le8 inventory management - mdhzoomin.idt.mdh.se/course/kpp227/documents/le8... · inventory...

Antti Salonen

KPP227 - HT 2015

KPP227 1 Antti Salonen

Inventory management

Inventory management concerns short-range decisions about supplies, inventories, production levels, staffing patterns, schedules and distribution. The decisions are often of a tactical (rather than strategic) character.

Strategic

Tac+c

Opera+onal


What is inventory?

An inventory is a stock or store of goods. Goods inventory management is essential to the successful operation of most organizations for a number of reasons, like:

•  the amount of money inventory represents (capital investment)

•  The impact on daily operations


What is inventory?

Inventory is a stock of anything, held to meet future demand. Firms typically stock a large amount of items, ranging from small items (such as screws and nuts) to large items (such as machines and castings), depending on the kind of business.

Manufacturing companies (for example) carry supplies of: •  raw material •  purchased parts •  sub assemblies/partially completed

items (Work in Process – WIP) •  finished goods •  spare parts for machines, tools and

other supplies.


Accounting categories

Inventories for a manufacturing plant exist in three forms (so called accounting categories): •  Raw material •  Work in process (WIP) •  Finished goods

1.  Raw material at the plant passes through one or more processes, which

transforms them into various levels of WIP inventory. 2.  When this inventory is processed at the final operation, it becomes

finished goods inventory. 3.  Finished goods can be held at a plant, a distribution center (DC), and

retail locations.


Nature and importance of inventory

Inventories are not only necessary for operations, but also for customer satisfaction. Hence, a typical firm can have about 30 % of it´s current assets and 90 % of it´s working capital invested in inventory.

Question: What can be possible benefits and drawbacks of inventory?


Functions of Inventory

1.  To meet anticipated customer demand Anticipation stock: Inventories are held to satisfy an expected average demand.

2.  To smooth production requirements

Seasonal inventories: Inventories are built during off-season to satisfy the demand during high season.

3.  To decouple operations

Buffers: Inventories are held between successive operations to maintain continuity of production despite e.g. breakdowns.

4.  To protect against stock outs Safety stocks: Inventories are held to cover for late deliveries and unexpected increases in demand.


Functions of Inventory

5.  To take advantage of order cycles Cycle stock: Inventories are held to minimize purchasing cost resulting in order cycles.

6.  To hedge against price increases Inventories are held to avoid a substantial price increase.

7.  To permit operations

Pipeline inventory: Inventories are held in order to avoid shortages of e.g. raw material which can result in production stops (work in process).


Types of inventory

1.  Cycle inventory Increased inventory and lower cost by ordering larger quantities. Lot sizing principles: •  The lot size Q must equal the demand during the time between orders •  The longer the time between orders, the greater the cycle inventory.

2.  Safety stock inventory Protects against uncertainties in demand, lead time and supply.

3.  Anticipation inventory Used to absorb uneven rates of demand or supply.

4.  Pipeline inventory Inventory that is created when an order for an item is issued but not yet placed in inventory. (Inventory moving from point to point in the material flow process)


Inventory levels

Inadequate control of inventories can result in both under- and over-stocking of items.


Inventory levels

Inadequate control of inventories can result in both under- and over-stocking of items. •  Under-stocking

Results in missed deliveries, lost sales, dissatisfied customers and production bottle necks.


Inventory levels



•  Over-stocking Results in unnecessary capital being tied up, that could have been used for something more productive.


Inventory levels



•  Over-stocking Results in unnecessary capital being tied up, that could have been used for something more productive.

Although overstocking may appear to be the lesser of the two evils, excessive overstocking can be staggering where holding costs are high. This is one factor dealt with by e.g. lean production (JIT, reduced waste etc).


Cost information The costs associated with inventories are: •  Holding costs

Relates to physically having items in storage (see next slide). •  Ordering cost (or setup costs)

Relates to ordering and receiving inventory, which vary with the actual placement of an order. These costs include e.g. determining how much is needed, preparing the invoice, shipping, goods inspection, moving the goods to temporary storages etc.

