Chapter 11 - Inventory Management.doc

7/30/2019 Chapter 11 - Inventory Management.doc

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Chapter 11INVENTORY MANAGEMENT

Inventory. A stock or goods of goods.

Independent and Dependent Demand.

A major distinction in the way inventory planning and control are managed is whether demandfor items in inventory is independent or dependent.Dependent demand. Demand for items in inventory that are subassemblies or componentparts to be used in the production of finished goods. Demand of subassemblies and componentparts is derived from the number of finished units that will be produced.Independent demand. Demand for items that are finished items. These items are sold or atleast shipped out rather than used in making another product.

The Nature and Importance of InventoriesA typical manufacturing firm carries different types of inventories, including the following:

1. Raw materials and purchased parts2. Partially completed goods, called work-in-process (WIP)3. Finished-goods inventories (manufacturing firms) or merchandise (retail stores)4. Replacement parts, tools, and supplies5. Goods-in-transit to warehouse or customers

Functions of Inventory1. To meet anticipated demand. A customer can be a person who walks in off the street

to buy a new stereo system, a mechanic who requests a tool at a tool crib, or amanufacturing operation. These inventories are referred to as anticipation stocksbecause they held to satisfy planned or expected demand.

2. To smooth production requirements. Firms that experience seasonal patterns indemand often build up inventories during off-season periods to meet overly highrequirements during certain seasonal periods. These inventories are aptly namedseasonal inventories.

3. To decouple operations. Manufacturing firms have used inventories as buffers betweensuccessive operations to maintain continuity of production that would otherwise be

disrupted by events such as breakdowns of equipment and accidents that cause aportion of the operation to shut down temporarily.

4. To protect against stock-outs. Delayed deliveries and unexpected increases in demandincrease the risk of shortages.

5. To take advantage of order cycles. To minimize purchasing and inventory costs, a firmoften buys in quantities that exceed immediate requirements. Inventory storageenables a firm to buy and produce in economic lot sizes without having to try to matchpurchases or production with demand requirements in the short run. This results inperiodic order or order cycles. The resulting stock is known as cycle stock.

6. To hedge against price increases. A firm will suspect that a substantial price increaseis about to be made and purchase larger-than-normal amounts to avoid the increase.

7. To permit operation. Take a certain amount of time means that there will generally besome work-in-process inventory.

Objectives of Inventory ControlInadequate control of inventories can result in both under- and overstocking of items.Understocking results in missed deliveries, lost sales, dissatisfied customers, and productionbottlenecks; overstocking unnecessarily ties up funds that might be more predictive elsewhere.Although overstocking may appear to be the lesser of the two evils, the price tag fro excessiveoverstocking can be staggering when inventory holding costs are high.


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Inventory management has two main concerns. On relates to the level of customer service,that is, to have the right goods, in sufficient quantities, in the right place, and at the righttime. The other relates to the costs of ordering and carrying inventories.

The overall objective of inventory management is to achieve satisfactory levels of customerservice while keeping inventory costs within reasonable bounds. The two fundamental

decisions that must be made relate to the timing and size of orders.

Requirements fro Effective Inventory Management1. A system to keep track of the inventory on hand and on order.2. A reliable forecast of demand that includes an indication of possible forecast error.3. Knowledge of leas times and lead time variability.4. Reasonable estimates of inventory holding costs, ordering costs, and shortage costs.5. A classification system for inventory items.

Inventory Counting SystemsPeriodic system. Physical count of items in inventory made at periodic intervals (weekly,monthly). Advantage is that orders for many items occur at the same time, which can result ineconomies in processing and shipping orders. Disadvantages are lack of control betweenreviews, the need to protect against shortages between review periods by carrying extra stock,and the need to make a decision on order quantities at each review.

