishing, while the latter is used for heavy construction because of its higher operating speed.

Some Major Types of Compaction Equipment

Drilling and Blasting

Rock excavation is an audacious task requiring special equipment and methods. The degree of difficulty depends on physical characteristics of the rock type to be excavated, such as grain size, planes of weakness, weathering, brittleness and hardness. The task of rock excavation includes loosening, loading, hauling and compacting. The loosening operation is specialized for rock excavation and is performed by drilling, blasting or ripping.

Major types of drilling equipment are percussion drills, rotary drills, and rotary-percussion drills. A percussion drill penetrates and cuts rock by impact while it rotates without cutting on the upstroke. Common types of percussion drills include a jackhammer which is hand-held and others which are mounted on a fixed frame or on a wagon or crawl for mobility. A rotary drill cuts by turning a bit against the rock surface. A rotary-percussion drill combines the two cutting movements to provide a faster penetration in rock.

Blasting requires the use of explosives, the most common of which is dynamite. Generally, electric blasting caps are connected in a circuit with insulated wires. Power sources may be power lines or blasting machines designed for firing electric cap circuits. Also available are non-electrical blasting systems which combine the precise timing and flexibility of electric blasting and the safety of non-electrical detonation.

Tractor-mounted rippers are capable of penetrating and prying loose most rock types. The blade or ripper is connected to an adjustable shank which controls the angle at the tip of the blade as it is raised or lowered. Automated ripper control may be installed to control ripping depth and tip angle.

In rock tunneling, special tunnel machines equipped with multiple cutter heads and capable of excavating full diameter of the tunnel are now available. Their use has increasingly replaced the traditional methods of drilling and blasting.

Lifting and Erecting

Derricks are commonly used to lift equipment of materials in industrial or building construction. A derrick consists of a vertical mast and an inclined boom sprouting from the foot of the mast. The mast is held in position by guys or stifflegs connected to a base while a topping lift links the top of the mast and the top of the inclined boom. A hook in the road line hanging from the top of the inclined boom is used to lift loads. Guy derricks may easily be moved from one floor to the next in a building under construction while stiffleg derricks may be mounted on tracks for movement within a work area.

Tower cranes are used to lift loads to great heights and to facilitate the erection of steel building frames. Horizon boom type tower cranes are most common in highrise building construction. Inclined boom type tower cranes are also used for erecting steel structures.

Mixing and Paving

Basic types of equipment for paving include machines for dispensing concrete and bituminous materials for pavement surfaces. Concrete mixers may also be used to mix portland cement, sand, gravel and water in batches for other types of construction other than paving.

A truck mixer refers to a concrete mixer mounted on a truck which is capable of transporting ready mixed concrete from a central batch plant to construction sites. A paving mixer is a self propelled concrete mixer equipped with a boom and a bucket to place concrete at any desired point within a roadway. It can be used as a stationary mixer or used to supply slipform pavers that are capable of spreading, consolidating and finishing a concrete slab without the use of forms.

A bituminous distributor is a truck-mounted plant for generating liquid bituminous materials and applying them to road surfaces through a spray bar connected to the end of the truck. Bituminous materials include both asphalt and tar which have similar properties except that tar is not soluble in petroleum products. While asphalt is most frequently used for road surfacing, tar is used when the pavement is likely to be heavily exposed to petroleum spills.

Construction Tools and Other Equipment

Air compressors and pumps are widely used as the power sources for construction tools and equipment. Common pneumatic construction tools include drills, hammers, grinders, saws, wrenches, staple guns, sandblasting guns, and concrete vibrators. Pumps are used to supply water or to dewater at construction sites and to provide water jets for some types of construction.

Automation of Equipment

The introduction of new mechanized equipment in construction has had a profound effect on the cost and productivity of construction as well as the methods used for construction itself. An exciting example of innovation in this regard is the introduction of computer microprocessors on tools and equipment. As a result, the performance and activity of equipment can be continually monitored and adjusted for improvement. In many cases, automation of at least part of the construction process is possible and desirable. For example, wrenches that automatically monitor the elongation of bolts and the applied torque can be programmed to achieve the best bolt tightness. On grading projects, laser controlled scrapers can produce desired cuts faster and more precisely than wholly manual methods.