•  Shortage costs

Relates to the case when demand exceeds supply. These costs include e.g. opportunity cost of making the sale, loss of customer goodwill or even cost of lost production (if the customer is internal)


Holding or carrying cost

Inventory holding (or carrying) cost is the cost of keeping items on hand. These cost components change with inventory level. The components of holding cost •  Cost of capital

To finance an investment (often up to 15 %) •  Storage and handling costs

Inventory needs space and must be moved in and out of storage •  Taxes, insurance and shrinkage

Shrinkage can take three forms: •  Pilferage/Theft •  Obsolescence due to e.g. model changes •  Deterioration implies a lower value


Pressures for low inventory

•  Inventory represents a temporary monetary investment => firm must pay (rather than receive) interest.

•  Inventory hides quality problems.

•  Inventory takes up space that could be used for a more profitable activity.

•  Inventory needs to be handled => increased materials handling requirements.


Pressures for high inventory

•  Customer service Inventory can speed up delivery and avoids stock outs and backlogs.

•  Ordering cost Minimize the cost of preparing purchase order.

•  Setup cost Producing inventory reduces the amount of setups between different items.

•  Labor and equipment utilization Increased productivity

•  Transportation cost Inventory on hands allows the possibility to optimize transportation.

•  Quantity discounts The more you buy at one time, the cheaper the price/item


However…

It is not unusual for managers to discover that their firm has a 10 year supply of some items => a balance is needed!


Inventory concerns

•  Level of customer service To have the right goods, in sufficient quantities, in the right place at the right time

•  Cost of ordering and carrying inventory

Overall objective To achieve satisfactory customer service levels while keeping inventory costs within reasonable bounds.


Inventory measures

The average aggregate inventory value is the total value of all items held in inventory and represents the inventory investments over a period of time. Average aggregate inventory value = ∑i (No of unit Xi* Value of unit Xi) However, it is also important to consider weeks of supply (how many weeks of demand the average inventory can cover) and inventory turnover (how many times the whole inventory is replaced per year). Weeks of supply = Average aggregate inventory/Weekly sales (at cost) Inventory turnover = Annual sales (at cost)/ Average aggregate inventory


EXAMPLE 1 Inventory measures


Problem to solve


Solution


The Pareto principle

The Pareto Principle (also called 80/20 rule) The 80/20 rule means that in anything, a few (20 percent) are vital and many (80 percent) are trivial.


ABC analysis

The product line of a typical firm is made up of individual products at different stages of their respective life cycles and with different degrees of sales success. E.g. 80 % of a firm’s sales are generated by 20 % of the product line items. => important to primarily control these (and not the other 80 %).

Percentage of items


ABC Analysis

Classification of articles in regards to e.g. item value. •  Class “A” items constitute the most important class of inventories so far as the

proportion in the total value of inventory. The “A” items consists of ~20% of the total items and accounts for ~80% of the total material usage. This items need a tightly controlled inventory system with constant attention.

•  Class “B” items constitute an intermediate position, which constitute ~30% of the total items, accounts for ~15% of the total material consumption. These items need a formalized inventory system and periodic attention.

•  Class “C” items are quite negligible. It consists of the remaining ~50% items, accounting for only ~5% of the monetary value of total material usage . Quite relaxed inventory procedures are used.


Now that we have identified the inventory items deserving the most attention, we devote the remainder of the lecture to the decisions of

how much to order and when.


Inventory Control Systems

•  Independent demand Items for which demand is influenced by market conditions and is not related to the inventory decisions for any other item held in stock or produced.

•  Dependent demand

Items required as components or inputs to a service or product. Dependent demand exhibits a pattern very different from that of independent demand and must be managed with different techniques. (will be covered in upcoming lectures)


Independent demand

•  Wholesale and retail merchandise •  Service support inventory (e.g. office supplies) •  Product and replacement-part distribution inventories •  Maintenance, repair, and operating (MRO) supplies


Demand forecast and lead time information

•  Inventories are used to satisfy order demand requirements, so it is essential to have reliable estimates of the amount and timing of demand.

