Purchasing and Supply Chain Managementby W.C. Benton

Chapter FiveInventory Management

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Learning Objectives1. To learn the relationship between the purchasing

function and inventory control.

2. To learn the primary reasons for holding inventory.

3. To identify the necessary requirements for effective inventory management.

4. To learn about ABC analysis.

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Learning Objectives5. To identify the cost components of the classical

EOQ model.

6. To learn the basic assumptions of the EOQ model.

7. To learn about quantity discounts.

8. To learn about service levels.

9. To identify the differences between fixed-order-quantity and variable-order inventory systems.

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Purchasing Raw Materials and Component Parts

• The purchasing function is taking on increasing importance in today’s industrial economy.

• Since materials constitute the largest single

percentage of their purchasing dollars, profit oriented firms have turned to professionally operated purchasing departments to make sure they are getting full value for their outlays on materials

• The purchasing professional must be able to make profitable buying decisions under these conditions. The purchasing professional person must make profitable inventory management decisions.

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Inventory Management• Inventory is the life blood of any business. Most firms

store thousands of different items. • The type of business a firm is in will usually

determine how much of the firm’s assets are invested in inventories.

• Hospitals carry beds, surgical instruments, food, pharmaceuticals, and other miscellaneous items.

• Manufacturing firms carry office supplies, raw materials, component parts, finished products, and many other industry-related items.

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Dependent Versus Independent Demand

• In order to manage the various types of inventory, attributes of the items first must be analyzed in terms of cost, lead time, past usage, and the nature of demand.

• The nature of demand is perhaps the most important attribute. The nature of demand can be either independent or dependent.

• Independent demand is unrelated to the demand for other items. In other words, an independent item must be forecasted independently.

• Dependent demand is directly derived from demand for another inventoried item demand

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Dependent Versus Independent Demand

• In order to manage the various types of inventory, attributes of the items first must be analyzed in terms of cost, lead time, past usage, and the nature of demand.

• The nature of demand is perhaps the most important attribute. The nature of demand can be either independent or dependent.

• Independent demand is unrelated to the demand for other items. In other words, an independent item must be forecasted independently. Dependent demand is directly derived from demand for another inventoried item demand.

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Inventory Management Overview

• Management of inventories is a major interest of purchasing managers.

• In many industries, the investment in inventories comprises a substantial share of the firm’s assets.

• If the productivity of the inventory asset can be enhanced, the improvement will go directly to the bottom line.

• How does the purchasing professional know how much inventory to carry?

• How does the purchasing professional know when to place a replenishment order?

• Specifically, what guidelines should be used for making purchasing decisions?

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Inventory Decisions

• In the area of inventory management, the purchasing professional should make explicit decisions regarding the following:

1. What to stock. The purchasing professional, at the very minimum, must meet the requirements and needs of the manufacturer on distribution operation.

2. How much to invest. The purchasing professional must first review the level of capital support for inventory. This decision is usually made at the vice president level.

3. How much service to offer. What level of protection against stockouts is acceptable for the competitive environment? It is impossible to achieve a service level of 100 percent

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Inventory Decisions

• As can be seen, none of these decisions is independent of the other. Moreover, combining these decisions is complex and may be closely correlated with the industry and the type of firm within the industry.

• In the case of a manufacturing firm, you must consider whether the production process is make to order, make to stock, or some hybrid of the two.

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Production Processing Strategy

• In this section, the production processing strategy is divided into two categories:

1. continuous systems 2. intermittent systems

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Production-Inventory Taxonomy• The taxonomy is based on continuous systems producing

standardized products through an assembly line, while intermittent systems are used to produce non standardized products through a job shop.

• Another subcategory (not shown in the taxonomy) associated with continuous systems is pure inventory systems.

• Pure inventory systems are distribution stocking points, such as warehouses or distributors.

• The purchasing manager must have a clear understanding of the role of inventory in the materials management system.

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ABC Classification of Inventory Items

• The inventory items that are the most important for a specific industry or firm should be items that account for the greatest dollar value.