Choice of Equipment and Standard Production Rates

Typically, construction equipment is used to perform essentially repetitive operations, and can be broadly classified according to two basic functions: (1) operators such as cranes, graders, etc. which stay within the confines of the construction site, and (2) haulers such as dump trucks, ready mixed concrete truck, etc. which transport materials to and from the site. In both cases, the cycle of a piece of equipment is a sequence of tasks which is repeated to produce a unit of output. For example, the sequence of tasks for a crane might be to fit and install a wall panel (or a package of eight wall panels) on the side of a building; similarly, the sequence of tasks of a ready mixed concrete truck might be to load, haul and unload two cubic yards (or one truck load) of fresh concrete.

In order to increase job-site productivity, it is beneficial to select equipment with proper characteristics and a size most suitable for the work conditions at a construction site. In excavation for building construction, for examples, factors that could affect the selection of excavators include:

1. Size of the job: Larger volumes of excavation will require larger excavators, or smaller excavators in greater number.

2. Activity time constraints: Shortage of time for excavation may force contractors to increase the size or numbers of equipment for activities related to excavation.

3. Availability of equipment: Productivity of excavation activities will diminish if the equipment used to perform them is available but not the most adequate.

4. Cost of transportation of equipment: This cost depends on the size of the job, the distance of transportation, and the means of transportation.

5. Type of excavation: Principal types of excavation in building projects are cut and/or fill, excavation massive, and excavation for the elements of foundation. The most adequate equipment to perform one of these activities is not the most adequate to perform the others.

6. Soil characteristics: The type and condition of the soil is important when choosing the most adequate equipment since each piece of equipment has different outputs for different soils. Moreover, one excavation pit could have different soils at different stratums.

7. Geometric characteristics of elements to be excavated: Functional characteristics of different types of equipment makes such considerations necessary.

8. Space constraints: The performance of equipment is influenced by the spatial limitations for the movement of excavators.

9. Characteristics of haul units: The size of an excavator will depend on the haul units if there is a constraint on the size and/or number of these units.

10. Location of dumping areas: The distance between the construction site and dumping areas could be relevant not only for selecting the type and number of haulers, but also the type of excavators.

11. Weather and temperature: Rain, snow and severe temperature conditions affect the job-site productivity of labor and equipment.

By comparing various types of machines for excavation, for example, power shovels are generally found to be the most suitable for excavating from a level surface and for attacking an existing digging surface or one created by the power shovel; furthermore, they have the capability of placing the excavated material directly onto the haulers. Another alternative is to use bulldozers for excavation.

The choice of the type and size of haulers is based on the consideration that the number of haulers selected must be capable of disposing of the excavated materials expeditiously. Factors which affect this selection include:

1. Output of excavators: The size and characteristics of the excavators selected will determine the output volume excavated per day.

2. Distance to dump site: Sometimes part of the excavated materials may be piled up in a corner at the job-site for use as backfill.

3. Probable average speed: The average speed of the haulers to and from the dumping site will determine the cycle time for each hauling trip.

4. Volume of excavated materials: The volume of excavated materials including the part to be piled up should be hauled away as soon as possible.

5. Spatial and weight constraints: The size and weight of the haulers must be feasible at the job site and over the route from the construction site to the dumping area.

Cost and Working hour Analysis

1. Define your CBA's unit of cost. Since a CBA's aim is to determine whether a certain project or venture is worth the cost it would take to enact, it's important to establish what exactly your CBA measures in terms of "cost" at the outset. Usually, a CBA measures literal cost in terms of money, but, in cases where money is not an issue, CBAs can measure cost in terms of time, energy usage, and more.For the purpose of demonstration, let's design an example CBA in this article. Let's say that we run a lucrative lemonade stand on weekends in the summer and that we want to perform a cost analysis to see whether it's worth expanding to a second location on the other side of town. In this case, we're primarily interested in whether this hypothetical second location would make us more money in the long run or whether the costs associated with expanding would be prohibitively high.