•  Similarly, it is essential to know how long it will take for orders to be delivered. •  Managers also need to know the extent to which demand and lead time (the time

between submitting an order and receiving it) might vary. The greater the variability, the greater the need for additional stock to reduce the risk of a shortage between deliveries.


Definitions: A reminder

•  Inventory holding cost is the sum of the cost of capital and the variable costs of keeping items on hand, such as storage and handling, taxes, insurance, and shrinkage.

•  Ordering cost is the cost of preparing a purchase order for a supplier or a production order for the shop.

•  Setup cost is the cost of changing over a machine to produce a different item.

Cycle inventory is the portion of total inventory that varies directly with lot size.


Economic Order Quantity (EOQ)

The lot size, Q, that minimizes total annual inventory holding and ordering costs. When to use EOQ: •  Constant and certain demand •  No lot size constraints •  Inventory holding cost and fixed cost per lot

are the only costs •  Decisions for an item can be made

independently •  Constant and certain lead time

EOQ is a reasonable approximation, not an optimization tool!


EOQ calculation

Q = Lot size (units) H = Holding cost for one unit during one year (SEK) D = annual demand (units/year) S = Ordering cost/Set up cost (SEK/lot)


EOQ calculation Total annual cycle-inventory cost = Annual holding cost + Annual ordering or setup cost

Economic order quantity:

C = total annual cycle-inventory cost Q = lot size, in units H = cost of holding one unit in inventory for a year, often expressed as a percentage of the item’s value D = annual demand, in units per year S = cost of ordering or setting up one lot


EOQ


Time Between Orders (TBOEOQ)

Sometimes, inventory policies are based on the time between replenishment orders, rather than on the number of units in the lot size. The Time Between Orders (TBO) for a particular lot size is the average elapsed time between receiving (or placing) replenishment orders of Q units. => TBO gives a hint on how often an order should be placed.


EXAMPLE 3 EOQ, Cost, TBO


a)


b)


Problem to solve


Solution


EOQ sensitivity analysis

TABLE 12.1 | SENSITIVITY ANALYSIS OF THE EOQ

Parameter EOQ Parameter Change

EOQ Change

Comments

Demand ↑ ↑ Increase in lot size is in proportion to the square root of D.

Order/Setup Costs ↓ ↓

Weeks of supply decreases and inventory turnover increases because the lot size decreases.

Holding Costs ↓ ↑ Larger lots are justified when holding

costs decrease.

2DS H

2DS H

2DS H


The EOQ and other lot-sizing methods answer the important question:

How much should we order?

Another important question that needs an answer is:

When should we place the order?


Continuous review (Q) system

A continuous review (Q) system, sometimes called a reorder point (ROP) system or fixed order-quantity system, tracks the remaining inventory of a SKU each time a withdrawal is made to determine whether it is time to reorder.

A Q system means that whenever the inventory position reaches a certain point, a new order is placed!



Q system when demand and lead time are constant and certain




Inventory position = On-hand inventory + Scheduled Receipts – Back Orders

IP = OH + SR – BO

If IP ≤ Reorder point => An order should be placed!


Problem to solve

Inventory position = On-hand inventory + Scheduled receipts – Backorders

IP = OH + SR – BO


Solution



Q system when demand is uncertain



Calculation of reorder point (ROP) when demand is uncertain: 1.  Choose an appropriate service-level policy.

E.g. choosing a 90 percent cycle service level means that the probability is 90 percent that the demand will not exceed the supply during the lead time.

2.  Determine the demand during lead time probability distribution

3.  Determine the safety stock and reorder point levels


Continuous review (Q) system The size of the safety stock depends on the variability, which is measured with probability distributions.