• To determine the usage value of an item, multiply the unit cost by annual sales volume. If a particular item costs $100 and 150 are sold in one year, then its usage value is $100 × 150, or $15,000.

• With only these two data points (sales and costs), you can not only rank all of your inventory items by importance, but also take the first step toward controlling independent demand and distribution inventories.

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ABC Classification of Inventory Items

• If you analyze what sells the most and what cost the most, a predictable pattern will emerge with most distribution inventories.

1. Certain items are demanded by a great many customers.

2. Most items are only demanded by certain customers.

3. Some items are demanded by few customers.

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• The following procedure is one way of implementing an ABC analysis.

1. Calculate the annual dollar value for each item.

2. List all items in descending order.

3. Develop a cumulative percentage of the items that reflect roughly 60–80 percent of the total cost.

4. Determine the percentage of the items that represent roughly 60–80 percent of the total cost. These are considered A items.

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Independent Demand• In this section, we are concerned with the control

of end items. The inventory management concepts covered in this section are also applicable to retailing and distribution.

There are five primary functions of inventories:1. Pipeline inventory. The supply pipelines of the entire

system require a considerable investment in inventory. If the system’s volume is 1,000 units per week and it takes one day to transport from the supplier to the plant, there are 1/7 × 1,000, or about 143, units in transit on the average.

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Independent Demand2. Cycle stocks. When units are transported from one

location point to another, how many units do we transport at one time? For example, say we place an order once each three weeks following a review of sales and projected needs.

1. Once the order is received, there is a two-day order processing delay at the suppliers plus three days for transit and receipt. Assume that the average unit sales volume is five units per week or 15 units in the three-week order period.

1. Thus, the buyer must have no less than 15 units of cycle stock on hand when an order is placed, for an average cycle stock level of 15/2 = 7.5 units.

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Independent Demand

3. Seasonal inventories. If demand follows a seasonal pattern, inventories can be accumulated during low sales periods and depleted during high usage periods to avoid problems associated with adjusting capacity.

4. Safety stocks. Safety stocks are designed to absorb random demand uncertainties.

5. Decoupling. Stocks of inventories at major stocking points throughout the system make it possible to carry on each activity independently. That is, the presence of inventories allows for each work center to begin at the same starting time.

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Costs in an Inventory System• The objective of an inventory

system is the minimization of total operating costs. The unavoidable costs of operating pure inventory systems are ordering costs, stockout costs, and holding costs.

• To illustrate the cost behavior of a fixed-order-size system, let’s look at the simple classical economic lot size model (EOQ). The EOQ derives the optimal lot size for purchasing by minimizing the cost components involved (ordering costs and holding cost).

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The EOQ Model

• Once the most economical order quantity is known, several other measures can be taken:

1. The expected number of orders during the year, NO = A/Q

1. The expected time between orders, TBO = 1/NO = Q/A

1. The reorder point, R = (A/12) * L, where L is expressed in months. If L is expressed in weeks, R = (A/52) * L.

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The EOQ Model• The minimum total cost per year is obtained by

substituting Q* for Q in equation (1). The classical EOQ model assumes the following:

1. Constant demand.2. Constant lead time.3. Constant unit price.4. Fixed order cost per order.5. Fixed holding cost per unit.6. Instantaneous replenishment.7. No stockouts allowed.8. No demand uncertainty.9. Quantity discounts are not available

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Quantity Discounts

• From time to time, buying firms receive discounted price schedules from their suppliers.

• This usually means that the price per unit is lower if larger orders are purchased. It may or may not be to the buyer’s advantage to accept the quantity discount.

• The buyer must be careful not to compromise the economies of his or her firm’s cost structure.

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Quantity Discounts

• The classical EOQ model assumes that the per-unit material price is fixed. The quantity discount condition invalidates the total cost curve.

• Quantity discounts induce a discontinuous total cost curve.

• Assuming the discount applies to all units (and not just in incremental units beyond the discount point), the minimum total cost point will be either at the point of discontinuity or at the traditional EOQ point compared with the original price.