2. Itemize the tangible costs of the intended project. Almost any project comes with costs. For instance, business ventures require initial monetary investments to buy goods and supplies, train staff, and the like. The first step of a CBA is to make a thorough, exhaustive, itemized list of these costs. You may want to investigate similar projects to find costs to include on your list that you may not otherwise have considered. Costs can be one-time events or ongoing expenses. Costs should be based on actual market prices and/or research when possible, but should be intelligent, researched estimates when this is not possible.

Below are the types of costs you'll want to include in your CBA: The price of goods or equipment associated with the venture Shipping, handling, and transportation costs Operating expenses Staffing costs (wages, training, etc.) Real estate (rented offices, etc.) Insurance and taxes. Utilities (electricity, water, etc.)

Let's make a quick itemized list of the costs our hypothetical new lemonade stand will require to launch:

Supplies in the form of lemons, ice, and sugar: $20/day Wages for 2 stand attendants: $40/day Good quality blender (for smoothies): one-time cost of $80 High-volume cooler: one-time cost of $15 Wood, cardboard, etc. for stand and sign: one-time cost of $20 Our income from the lemonade stands isn't taxed, the cost of the water used to make the lemonade is

negligible, and we have a policy of setting up our stands in public parks, so we don't have to account for taxes, utilities, or real estate expenses.

3. Itemize any and all intangible costs. It is rare for a project's costs solely to be composed of tangible, real expenses. Usually, CBAs also take into account a project's intangible demands - things like the time and energy required to complete the project. Though these things can't actually be bought and sold, real-world costs can be assigned to them by determining the amount of money one would hypothetically be able to make if they were used for another purpose. For instance, though taking a year off from a job to write a novel is technically free, one must take into account the fact that doing so means going without wages for a year. Thus, in such a situation, we're basically exchanging money for time, buying a year for ourselves at the price of a year's wages.

Below are the types of intangible costs you'll want to consider for your CBA: The cost of the time spent on a project - i.e., the money that could be made if this time was spent doing

something else The cost of the energy spent on a project The cost of adjusting an established routine The cost of any possible lost business during the implementation of the projected venture The risk factor value of intangibles like safety and customer loyalty

Let's take into account the intangible costs of opening a new lemonade stand. We'll assume that our current stand generates about $20/hour for 8 hours each day, 2 days each week (Saturday and Sunday):

Closing the existing lemonade stand for one day so that the new stand can be built, signs can be made, and new sites can be scouted: one-time loss of $160 in profits.

Spending 2 hours each week for the first two weeks working out issues in the supply chain: one-time loss of $80 in profits over the first two weeks.

4. Itemize the projected benefits. The purpose of any CBA is to compare the benefits of a project to the costs - if the former clearly outweigh the latter, the project will probably be given the go-ahead. Itemizing the benefits is done in the same way as the cost portion of the analysis, though you will most likely need to rely on educated estimates more than you will with the costs. Try to back up your estimates with evidence from research or similar projects and assign a monetary amount to any tangible or intangible ways in which you will see a positive return on your venture.

Below are the types of benefits you'll want to consider in your CBA: Income produced Money saved Interest accrued Equity built Time and effort saved Repeat customer business Intangibles like referrals, customer satisfaction, happier employees, a safer workplace, etc.

Let's calculate the projected benefits of our new lemonade stand and provide a rationale for each estimate:

Due to high walking traffic, a competing lemonade stand near the hypothetical site of our new stand makes a whopping $40/hour. Since our new stand would compete with this stand for the same customer base and we don't have word-of-mouth recognition in this area yet, we'll conservatively assume we'll make less than half that - $15/hour or $120/day - and that this will potentially grow as word of our lower prices spreads.