Normal distribution

Average demand during lead time

Cycle-service level = 85%

Probability of stockout (1.0 – 0.85 = 0.15)

zσdLT

R

Finding Safety Stock with a Normal Probability Distribution for an 85 Percent Cycle-Service Level


EXAMPLE 4 Reorder point (ROP) & safety stock

(normal distribution)


a) Normal distribution

vv

v


a)


b) Normal distribution


Problem to solve


Solution



Discrete distribution •  Data are unavailable •  Each possible demand during lead time, along with it’s probability is listed. •  R is selected from the list of demand levels.

Find the smallest value of R that meets the desired service level. E.g. if the desired cycle-service level is 95% and R is set at 500 units the probabilities of all demands ≤500 must equal or exceed 0.95, and R is the smallest such quantity.

The size of the safety stock depends on the variability, which is measured with probability distributions.


EXAMPLE 5 Reorder point (ROP) & Safety stock

(discrete distribution)


Periodic review (P) system

A periodic review (P) system, sometimes called a periodic reorder system or fixed interval reorder system, reviews an item’s inventory position periodically rather than continuously (=> TBO is fixed). The lot size, Q, may change from one order to the next (demand is uncertain).

Essential assumptions: •  item is delivered in lots •  inventory holding cost is not affected by lot sizing decisions •  decisions for one item are independent of decisions for other items •  amount received is exactly amount ordered

A P system means that on a regular basis, a new order is placed.



P system when demand is uncertain and lead time is certain

Inventory position = On-hand inventory + Scheduled Receipts – Back Orders

IP = OH + SR – BO

An order is placed every period P and the amount to order = T-IP !


EXAMPLE 6 Order quantity



Two decisions must be made:

•  P: Length of time between reviews Could e.g. be based on the cost trade-offs of the EOQ, average time between orders of the EOQ (= TBO).

•  T: Target inventory level

Must equal to the expected demand during protection interval (P + L) plus enough safety stock to protect against demand and lead time uncertainties.

T = average demand during the protection interval + safety stock for protection interval ! = ! ! + ! + !! !!! = ! ! + ! + !!!! ! + !!


EXAMPLE 7 P system


Demand for a bird feeder is normally distributed with a mean of 18 units per week and a standard deviation in weekly demand of 5 units. The lead time is 2 weeks, and the business operates 52 weeks per year. EOQ is 75 units and the safety stock is 9 units for a cycle-service level of 90 percent. What is the equivalent P system? Find P and T! Answers are to be rounded to the nearest integer.


Q system vs. P system

Primary advantages of Q systems •  Review frequency may be individualized •  Fixed lot sizes can result in quantity discounts •  Lower safety stocks Primary advantages of P systems •  Convenient •  Orders can be combined •  Only need to know IP when review is made


Hybrid systems

Optional replenishment systems •  Optimal review, min-max, or (s,S) system, like the P system •  Reviews IP at fixed time intervals and places a variable-sized order to

cover expected needs •  Ensures that a reasonable large order is placed

Base-stock system •  Replenishment order is issued each time a withdrawal is made •  Order quantities vary to keep the inventory position at R •  Minimizes cycle inventory, but increases ordering costs •  Appropriate for expensive items

Visual systems •  Allows employees to place orders when inventory visibly reaches a

certain marker. (E.g. Kanban)


Non-instantaneous replenishment

If an item is being produced internally (rather than purchased) finished units may be used or sold as soon as they are completed, without waiting until a full lot is completed! Usually production rate, p, exceeds the demand rate, d, so there is a build-up of (p – d) units for Q/p days!



