Chapter 6 Inventory Control Models 6-1 To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-1

Chapter Learning Objectives Students will be able to: Understand the importance of inventory control. Use the economic order quantity (EOQ) to determine how much to order. Compute the reorder point (ROP) in determining when to order more inventory. Perform sensitivity analysis on basic inventory quantities. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-2

Chapter Learning Objectives continued Students will be able to: Determine the economic order quantity without the instantaneous receipt assumption. Handle inventory problems that allow quantity discounts or have planned shortages. Understand the use of safety stock with known and unknown stockout costs. Perform ABC analysis. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-3

Chapter Outline 6.1 Introduction 6.2 Importance of Inventory Control 6.3 Inventory Decision 6.4 Economic Order Quantity(EOQ): Determining How Much to Order 6.5 Reorder Point: Determining When to Order To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-4

Chapter Outline - continued 6.6 EOQ without the Instantaneous Receipt Assumption 6.7 Quantity Discount Models 6.8 Use of Safety Stock 6.9 ABC Analysis 6.10 Sensitivity Analysis To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-5

Inventory as an Important Asset Inventory can be the most expensive and the most important asset for an organization Inventory 40% Other Assets 60% Inventory as a percentage of total assets To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-6

Inventory Planning and Control - Fig. 6.1 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 To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-7

The Inventory Process Suppliers Customers Finished Goods Raw Materials Work in Process Fabrication and Assembly Inventory Storage Inventory Processing To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-8

Importance of Inventory Control Five Functions of Inventory Decoupling Storing resources Adapting to irregular supply and demand Enabling the company to take advantage of quantity discounts Avoiding stockouts and shortages To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-9

wish to minimize total inventory cost Inventory Decisions How much to order When to order wish to minimize total inventory cost To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-10

Inventory Costs Cost of the items Cost of ordering Cost of carrying, or holding inventory Cost of safety stock Cost of stockouts To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-11

Ordering Costs Developing and sending purchase orders Processing and inspecting incoming inventory Bill paying Inventory inquiries Utilities, phone bills, etc., - purchasing department. Salaries/wages - purchasing department employees Supplies (e.g., forms and paper) - purchasing department To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-12

Carrying Costs Cost of capital Taxes Insurance Spoilage Theft Obsolescence Salaries/wages - warehouse employees Utilities/building costs - warehouse Supplies (e.g., forms, paper) - warehouse To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-13

Inventory Usage Over Time - Fig. 6.2 To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-14

Costs as Functions of Order Quantity - Fig. 6.3 Annual Cost Order Quantity Q* Total Cost Curve Carrying (holding) Cost Curve Ordering (set-up) Minimum To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-15

Costs as Functions of Order Quantity - Fig. 6.3 Total Cost Minimum Cost Carry Cost Order Cost Optimal Quantity To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-16

Steps in Finding the Optimum Inventory Develop an expression for the ordering cost. Develop and expression for the carrying cost. Set the ordering cost equal to the carrying cost. Solve this equation for the optimum desired. To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-17

EOQ : Basic Assumptions Demand is known and constant Lead time is known and constant Receipt of inventory is instantaneous Quantity discounts are not possible The only variable costs are the cost of setting up or placing an order, and the cost of holding or storing inventory over time Stockouts can be completely avoided if orders are placed at the appropriate time To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-18

Developing the EOQ Annual ordering cost: Annual holding or carrying cost: Total inventory cost: To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-19

EOQ 2 DC IP Per Unit Carrying Cost: 2DC * = Q C h Percentage Carrying Cost: IP DC 2 To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-20

Inputs and Outputs of the EOQ Model Models Input Values Output Values Annual Demand (D) Ordering Cost (Co) Carrying Cost (Ch) Lead Time (L) Demand Per Day (d) Economic Order Quantity (EOQ) Reorder Point (ROP) To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-21

The Reorder Point (ROP) Curve - Fig. 6.4 ROP = (Demand per day) x (Lead time for a new order, in days) = d x L Inventory Level (Units) Q* ROP (Units) Slope = Units/Day = d Lead Time (Days) L To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-22

Inventory Control and the Production Process Portion of Cycle Maximum Inventory Level Inventory Level Demand Portion of Cycle Demand Portion of Cycle Time To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-23

Production Quantity EOQ Annual Carrying Cost: Annual Ordering Cost: Setup Cost: Ordering Costs: To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-24

Production Quantity EOQ To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-25

Quantity Discount Models - Fig. 6.6 To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-26

Quantity Discount Steps 1. Calculate Q for each discount 2. Adjust Q upward if quantity is too low for discount 3. Compute total cost for each discount 4. Select Q with the the lowest total cost To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-27

The Use of Safety Stock Fig. 6.7 Inventory on Hand Stockout Time is avoided Safety Stock To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-28

The Use of Safety Stock Known stockout costs: Unknown stockout costs: Given probability of demand, find total cost for each safety stock alternative Unknown stockout costs: Set service level; use normal distribution To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-29

Service Level versus Carrying Costs To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-30

Summary of ABC Analysis Table 6.6 Group A Items - Critical Group B Items - Important Group C Items - Not That Important Inventory Group Dollar Usage (%) Items (%) Are Complex Quantitative Control Techniques Used? A B C 70 20 10 Yes In some cases No To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-31

ABC Inventory Analysis 100 90 80 70 60 50 40 30 20 10 Percent of Inventory Items Percent of Annual Dollar Usage 1 2 3 4 5 6 7 8 9 10 A Items B Items C Items To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-32

ABC Inventory Policies Greater expenditure on supplier development for A items than for B items or C items Tighter physical control on A items than on B items or on C items Greater expenditure on forecasting A items than on B items or on C items To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-33