Most weeks, we end up throwing out about $5 of lemons which have spoiled. We project that we'll be able to more efficiently split our supplies between the two stands, eliminating this loss. Because we're open two days each week (Saturday and Sunday), these savings are about $2.5/day.

One of our current stands attendants happens to live very near to the site of the new stand. If we allow her to work at the new stand (by hiring someone to replace her at the old stand), she estimates she would be able to use the reduced commute time to keep the stand open for an extra half hour each day, which equates to about an extra $7.5/day, given our estimate of the stand's money-making potential.

5. Add up and compare the project's costs and benefits. This is the crux of any CBA. Finally, we determine whether the benefits of our project outweigh the costs. Subtract the ongoing costs from the ongoing benefits, then add up all the one-time costs to get a sense of the size of the initial investment needed to start the project. Using this information, you should be able to determine whether a project is profitable and feasible.

Let's compare the costs and benefits of opening a second lemonade stand: Ongoing costs: $20/day (supplies) + $40/day (wages) = $60/day Ongoing benefits: $120/day (income) + $7.5/day (extra half hour) + $2.5/day (lemon savings)

= $130/day One-time costs: $160 (closing the first stand for a day) + $80 (supply chain issues) + $80 (blender) + $15

(cooler) + $20 (wood, cardboard) =$355So, with an initial investment of $355, we can expect to make about $130-$60 =$70/day. Not bad.

6. Calculate a payback time for the venture. The quicker a project can pay for itself, the better. Taking the cost and benefit totals into account, determine the amount of time it will take to recoup the projected costs of your initial investment. In other words, divide the cost of your initial investment by the projected income per day, week, month, etc. to determine how many days, weeks, months, etc. it will take to pay back your initial investment and start generating profit.Our hypothetical lemonade stand has an initial cost of $355 and is estimated to generate $70/day. 355/70 = about 5, so we know that, assuming our estimates are correct, our new stand will pay for itself in about 5 days of operation. Because our stands are open on the weekends, this equates to about 2-3 weeks.

7. Use your CBA to inform your decision about whether to pursue your project. If the projected benefits of your venture clearly outweigh the costs and the project can pay for its initial investment in a reasonable amount of time, you may want to consider putting your project into action. However, if it's not clear that a project can generate additional profit in the long run or pay for itself in a reasonable amount of time, you will probably want to reconsider the project or even scrap it all together.

Based on our CBA, our new lemonade stand looks like a sure thing. It's projected to pay for itself in just a few weeks, after which point it will generate profit. Summer is several months long, so, with any luck, we'll be able to make much more money in the long run this summer with two lemonade stands than with one.

Depreciation Analysis

It represents the reduction in market value of an asset due to age, wear and tear and obsolescence. The physical deterioration of the asset occurs due to wear and tear with passage of time. Obsolescence occurs due to availability of new technology or new product in the market that is superior to the old one and the new one replaces the old even though the old one is still in working condition. The examples of tangible assets for which the depreciation analysis is carried out are construction equipment, buildings, machinery, vehicles, etc. Depreciation amount for an asset is usually calculated on yearly basis. Depreciation is considered as expenditure in the cash flow of the asset, although there is no physical cash outflow. Depreciation affects the income tax to be paid by an individual or a firm as it is considered as an allowable deduction in calculating the taxable income. Generally the income tax is paid on taxable income which is equal to gross income less the allowable deductions (expenditures). Depreciation reduces the taxable income and hence results in lowering the income tax to be paid.

Before discussing about different methods of depreciation, it is necessary to know the common terms used in depreciation analysis. These terms are initial cost, salvage value, book value and useful life. Initial cost is the total cost of acquiring the asset. Salvage value represents estimated market value of the asset at the end of its useful life. It is the expected cash inflow that the owner of the asset will receive by disposing it at the end of useful life. Book value is the value of asset recorded on the accounting books of the firm at a given time period. It is generally calculated at the end of each year. Book value at the end of a given year equals the initial cost less the total depreciation amount till that year.  Useful life represents the expected number of years the asset is useful in terms of generating revenue. The asset may still be in working condition after the useful life but it may not be economical. Useful life is also known as depreciable life. The asset is depreciated over its useful life.

