Inventory Control Models

Transcription

1 Chapter 6 Inventory Control Models To accompany uantitative Analysis for Management, Eleventh Edition, by Render, Stair, and Hanna Power Point slides created by Brian Peterson

2 Introduction Inventory is an expensive and important asset to many companies. Inventory is any stored resource used to satisfy a current or future need. Common examples are raw materials, workin-process, and finished goods. Most companies try to balance high and low inventory levels with cost minimization as a goal. Lower inventory levels can reduce costs. Low inventory levels may result in stockouts and dissatisfied customers. Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-2

3 Introduction All organizations have some type of inventory control system. Inventory planning helps determine what goods and/or services need to be produced. Inventory planning helps determine whether the organization produces the goods or services or whether they are purchased from another organization. Inventory planning also involves demand forecasting. Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-3

4 Introduction Inventory planning and control Planning on What Inventory to Stock and How to Acquire It Forecasting Parts/Product Demand Controlling Inventory Levels Feedback Measurements to Revise Plans and Forecasts Figure 6.1 Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-4

5 Inventory Decisions There are two fundamental decisions in controlling inventory: How much to order. When to order. The major objective is to minimize total inventory costs. Common inventory costs are: Cost of the items (purchase or material cost). Cost of ordering. Cost of carrying, or holding, inventory. Cost of stockouts. Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-5

6 Economic Order uantity The economic order quantity (EO) model is one of the oldest and most commonly known inventory control techniques. It is easy to use but has a number of important assumptions. Objective is to minimize total cost of inventory. Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-6

7 Inventory Usage Over Time Inventory Level Order uantity = = Maximum Inventory Level Minimum Inventory Figure Time Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-7

8 Inventory Costs in the EO Situation Computing Average Inventory Average inventory level 2 Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-8

9 Inventory Costs in the EO Situation Mathematical equations can be developed using: = number of pieces to order EO = * = optimal number of pieces to order D = annual demand in units for the inventory item C o = ordering cost of each order C h = holding or carrying cost per unit per year Annual ordering cost Number of orders placed per year Ordering cost per order D C o Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-9

10 Inventory Costs in the EO Situation Mathematical equations can be developed using: = number of pieces to order EO = * = optimal number of pieces to order D = annual demand in units for the inventory item C o = ordering cost of each order C h = holding or carrying cost per unit per year Annual holding cost Average inventory Carrying cost per unit per year 2 C h Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-10

11 Inventory Costs in the EO Situation Total Cost as a Function of Order uantity Cost Minimum Total Cost Curve of Total Cost of Carrying and Ordering Carrying Cost Curve Ordering Cost Curve Figure 6.3 Optimal Order uantity Order uantity Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-11

12 Finding the EO According to the graph, when the EO assumptions are met, total cost is minimized when annual ordering cost equals annual holding cost. Solving for 2DC C D C 2DC h 2DC C o h 2 o C h 2 o C h o Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall EO *

13 Economic Order uantity (EO) Model Summary of equations: Annual ordering cost Annual holdingcost D 2 C o C h EO * 2DC C h o Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-13

14 Sumco Pump Company Sumco Pump Company sells pump housings to other companies. The firm would like to reduce inventory costs by finding optimal order quantity. Annual demand = 1,000 units Ordering cost = $10 per order Average carrying cost per unit per year = $0.50 * 2DCo 2( 1000, )( 10) 40, 000 C h 200 units Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-14

15 Sumco Pump Company Total annual cost = Order cost + Holding cost TC D C 2 o C h 1000, ( 10) $ 50 $ 50 $ 100 ( 0. 5) Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-15

16 Purchase Cost of Inventory Items Total inventory cost can be written to include the cost of purchased items. Given the EO assumptions, the annual purchase cost is constant at D C no matter the order policy, where C is the purchase cost per unit. D is the annual demand in units. At times it may be useful to know the average dollar level of inventory: Average dollar level (C) 2 Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-16

17 Purchase Cost of Inventory Items Inventory carrying cost is often expressed as an annual percentage of the unit cost or price of the inventory. This requires a new variable. I Annual inventory holding charge as a percentage of unit price or cost The cost of storing inventory for one year is then C h IC thus, * 2DC IC o Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-17

18 Reorder Point: Determining When To Order Once the order quantity is determined, the next decision is when to order. The time between placing an order and its receipt is called the lead time (L) or delivery time. When to order is generally expressed as a reorder point (ROP). ROP Demand per day Lead time for a new order in days d L Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-18

19 Procomp s Computer Chips Demand for the computer chip is 8,000 per year. Daily demand is 40 units. Delivery takes three working days. ROP d L 40 units per day 3 days 120 units An order based on the EO calculation is placed when the inventory reaches 120 units. The order arrives 3 days later just as the inventory is depleted. Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-19

20 Reorder Point Graphs Figure 6.4 Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-20

21 uantity Discount Models uantity discounts are commonly available. The basic EO model is adjusted by adding in the purchase or materials cost. Total cost Material cost + Ordering cost + Holding cost where Total cost DC D C 2 o C h D annual demand in units C o ordering cost of each order C cost per unit C h holding or carrying cost per unit per year Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-21

22 uantity Discount Models uantity Because discounts unit are cost commonly is now variable, available. The basic EO model is adjusted by adding in the Holding cost C purchase or materials cost. h IC I holding cost as a percentage of the unit cost (C) Total cost Material cost + Ordering cost + Holding cost where Total cost DC D C 2 o C h D annual demand in units C o ordering cost of each order C cost per unit C h holding or carrying cost per unit per year Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-22

23 uantity Discount Models A typical quantity discount schedule can look like the table below. However, buying at the lowest unit cost is not always the best choice. DISCOUNT NUMBER DISCOUNT UANTITY DISCOUNT (%) DISCOUNT COST ($) 1 0 to ,000 to 1, ,000 and over Table 6.3 Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-23

24 Brass Department Store Brass Department Store stocks toy race cars. Their supplier has given them the quantity discount schedule shown in Table 6.3. Annual demand is 5,000 cars, ordering cost is $49, and holding cost is 20% of the cost of the car The first step is to compute EO values for each discount. EO EO EO ( 2)( 5, 000)( 49) ( 0. 2)( 5. 00) 1 ( 2)( 5, 000)( 49) ( 0. 2)( 4. 80) 2 ( 2)( 5, 000)( 49) ( 0. 2)( 4. 75) cars per 714 cars per 718 cars per order order order Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-24

25 Brass Department Store Example The second step is adjust quantities below the allowable discount range. The EO for discount 1 is allowable. The EOs for discounts 2 and 3 are outside the allowable range and have to be adjusted to the smallest quantity possible to purchase and receive the discount: , ,000 Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-25

26 Brass Department Store The third step is to compute the total cost for each quantity. DISCOUNT NUMBER UNIT PRICE (C) ORDER UANTITY () ANNUAL MATERIAL COST ($) = DC ANNUAL ORDERING COST ($) = (D/)C o ANNUAL CARRYING COST ($) = (/2)C h TOTAL ($) 1 $ , , ,000 24, , ,000 23, , The final step is to choose the alternative with the lowest total cost. Table 6.4 Copyright 2012 Pearson Education, Inc. publishing as Prentice Hall 6-26