( ) ⎟⎠

⎞⎜⎝

⎛ −=−=

pdpQdp

pQImax

Maximum cycle inventory (Imax): where

p = production rate d = demand rate Q = lot size

Average cycle inventory is no longer Q/2 (as in EOQ). Instead it is Imax /2



Total annual cost = Annual holding cost + Annual ordering or setup cost

=>

=> Economic production lot size:

( ) ( )SQDHIC +=

2max ( ) ( )S

QDH

pdpQC +⎟⎟⎠

⎞⎜⎜⎝

⎛ −=2

dpp

HDSELS

−=2

I = inventory D = annual demand p = production rate d = demand rate Q = lot size H = holding cost S = ordering/setup cost


EOQ vs. ELS Do NOT mix up

Economic order size

EOQ =

Economic production lot size

ELS = dpp

HDS

−

2

HDS2


EXAMPLE 8 Non-instantaneous replenishment


Solution


Problem to solve

Skärmurklipp gjort: 2010-11-21; 13:18

A toy manufacturer uses 48000 rubber wheels per year for its popular dump truck series. The firm makes its own wheels, which it can produce at a rate of 8 per day. The toy trucks are assembled uniformly over the entire year. Carrying cost is €1 per wheel a year. Setup cost for a production run of wheels is €45. The firm operates 240 days per year. Determine the: a. Optimal run size b. Minimum total annual cost for carrying and setup c. Cycle time for the optimum run size d. Run time

D = 48000 wheels per year S = €45 H = €1 per wheel per year p = 800 wheels per day d = 48000 wheels per 240 days, or 200 wheels per day


Solution

Skärmurklipp gjort: 2010-11-21; 13:18

√ 2DS

H √ p

p - d √ 2x48000x45

1 √ 800

800 - 200 = = 2400 wheels a: ELS =

b: Cmin = Carrying cost + Setup cost = Imax

2 ( ) H + ( ) S D ELS

Imax = (p – d) = (800 – 200) = 1800 wheels ELS p

2400 800

Cmin = 1800

2 ( ) 1 + ( ) 45 = 900 + 900 = €1800 48000 2400

c: Cycle time = ELS

d ( ) = = 12 days 2400 200

d: Run time = ELS

p ( ) = = 3 days 2400 800


Quantity discounts

Price incentives to purchase large quantities, create pressure to maintain a large inventory. Hence, a new approach is needed to find the best lot size - one that balances the advantages of lower prices for purchased materials and fewer orders (which are benefits of large order quantities) against the disadvantage of the increased cost of holding more inventory.


Quantity discounts

Total annual cost =Annual holding cost + Annual ordering or setup cost + Annual cost of materials where

Q = lot size H = holding cost D = annual demand d = demand rate S = ordering and/or setup cost P = price/unit

( ) ( ) PDSQDHQC ++=

2


Quantity discounts Step 1. Beginning with lowest price, calculate the EOQ for each price level until a feasible EOQ is found. It is feasible if it lies in the range corresponding to its price. Each subsequent EOQ is smaller than the previous one, because P, and thus H, gets larger and because the larger H is in the denominator of the EOQ formula.

Step 2. If the first feasible EOQ found is for the lowest price level, this quantity is the best lot size. Otherwise, calculate the total cost for the first feasible EOQ and for the larger price break quantity at each lower price level. The quantity with the lowest total cost is optimal.


EXAMPLE 9 Quantity discounts


One period decisions

One of the dilemmas facing many retailers is how to handle seasonal goods. Often, they cannot be sold at full markup the next year because of changes in styles. This type of situation is often called the newsboy problem. Step 1: List different demand levels and probabilities. Step 2: Develop a payoff table that shows the profit for each

purchase quantity, Q, at each assumed demand level, D. Each row represents a different order quantity and each column represents a different demand. The payoff depends on whether all units are sold at the regular profit margin which results in two possible cases.



Case 1.

Case 2.



Step 3: Calculate the expected payoff of each Q by using the

expected value decision rule: For a specific Q, first multiply each payoff by its demand probability, and then add the products.

Step 4: Choose the order quantity Q with the highest expected

payoff.


EXAMPLE 10 One period decisions


Supply exceeds demand => Case 2

Demand exceeds supply => Case 1


Relevant book chapters

•  Chapter: Managing inventories

•  Supplement C: Special inventory models


Questions?

[email protected]

Next lecture on Tuesday 2015-12-08

Scheduling, Assignment


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