The commonly used depreciation methods are straight-line depreciation method, declining balance method, sum-of-years-digits method and sinking fund method.

Straight-line (SL) depreciation method:-

It is the simplest method of depreciation. In this method it is assumed that the book value of an asset will decrease by same amount every year over the useful life till its salvage value is reached. In other words the book value of the asset decreases at a linear rate with the time period.

The expression for annual depreciation in a given year ‘ m ' is represented as follows;

(3.1)

Where

In equation (3.1),   is the constant annual depreciation rate which is denoted by the term ‘dm'.

Since the depreciation amount is same every year, D1 = D2 = D3 = D4 = ……… = Dm

The book value at the end of 1st year is equal to initial cost less the depreciation in the 1st year and is given by;

BV1 = P − Dm (3.2)

Book value at the end of 2nd year is equal to book value at the beginning of 2nd year (i.e. book value at the end of 1st year) less the depreciation in 2nd year and is expressed as follows;

BV2 = BV1 -Dm (3.3)

As already stated depreciation amount is same in every year.

Now putting the expression of ‘BV1' from equation (3.2) in equation (3.3);

BV2 = (P-Dm) − Dm = P - 2Dm (3.4)

Similarly the book value at the end of 3rd year is equal to book value at the beginning of 3 rd year (i.e. book value at the end of 2nd year) less the depreciation in 3rd year and is given by;

BV3 = BV2 - Dm

BV3 = (P - 2Dm) − Dm = P - 3Dm

(3.5)

(3.6)

In the same manner the generalized expression for book value at the end of any given year ‘  m ' can be written as follows;

BVm = P - mDm (3.7)

Declining balance (DB) depreciation method:-

It is an accelerated depreciation method. In this method the annual depreciation is expressed as a fixed percentage of the book value at the beginning of the year and is calculated by multiplying the book value at the beginning of each year with a fixed percentage. Thus this method is also sometimes known as fixed percentage method of depreciation. The ratio of depreciation amount in a given year to the book value at the beginning of that year is constant for all the years of useful life of the asset. When this ratio is twice

the straight-line depreciation rate i.e.  , the method is known as double-declining balance (DDB) method. In other words the depreciation rate is 200% of the straight-line depreciation rate. Double-declining balance (DDB) method is the most commonly used declining balance method. Another declining

balance method that uses depreciation rate equal to 150% of the straight-line depreciation rate i.e.  is also used for calculation of depreciation. In declining balance methods the depreciation during the early years is more as compared to that in later years of the asset's useful life.

In case of declining balance method, for calculating annual depreciation amount, the salvage value is not subtracted from the initial cost. It is important to ensure that, the asset is not depreciated below the estimated salvage value. In declining-balance method the calculated book value of the asset at the end of

useful life does not match with the salvage value. If the book value of the asset reaches its estimated salvage value before the end of useful life, then the asset is not depreciated further.

Representing constant annual depreciation rate in declining balance method as ‘dm', the expressions for annual depreciation amount and book value are presented as follows;

The depreciation in 1st year is calculated by multiplying the initial cost (i.e. book value at beginning) with the depreciation rate and is given by;

(3.8)

Where

Now putting the expression of ‘ D1 'from equation (3.8) in the above expression;

(3.9)

The depreciation in 2nd year i.e. ‘ D2' is calculated by multiplying the book value at the beginning of 2nd year (i.e. book value at the end of 1st year) with the depreciation rate ‘ dm' and is given as follows;

(3.10)

Now putting the expression of ‘BV1' from equation (3.9) in equation (3.10) results in the following;

(3.11)

Book value at the end of 2nd year is equal to book value at the beginning of 2nd year (i.e. book value at the end of 1st year) less the depreciation in 2nd year and is expressed as follows;

Now putting the expressions of ‘BV1' and ‘D2' from equation (3.9) and equation (3.11) respectively in above expression results in the following;

(3.12)

