To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Chapter 6 Inventory Control Models

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-2 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 6-3 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 6-4 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 6-5 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 6-6 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Inventory as an Important Asset Inventory can be the most expensive and the most important asset for an organization Other Assets 60% Inventory 40% Inventory as a percentage of total assets

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-7 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 6-8 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ The Inventory Process SuppliersCustomers 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 6-9 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 6-10 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 6-11 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 6-12 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 6-13 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 6-14 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Inventory Usage Over Time - Fig. 6.2

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-15 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Costs as Functions of Order Quantity - Fig. 6.3 Annual Cost Order QuantityQ*Q* Total Cost Curve Carrying (holding) Cost Curve Ordering (set-up) Cost Curve Minimum Cost

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-16 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Costs as Functions of Order Quantity - Fig. 6.3 Order Cost Carry Cost Total Cost Optimal Quantity Minimum Cost

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-17 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 6-18 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 6-19 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Annual ordering cost: Annual holding or carrying cost: Total inventory cost: Developing the EOQ

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-20 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ EOQ h C 2DC * Q  Per Unit Carrying Cost: Percentage Carrying Cost: IP DC Q *    0

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-21 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Inputs and Outputs of the EOQ Model EOQ Models Input ValuesOutput Values Annual Demand (D) Ordering Cost (C o ) Carrying Cost (C h ) 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 6-22 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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*Q* ROP (Units) Slope = Units/Day = d Lead Time (Days) L

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-23 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Inventory Control and the Production Process Inventory Level Demand Portion of Cycle Demand Portion of Cycle Maximum Inventory Level Time Production Portion of Cycle

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-24 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Production Quantity EOQ Annual Carrying Cost: Annual Ordering Cost: Setup Cost: Ordering Costs:

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-25 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Production Quantity EOQ

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-26 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Quantity Discount Models - Fig. 6.6

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-27 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 6-28 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ The Use of Safety Stock Fig. 6.7 Inventory on Hand Inventory on Hand Stockout Time Stockout is avoided Time Safety Stock

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-29 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ The Use of Safety Stock Known 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 6-30 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Service Level versus Carrying Costs

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-31 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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 (%) Inventory Items (%) Are Complex Quantitative Control Techniques Used? ABCABC Yes In some cases No

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-32 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ ABC Inventory Analysis Percent of Inventory Items Percent of Annual Dollar Usage A Items B Items C Items

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna 6-33 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ 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