INVENTORYThe value of materials and goods held by an organization to support production (raw materials, subassemblies, work in process), for support activities (repair, maintenance, consumables), or for sale or customer service (merchandise, finished goods, spare parts)

For many firms the inventory is the largest current asset. Inventory difficulties can and do contribute to business failures. When a firm does no more than unintentionally run out of an item, results are not pleasant. If the firm is a manufacturer, the stock out (inability to supply an item from inventory) could in extreme cases, bring production to a halt. Conversely, if a firm carries excessive inventories, the added carrying cost may represent the difference between profit and loss. Skilful inventory management can make a significant contribution to a firm’s profit.

2 KINDS OF INVENTORYs

A. Single Period InventoryThis model is also known as the ‘newsboy problem’ as it describes the problem of a newspaper vendor who must decide on how many papers to order per day and any that are leftover must still be paid for. It is a model for ordering of perishables and other items with limited useful lives.

B. Multiple-Period InventoryInvolves that will be maintained in inventory long enough that units which have been consumed may be replenished. In a multi-period model, all the items unsold at the end of one period are available in the next period.

IMPORTANCE OF INVENTORY CONTROLIn any organization, inventories add an operating flexibility that would not otherwise exist. In manufacturing, work-in-process inventories are an absolute necessity unless each individual part is to be carried from machine to machine and those machines set up to produce that single part. Patients in a hospital are really inventory for the physician; true, they are there because they are too sick to be at home, but it must be recognized that having them in one location enables the physician to see all his or her patients during “rounds.” The many functions inventory performs can be summarized as follows:

1. SMOOTHING OUT IRREGULARIETIES IN SUPPLYTobacco is harvested during the late summer months, but the manufacture of tobacco products such as cigarettes and cigars continues throughout the entire year. In cases like this, sufficient raw material must be purchased during the tobacco-producing period to last the entire year; this forces the manufacturer to carry an inventory.In a simpler sense, because a truck may go 100 miles without passing a gasoline station, its tanks must carry enough fuel to avoid run outs.

2. BUYING OR PRODUCING IN LOTS OR BATCHESWhen the demand for an item will not support its continued production throughout the entire year, it is usually produced in batches or lots on an intermittent basis. During the time when the

item is not being produced, sales are made from inventory which is accumulated while the item is being produced. Similarly, a retailer of men’s clothing does not purchase a new shirt from the manufacturer each time the store sells one; rather, the retailer chooses to carry in the store an inventory of these shirts sot that purchasing can be done in larger quantities, thereby allowing lower costs, less paperwork, and greater customer selection.

3. ALLOWING ORGANIZATIONS TO COPE WITH PERISHABLE MATERIALSThe packers of frozen lobster tails operate a peak production only a few months each year; they too must store up, or inventory, a supply sufficient to last them through a year’s anticipated demand until the nest lobster season. The entire production process which deals with freezing fresh fruits and vegetable must also give thoughtful consideration to the rate of inventory accumulation and depletion throughout the peak production and sales periods each year.

4. STORING LABORAlthough it may be conceptually difficult to think of “inventorying” labor, it is routine practice to do just that. The peak demand for the installation of replacement heating units comes in the fall, just after the old units have been operated for the first time. The manufacturers of heating units store up excess labor by having their worker produce at a designated rate all year long; then, having converted labor into finished heating units, they hold the units in inventory until the point when demand increases rapidly. Even if demand exceeds current productive capacity, a manufacturer can supply the difference out of inventory at that time.

Inventory Decisions: EOQEconomic order quantity also known as Wilson EOQ Model or Wilson Formula was developed by Ford W. Harris in 1913. It is the oldest and best-known inventory model; its origins date all the way back to 1915. It is the order quantity that minimizes total inventory holding costs and ordering costs. Let us look for a moment at these costs:Assumptions: 

1. The ordering cost is constant.2. The rate of demand is known, and spread evenly throughout the year.3. The lead time is fixed.4. The purchase price of the item is constant i.e. no discount is available5. The replenishment is made instantaneously; the whole batch is delivered at once.6. Only one product is involved.

EOQ is the quantity to order, so that the sum of ordering cost and holding cost is at its minimum. These costs will be equal to one another at the minimized cost point.

As we mentioned, the economic order quantity is the order size that minimizes the sum of carrying costs and ordering costs. These two costs react inversely to each other. As the order size increases, fewer orders are required, causing the ordering cost to decline, whereas the average amount of inventory on hand will increase, resulting in an increase

in carrying costs. Thus, in effect, the optimal order quantity represents a compromise between these two inversely related costs.

The total annual ordering cost is computed by multiplying the cost per order, designated as Co, times the number of orders per year. Since annual demand, D, is assumed to be known and to be constant, the number of orders will be D/Q, where Q is the order size and

Annual Ordering Cost = CoD/Q

The only variable in this equation is Q; both Co and D are constant parameters. Thus, the relative magnitude of the ordering cost is dependent upon the order size.

Total annual carrying cost is computed by multiplying the annual per-unit carrying cost, designated as Cc, times the average inventory level, determined by dividing the order size, Q, by 2: Q/2;

Annual Carrying Cost= CcQ/2

The total annual inventory cost is the sum of the ordering and carrying costs:TC=CoD/Q + CcQ/2

The graph above shows the inverse relationship between ordering cost and carrying cost, resulting in a convex total cost curve.