Similarly the depreciation in 3rd year i.e. ‘D3' is calculated as follows;

(3.13)

Now putting the expression of ‘BV2' from equation (3.12) in equation (3.13);

(3.14)

Book value at the end of 3rd year is calculated as follows;

(3.15)

In the same manner the generalized expression for depreciation in any given year ‘m ' can be written as follows (referring to equations (3.8), (3.11) and (3.14));

(3.16)

Similarly the generalized expression for book value at the end of any year ‘m' is given as follows (referring to equations (3.9), (3.12) and (3.15));

(3.17)

The book value at the end of useful life i.e. at the end of ‘n ' years is given by;

(3.18)

The book value at the end of useful life is theoretically equal to the salvage value of the asset. Thus equating the salvage value (SV) of the asset to its book value (BVn) at the end of useful life results in the following;

(3.19)

Thus for calculating the depreciation of an asset using declining balance method, equation (3.19) can be used to find out the constant annual depreciation rate, if it is not stated for the asset. From equation (3.19), the expression for constant annual depreciation rate ‘dm' from known values of initial cost ‘ P ' and salvage value (SV > 0) is obtained as follows;

 

 

 

(3.20)

In double-declining balance (DDB) method, for calculating annual depreciation amount and book value at

the end of different years, the value of constant annual depreciation rate ‘dm' is replaced by ‘  ' in the above mentioned equations.

Example -1

The initial cost of a piece of construction equipment is Rs.3500000. It has useful life of 10 years. The estimated salvage value of the equipment at the end of useful life is Rs.500000. Calculate the annual depreciation and book value of the construction equipment using straight-line method and double-declining balance method.

Solution:

Initial cost of the construction equipment = P = Rs.3500000

Estimated salvage value = SV = Rs.500000

Useful life = n = 10 years

For straight-line method, the depreciation amount for a given year is calculated using equation (3.1).

The book value at the end of a given year is calculated by subtracting the annual depreciation amount from previous year's book value.

Book value at the end of 1st year = 

Book value at the end of 2 nd year = 

Similarly the book values at the end of other years have been calculated in the same manner. The annual depreciation amount and book values at end of years using straight-line depreciation method are presented in Table 3.1. For straight-line method, the book value at the end of different years can also be calculated by using equation (3.7). For example, the book value at the end of 2nd year is given by;

For double-declining balance method , the constant annual depreciation rate ‘dm' is given by;

The book value at the end of a given year is calculated by subtracting the annual depreciation amount from previous year's book value.

Book value at the end of 1 st year = 

Book value at the end of 2nd year = 

Similarly the annual depreciation and book value at the end of other years have been calculated in the same manner and are presented in Table 3.1.

The book value at the end of different years can also be calculated by using equation (3.17). Using this equation, the book value at the end of 2nd year is given by;

Depreciation and book value of the construction equipment using straight-line method and double-declining balance method

From above table, it is observed that the book value at the end of useful life i.e. 10 years in double-declining balance method is less than salvage value. Thus the equipment will be depreciated fully before the useful life. In other words the book value reaches the estimated salvage value before the end of useful life. As the book value of the equipment is not depreciated further after it has reached the estimated salvage value, the depreciation amount is adjusted accordingly. The book value of the construction equipment at the end of 8th , 9th , and 10th years are Rs.587202.56, Rs.469762.05 and Rs.375809.64 respectively (from Table 3.1, Double-declining balance method). Similarly the depreciation amounts for 9th and 10th years are Rs.117440.51 and Rs.93952.41 respectively. Thus to match the book value with the estimated salvage value, the depreciation in 9th year will be Rs.87202.56 (Rs.587202.56 – Rs.500000) and that in 10th year will be zero. This will lead to book value of Rs.500000 (equal to salvage value) at the end of 9th year and 10th year. For this case, the switching from double-declining balance method to straight-line method can be carried out to ensure that the book value does not fall below the estimated salvage value and this procedure of switching is presented in Lecture 3 of this module.