Perpetual inventory system. System that keeps track of removals from inventorycontinuously, thus monitoring current levels of each item. Advantage of this system is thecontrol provided by the continuous monitoring of inventory withdrawals. Another is the fixed-order quantity; management can identify an economic order size. Disadvantage is the addedcost of record keeping.Two-bin systems is tow containers of inventory; reorder when the first is empty. Advantage isthere is no need to record each withdrawal from inventory; disadvantage is that the reordercard may not be turned in for a variety of reasons.

Perpetual systems can be either batch or on-line. In batch systems, inventory records arecollected periodically and entered into the system. In on-line systems, the transactions are

recorded instantaneously. The advantage of on-line systems is that they are always up-to date.In batch systems, however, a sudden surge in demand could result in reading the amount ofinventory below the reorder point between the periodic read-ins. Frequent batch collectionscan minimize that problem.

Universal Product Code. Bar code printed on a label that has information about the item towhich it is attached.

Demand Forecasts and Lead Time informationInventories are used to satisfy demand requirements, so it is essential to have reliableestimates of the amount and timing of demand. Lead time is time interval between orderingand receiving the order.

Cost InformationThree basic costs are associated with inventories:

1. Holding (carrying) cost. Cost to carry an item in inventory for a length of time, usuallya year. Costs include interest, insurance, taxes, depreciation, obsolescence,deterioration, spoilage, pilferage, breakage, and warehousing costs. Holding costs arestated in either of two ways: as a percentage of unit price or as in dollar amount perunit.

2. Ordering costs. Costs of ordering and receiving inventory. These include determininghow much is needed, preparing invoices, inspecting goods upon arrival for quality and


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quantity, and moving the goods to temporary storage. Ordering costs are generallyexpressed as a fixed dollar amount per order.

3. Shortage costs. Costs resulting when demand exceeds the supply of inventory on hand;often unrealized profit per unit. These costs can include the opportunity cost of notmaking a sale, loss of customer goodwill, late charges, and similar costs.

Classification System

A-B-C approach. Classifying inventory according to some measure of importance, andallocating control efforts accordingly. Three classes used; A (very important), B (moderatelyimportant), and C (least important). Another application of the A-B-C concept is a guide tocycle counting. Cycle counting is a physical count of items in inventory. The purpose of cyclecounting is to reduce discrepancies between the amounts indicated by inventory records andthe actual quantities of inventory on hand.The American Production and Inventory Control Society (APICS) recommend the followingguidelines for inventory record accuracy: +0.2 percent for A items, +1 percent for B items, and+5 percent for C items.

How Much to Order: Economic Order Quantity ModelsEconomic order quantity. The order size that minimizes total cost. Three ordered sizemodels are described:

1. The economic order quantity model.2. The economic order quantity model with noninstantaneous delivery.3. The quantity discount model.

Basic Economic Order Quantity (EOQ) ModelThe basic EOQ model is the simplest of the three models. It is used to identify the order sizethat will minimize the sum of the annual costs of holding inventory and ordering inventory.Assumptions:

1. Only one product is involved.2. Annual demand requirements are known.3. Demand is spread evenly throughout the year so that the demand rate is reasonably

constant.

4. Lead time does not vary.5. Each order is received in a single delivery.6. There are no quantity discounts.

Annually carrying cost is computed by multiplying the average amount of inventory on hand bythe cost to carry one unit for one year, even though any given unit would not be held for ayear.

Annual carrying cost = (Q/2)HAnnual ordering cost is a function of the number of orders per year and the ordering cost perorder:

Annual ordering cost = (D/Q)SWhere S ordering cost

The total annual cost associated with carrying and ordering inventory when Q units are orderedeach time is:

TC = Annual carrying cost + Annual ordering cost

An expression for the optimal order quantity, Qo can be obtained:Qo = 2DS/H

The length of an orderLength of order cycle = Qo /D


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EOQ with Non instantaneous ReplenishmentThe basic EOQ model assumes that each order is delivered at a single point in time(instantaneous replenishment).Total cost

TCmin = (Imax/2) + (D/Qo)SWhere

Imax Maximum Inventory

The economic run quantity isQ0 = 2DS/H x p/p u

Wherep production or delivery rateu usage rate

The maximum and average inventory levelsImax = (Qo/p)(p u) and Iaverage = Imax/2

The cycle time for the economic run size is a function of the run size and usage rateCycle time = Qo/u

The run time is a function of the run size and the production rateRun time = Qo/p

Quantity discountsQuantity discounts. Price reductions for large orders.