The optimal order quantity occurs above where the total cost curve is at a minimum, which coincides exactly with the point where the carrying cost curve intersects the ordering cost curve. This enables us to determine the optimal value of Q by equating the two cost functions and solving for Q:

Alternatively, the optimal value of Q can be determined by differentiating the total cost curve with respect to Q, setting the resulting function equal to zero (the slope at the minimum point on the total cost curve), and solving for Q:

The total minimum cost is determined by substituting the value for the optimal order size, Qopt, into the total cost equation:

Example:The I-75 Carpet Discount Store in North Georgia stocks carpet in its warehouse and sells it through an adjoining showroom. The store keeps several brands and styles of carpet in stock; however, its biggest seller is Super Shag carpet. The store wants to determine the optimal order size and total inventory cost for this brand of carpet given an estimated annual demand of 10,000 yards of carpet, an annual carrying cost of $0.75 per yard, and an ordering cost of $150. The store would also like to know the number of orders that will be made annually and the time between orders (i.e., the order cycle) given that the store is open every day except Sunday, Thanksgiving Day, and Christmas Day (which is not on a Sunday).SOLUTION:Cc = $0.75 per yardCo = $150D = 10,000 yardsThe optimal order size is

The total annual inventory cost is determined by substituting Qopt into the total cost formula:

The number of orders per year is computed as follows:

Given that the store is open 311 days annually (365 days minus 52 Sundays, Thanksgiving, and Christmas), the order cycle is

INVENTORY COSTSThe core of inventory analysis lies in finding and measuring relevant costs. Six major

Cost are listed :

1. Ordering costs (Co) include operating systems to signal need; determining from whom to order and how much; placing the order; receiving, inspecting, storing items, documenting receipt, paying suppliers, and notifying users.

2. Setup, takedown, and changeover functions (Cs) are job shop costs. Efforts have led to major cost-cutting. This has promoted higher production variety levels. Such cost savings are termed economy of scope.

3. Costs of carrying inventory (Cc) are best summarized by Table 14-1 which has estimates for high, medium, and low carrying cost rates (Cc). The per unit costs (c) of inventoried items are charged a tax (Cc) for interest that is not earned, storage, spoilage, pilferage, insurance, etc.

4. Accepting discounts offered for buying larger volumes entails extra carrying costs and reductions in ordering costs. Discounts must at least offset any net additional costs to make them worth consideration.

5. Out-of-stock costs can vary from trivial to significant penalties. If the outage applies to a critical item, the problem can assume major proportions.

6. Costs of running the inventory system include processing data, updating information, etc. These systemic costs will vary according to the size and geographic dispersion of the inventory, the need to be up-to-the-minute, the capabilities of the computer system, and the training of personnel. It will also depend on whether the inventory system is perpetual or periodic

INVENTORY CONTROL

Inventory control is a set of policies and operating procedures that are designed to maximize a company’s use of inventory, so that it generates the maximum profit from the least amount of inventory investment without intruding upon customer satisfaction levels.

Some of the more common areas in which to exercise inventory control are:

1. Raw materials availability

There must be enough raw materials inventory on hand to ensure that new jobs are launched in the production process in a timely manner, but not so much that the company is invest in an in ordinate amount of inventory. The key control designed to address this balance is ordering frequently in small lot sizes from suppliers. Few suppliers are willing to do this, given the cost of frequent deliveries, so a company may have to engage in sole sourcing of goods in order to entice suppliers into engaging in just-in-time deliveries.

2. Finished goods availability

A company may be able to charge a higher price for its products if it can reliably ship them to customers at once. Thus, there may be a pricing premium associated with having high levels of finished goods on hand. However, the cost of investing in so much inventory may exceed the profits to be gained from doing so, so inventory control involves balancing the proportion of allowable backorders with a reduced level of on hand finished goods. This may also lead to the use of a just-in-time manufacturing system, which only produces goods to specific customer orders.

3. Work in process

It is possible to reduce the amount of inventory that is being worded on in the production process, which further reduces the inventory investment. This can involve a broad array of actions such as using production cells to work on subassemblies, shifting the work area into a smaller space to reduce the amount of inventory travel time, reducing machine setup times to switch to new jobs, and minimizing job sizes.

4. Reorder point

A key part of inventory control is deciding upon the best inventory level at which to reorder additional inventory. If the reorder level is set very low, this keeps the investment in inventory low, but also increases the risk of a stock out, which may interfere with the production process or sales to customers. The reverse problems arise if the reorder point is set too high. There can be considerable amount of ongoing adjustment to reorder levels to fine tune these issues. An

alternative method is to use a material requirements planning system to order only enough inventory for expected production levels.

5. Bottleneck enhancement

There is nearly always a bottleneck somewhere in the production process that interferes with the ability of the entire operation to increase its output. Inventory control can involve placing an inventory buffer immediately in front of the bottleneck operation, so that the bottleneck can keep running even if there are production failures upstream from it that would otherwise interfere with any inputs that it requires.

6. Outsourcing

Inventory control can also involve decisions to outsource some activities to suppliers, thereby shifting the inventory control burden to the suppliers (though usually in exchange for a reduced level of profitability.)

The issues noted here highlight how difficult it can be to manage the inventory control function. Your operating boundaries are to either invest too much in inventory or to have too little inventory on hand to satisfy the production manager or customers.

INVENTORYIN

OPERATIONS RESEARCH

MEMBERS:AREVALO, AMANDA ROSA BLANCAEVORA, RACHEL R.FALTADO, MARIEL ANGELICA G. LORENZO, LOUIE ANDREWMENDOZA, RANDY C.