Sum-of-years-digits (SOYD) depreciation method:-

It is also an accelerated depreciation method. In this method the annual depreciation rate for any year is calculated by dividing the number of years left (from the beginning of that year for which the depreciation is calculated) in the useful life of the asset by the sum of years over the useful life.

The depreciation rate ‘dm' for any year ‘m' is given by;

(3.21)

Where n = useful life of the asset as stated earlier

SOY = sum of years' digits over the useful life = 

Rewriting equation (3.21);

(3.22)

The depreciation amount in any year is calculated by multiplying the depreciation rate for that year with the total depreciation amount (i.e. difference between initial cost ‘P' and salvage value ‘SV ') over the useful life.

Thus the expression for depreciation amount in any year ‘m ' is represented by;

(3.23)

Putting the value of ‘dm' from equation (3.21) in equation (3.23) results in the following;

(3.24)

The depreciation in 1st year i.e. ‘D1' is obtained by putting ‘m ' equal to ‘1' in equation (3.24) and is given by;

(3.25)

The book value at the end of 1st year is equal to initial cost less the depreciation in the 1st year and is given by;

Now putting the expression of ‘D1' from equation (3.25) in the above expression results in following;

(3.26)

The depreciation in 2nd year i.e. ‘D2' is given by;

(3.27)

Book value at the end of 2nd year is equal to book value at the beginning of 2nd year (i.e. book value at the end of 1st year) less the depreciation in 2nd year and is given by;

Now putting the expressions of ‘BV1' and ‘D2' from equation (3.26) and equation (3.27) respectively in above expression results in the following;

 

 

(3.28)

Similarly the expressions for depreciation and book value for 3rd year are presented below.

(3.29)

 

 

(3.30)

The expressions for depreciation and book value for 4th year are given by;

(3.31)

 

 

(3.32)

Similarly the expressions for depreciation and book value for 5th year are given by;

(3.33)

 

 

(3.34)

The expressions for book value in different years are presented above to find out the generalized expression for book value at end of any given year. Now referring to the expressions of book valuesBV1 , BV2 , BV3 , BV4 , BV5 in above mentioned equations, it is observed that the variable terms are ‘n', ‘(2n- 1)', ‘(3n -3)', ‘(4n-6)' and ‘(5n-10)' respectively. These variable terms can also be written ‘(n+1- 1 )', ‘(2n+1 - 2 )', ‘(3n +1- 4 )', ‘(4n+1- 7 )' and ‘(5n+1- 11 )' respectively. The numbers 1, 2, 4, 7, and 11 in these variable terms follow a series and it is observed that value of each term is equal to value of previous term plus the difference in the values of current term and previous term. On this note, the general expression for value of ‘m ' term of this series is given by;

(3.35)

Now the generalized expression for book value for any year ‘m ' is given by;

 

 

(3.36)

In this method also, the annual depreciation during early years is more as compared to that in later years of the asset's useful life.

Sinking fund (SF) depreciation method:-

In this method it is assumed that money is deposited in a sinking fund over the useful life that will enable to replace the asset at the end of its useful life. For this purpose, a fixed amount is set aside every year from the revenue generated and this fixed sum is considered to earn interest at an interest rate compounded annually over the useful life of the asset, so that the total amount accumulated at the end of useful life is equal to the total depreciation amount i.e. initial cost less salvage value of the asset. Thus the annual depreciation in any year has two components. The first component is the fixed sum that is deposited into the sinking fund and the second component is the interest earned on the amount accumulated in sinking fund till the beginning of that year.

For this purpose, first the uniform depreciation amount (i.e. fixed amount deposited in sinking fund) at the end of each year is calculated by multiplying the total depreciation amount (i.e. initial cost less salvage value) over the useful life by sinking fund factor. After that the interest earned on the accumulated amount is calculated. The calculations are shown below.

The first component of depreciation i.e. uniform depreciation amount ‘A' at the end of each year is given by;

(3.37)

Where i = interest rate per year

Depreciation amount for 1st year is equal to only ‘A' as this is the amount (set aside every year from the revenue generated) to be deposited in sinking fund at the end of 1st year and hence there is no interest accumulated on this amount.