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Quantity Discounts• A five-step method can easily be used for determining the

minimum cost order quantity:

1. Calculate the economic order quantity using the minimum unit prices. If this quantity falls within the range for which the vendor offers the discount price, it is a valid economic order quantity and will result in the minimum cost for the particular item.

1. If the EOQ calculated in step 1 is not valid (i.e., is less than the break quantity), find the total annual cost for each price break quantity.

1. Calculate an EOQ for each unit price.

1. Calculate the total annual cost for each valid EOQ determined in step 3.

1. The minimum cost order quantity is that associated with the lowest cost in either step 2 or step 4.

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Safety Stock• When there is uncertainty in demand, safety stock must be

considered. Safety stocks are extra inventory held to protect against randomness in demand or lead time.

• Safety stock is needed to cover the demand during the replenishment lead time in case actual demand is greater than expected demand.

---------------------------------------------------------------------------• The safety stock adjusted reorder point is• ROP = (Expected demand during lead time) + (Safety stock)• = DDLT + Z√(Lead time expressed as some multiple of forecast

interval) * (Standard deviation of demand)• = DDLT + Z√L * σd

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Dependent Demand Systems• Order-point (statistical inventory control) techniques are

based on the assumption of uniform requirements per unit time. If this assumption of the demands is unrealistic, these techniques can lead to inappropriate inventory decisions.

• For components of assembled products, the demands are not usually constant per unit time, and depletion is anything but gradual. Inventory depletion for component parts tends to occur in discrete “lumps”

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Dependent Demand Systems• Customer demand is fairly uniform but, because of

the build schedules, the requirements for the components are “lumpy.”

• The build schedule shows periods of zero requirements before a requirement of 50 component parts is encountered.

• This requirement sequence, very common to component parts, is not handled well with traditional non-time-phased order-point techniques.

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Dependent Demand Systems• MRP systems utilize substantially better information

on future requirements than is possible by the traditional non-time-phased order-point system.

• MRP systems are helpful for companies with assembled products that have component requirements dependent on the final product.

• The system provides information to better determine the quantity and timing of component parts and purchase orders than is possible with the non-time-phased order-point system.

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The Material Requirements Concept

• The MRP concept provides the basis for projecting future inventories in a manufacturing operation.

• MRP can help improve the traditional non-time-phased order-point system because it allows the operating manager to plan requirements (raw material, component parts) to meet the final assembly schedule.

• That is, MRP provides a plan for component and subassembly availability that allows certain end products to be scheduled for final assembly in the future.

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The General Lot-Sizing Problem• The general lot-sizing problem for time-phased requirements

for a component part involves converting the requirements over the planning horizon (the number of periods into the future for which there are requirements) into planned orders by batching the requirements into lots.

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Quantity Discounts for the Variable Demand Case

• It has been shown in the previous section that MRP provides time-phased requirements to determine planned orders using lot-sizing procedures.

• The general lot-sizing problem is to batch requirements to minimize the sum of ordering and carrying cost each time an order is to be placed.

• Up until now, conditions for quantity discounts have not been discussed.

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Quantity Discounts for the Variable Demand Case

• The safety stock should be set to achieve a prespecified service level. Setting safety stock so as to achieve a prespecified service level enables fair comparison of the alternative lot-sizing procedures. The service level, S, is defined as

• S = (The number of units required that were in inventory)/(The number of units required)

• If a discount is available, there is a price differential (lower price) for ordering an increased number of units. In this chapter, the discount applies to all units provided an amount at least as big as the discount quantity is purchased.

• In situations where discounts are not available, the price per unit is constant regardless of the number of units ordered.

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Illustration of Various Variable-demand Lot-sizing Models

• There has been a significant amount of attention given to the variable-demand order size lot-sizing problem.

• Both developmental and comparative literature will be discussed in this section.

• Among the better-known lot-sizing methods for the single item, nondiscount, time-phased, certain-demand models are(1) lot for lot, (2) economic order quantity,(3) periodic order quantity, (4) least unit cost,(5) McLaren’s order moment, (6) Silver-Meal, and(7) the Wagner-Whitin dynamic programming algorithm.

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