TC = (Q/2)H + (D/Q)S + PDWhere PD unit priceThe objective of the quantity discount model is identify an order quantity that will representthe lowest total cost for the entire set of curves.

The procedure for determining the overall EOQ differ slightly, depending on which of these twocases is relevant. For carrying costs that are constant, the procedure is as follows:

1. Compute the common EOQ.2. Only one of the unit prices will have the EOQ in its feasible range since the ranges do

not overlap. Identify that range.a. If the feasible EOQ is on the lowest price range, that is the optimal order

quantity.b. If the feasible EOQ is in any other range, compute the total cost for the EOQ

and for the price breaks of all lower unit costs. Compare the total costs; thequantity that yields the lowest total cost is the optimal order quantity.

When carrying costs are expressed as a percentage of price, determine the best purchasequantity with the following procedure:

1. Beginning with the lowest price, compute the EOQs for each price range until a feasibleEOQ is found.

2. If the EOQ for the lowest price is feasible, it is the optimal order quantity. If the EOQ

is not the lowest price range, compare the total cost at the price break for all lowerprices with the total cost of the largest feasible EOQ. The quantity that yields thelowest total cost is the optimum.

When to Reorder with EOQ OrderingReorder point (ROP). When the quantity on hand of an item drops to this amount, the item isreordered.


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The basic concern of the manager is to place an order when the amount of inventory on hand issufficient to satisfy demand during the time it takes to receive that order. There are fourdeterminants of the reorder point quantity:

1. The rate of demand2. The length of lead time3. The extent of demand and/or lead time variability

4. The degree of stock-out risk acceptable to management

ROP = d x LTWhered demand per day or weekLT lead time in days or weeks

Safety stock. Stock that is held in excess of expected demand due to variable demand rateand/or lead time.

ROP = Expected demand during lead time + Safety stockService level. Probability that demand will not exceed supply during lead time.

Service level = 100 percent Stock-out risk

The amount of safety stock that is appropriate for a given situation depends on the followingfactors:

1. the average demand rate and average lead time2. demand and lead time variability3. desired service level

Several models will be described that can be used in cases when variability is present. Thefirst model can be used if an estimate of expected demand during lead time and its standarddeviation are available.

ROP = expected demand during lead time + zdLTWherez number of standard deviationsdLT the standard deviation of lead time demand

Shortages and Service LevelsThe ROP computation does not reveal the expected amount of shortage for a given lead timeservice level.

E(n) = E(z) dLTWhereE(n) expected number of units short per order cycleE(z) standardized number of units short obtaineddLT standard deviation of lead time demand

Having determined the expected number of units short for an order cycle, determine theexpected number of units short per year. It is simply the expected number of units short per

cycle multiplied by the number per year.E(N) = E(n) D/Q

WhreE(N) expected number of units short per year

The annual service level and the lead time service level can be related using the followingformula:

SLannual= 1 [E(N)/D]


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SLannual= 1 [E(z) dLT /Q]

How Much to Order: Fixed-Order-Interval ModelFixed-order-interval model. Order are placed at fixed time intervals.

There are number of differences between these two approaches to reordering. Both aresensitive to demand to demand experience just prior to reordering, but in somewhat differentways. In the fixed-quantity model, a higher than normal demand causes a shorter timebetween orders, whereas in the fixed interval model, the result is a large order size. Anotherdifference is that the fixed quantity model requires close monitoring of inventory levels inorder to know when the amount on hand has reached the reorder point. The fixed-intervalmodel requires only a periodic review of inventory levels just prior to placing an order todetermine how much is needed.