Therefore

(3.38)

Now book value at the end of 1st year is given by;

(3.39)

Depreciation amount for 2nd year is equal to uniform amount ‘A' to be deposited at the end of 2ndyear plus the interest earned on the amount accumulated till beginning of 2nd year i.e. on depreciation amount for 1st year. Thus depreciation for amount for 2nd year is given by;

Now putting ‘D1' equal to ‘ A ' in the above expression results in;

(3.40)

Book value at the end of 2nd year is given by;

Now putting the expressions of ‘BV1' and ‘D2' from equation (3.39) and equation (3.40) respectively in above expression results in the following;

(3.41)

Depreciation amount for 3rd year is equal to uniform amount ‘A' to be deposited at the end of 3rdyear plus the interest earned on the amount accumulated till beginning of 3 rd year i.e. on sum of depreciation amounts for 1st year and 2nd year. Thus depreciation for amount for 3rd year is given by;

Putting the expressions of ‘D1' and ‘D2' from equation (3.38) and equation (3.40) respectively in above expression results in the following;

On simplifying the above expression;

(3.42)

Now book value at the end of 3rd year is given by;

Putting the expressions of ‘BV2' and ‘D3' from equation (3.41) and equation (3.42) respectively in above expression results in;

(3.43)

Now the generalized expression for depreciation in any given year ‘m ' can be written as follows (referring to equations (3.38), (3.40) and (3.42));

(3.44)

Putting the value of ‘ A ' from equation (3.37) in equation (3.44) results in the following;

(3.45)

Similarly the generalized expression for book value at the end of any year ‘m' is given by (referring to equations (3.39), (3.41) and (3.43));

(3.46)

The expression in the square bracket of equation (3.46) is in the form of a geometric series and its sum represents the factor known as uniform series compound amount factor (stated in Module-1). Therefore replacing the expression in square bracket of equation (3.46) with uniform series compound amount factor results in;

(3.47)

Putting the value of ‘ A ' from equation (3.37) and expression for uniform series compound amount factor in equation (3.47) results in the following generalized expression for book value at the end of any year ‘m' (1 ≤ m ≤ n ).

 

 

(3.48)

In this method, the depreciation during later years is more as compared to that in early years of the asset's useful life.

Example -2

Using the information provided in previous example, calculate the annual depreciation and book value of the construction equipment using sum-of-years-digits method and sinking fund method. The interest rate is 8% per year.

Solution:

P = Rs.3500000

SV = Rs.500000

n = 10 years

For sum-of-years-digits method, the depreciation amount for a given year is calculated using equation (3.24).

SOY = sum of years' digits over the useful life 

Depreciation for 1st year 

Book value at the end of 1st year:

Depreciation for 2nd year 

Book value at the end of 2nd year:

Similarly the annual depreciation and book value at the end of other years for the construction equipment have been calculated and are presented in Table 3.2.

The book value at the end of different years can also be calculated by using equation (3.36). Using this equation, the book value at the end of 2nd year is calculated as follows;

For sinking fund method, the depreciation amount for a given year is calculated using equation (3.45).

The interest rate per year = i = 8%

Depreciation amount for 1st year:

Similarly the annual depreciation and book value at the end of other years are calculated in the same manner and are given in Table 3.2.

The book value at the end of a given year can also be calculated by using equation (3.48). Using this equation, the book value at the end of 2nd year is given by;

Depreciation and book value of the construction equipment using sum-of-years-digits method and sinking fund method

* This minor difference is due to effect of decimal points in the calculation.

The book value at the end of all years over the useful life of the construction equipment obtained from different depreciation methods (Example 1 and Example 2) are shown in Fig below.

Book value of the construction equipment using different depreciation methods

In the above figure, the line representing the salvage value is also shown. In double-declining balance method only, the calculated book value at the end of useful life i.e. 10th year is not same as the estimated salvage value.