Reasons for Using the Fixed Order Interval ModelUnder certain conditions, the use of fixed order intervals is very practical. The alternative forthem is to use fixed interval ordering, which requires only periodic checks of inventory levels.

Determining the Amount to OrderIf both the demand rate and lead time are constant, the fixed interval model and the fixedquantity model function identically. The differences in the two models become apparent onlywhen examined under conditions of variability.In the fixed quantity arrangement, orders are triggered by a quantity while in the fixed intervalarrangement orders are triggered in time. Therefore, the fixed interval system must havestock out protection for lead time plus the next order cycle, but the fixed quantity systemneeds protection only during lead time since additional orders can be placed at any time andwill be received shortly thereafter.Order size in the fixed interval model is determined by the following computation:

Amount to order = Expected demand during protection interval + Safety stock Amount onhand at reorder time

Benefits and Disadvantages

The fixed interval system results in the tight control needed for A items in an ABC classificationdue to the periodic reviews it requires. In addition, when two or more items come from thesame supplier, grouping orders can yield savings in ordering, packing, and shipping costs.Moreover, it may be the only practical approach if inventory withdrawals cannot be closelymonitored.On the negative side, the fixed interval system necessitates a larger amount of safety stock fora given risk of stock out because of the need to protect against shortages during an entireorder interval plus lead time, and this increases the carrying cost. Also, there are the costs ofthe periodic reviews

Single-period model. Model ordering of perishables and other items with limited useful lives.Analysis of single-period situations generally focuses on two costs:Shortage cost. May include a charge a loss of customer goodwill as well as the opportunity cost

of lost sales.Cs = Revenue per unit Cost per unit

Excess cost. Difference between purchase cost and salvage value of items left over at the endof a period.

Ce = original cost per unit salvage value per unitThe goal of the single-period model is to identify the order quantity, or stocking level, that willminimize the long run excess cost per unit.


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There are two general categories of problems that we will consider: those for which demandcan be approximated using a continuous distribution and those for which demand can beapproximated using a discrete distribution.

Continuous Stocking LevelsThe concept of identifying an optimal stocking level is perhaps easiest to visualize when

demand is uniform. Choosing the stocking level is similar to balancing a seesaw, but instead ofa person on each end of the seesaw, we have excess cost per unit (C e) on one end of thedistribution and shortage cost per unit (Cs) on the other. The optimal stocking level isanalogous to the fulcrum of the seesaw; the stocking level equalizes the cost weights.

The service level is the probability that demand will not exceed the stocking level, andcomputation of the service level is the key to determining the optimal stocking

Service level = Cs/(Cs+ Cs)WhereCs Shortage cost per unitCe Excess cost per unit

Discrete Stocking LevelsWhen stocking levels are discrete rather than continuous, the service lead computed using theratio Cs/(Cs + Ce) usually does not coincide with a feasible stocking level. The solution is tostock at the next higher level. In other words, choose the stocking level so that the desiredservice level is equaled ore exceeded.

One final point about discrete stocking levels: If the computed service level is exactly equal tothe cumulative probability associated with one of the stocking levels, there are two equivalentstocking levels in terms of minimizing long-run cost the one with equal probability and thenext higher one.

OPERATIONS STRATEGYInventories are a necessary part of doing business, but having too much inventory is not good.One reason is that inventories tend to hide problems; they make it easier to live with

problems rather than eliminate them. Another reason is that inventories are costly tomaintain. Consequently, a wise operation strategy is to work toward cutting back inventoriesby (1) reducing lot size and (2) reducing safety stocks.

Japanese manufacturers use smaller lot sizes than their Western counterparts because theyhave a different perspective on inventory carrying costs. In addition to the usual components,the Japanese recognize the opportunity costs of disrupting the work flow, inability to placemachines and workers closer together, and hiding problems related to product quality andequipment breakdown. When these are factored in, carrying costs become higher perhapsmuch higher than before.

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Chapter 11 - Inventory Management.doc