1 Operations Management Inventory Management

2 The Functions of Inventory To have a stock of goods that will provide a “selection” for customers To take advantage of quantity discounts To hedge against inflation and upward price changes

3 Higher costs Item cost (if purchased) Ordering (or setup) cost Costs of forms, clerks’ wages etc. Holding (or carrying) cost Building lease, insurance, taxes etc. Difficult to control Hides production problems Disadvantages of Inventory

4 Types of Inventory Raw material Work-in-process (WIP) Maintenance/repair/operating supplies (MRO) Finished goods

5 Inventory Management Two ingredients of inventory mgmt systems Classification of inventory items Basis for establishing inventory policies Maintenance of accurate inventory records

6 ABC Analysis Divides on-hand inventory into 3 classes A class, B class, C class Basis is usually annual $ volume $ volume = Annual demand x Unit cost A (70%-80% of total annual $ volume); B (15- 25%), C (5%) Other criteria could include Delivery problems Quality problems High unit cost

7 Classifying Items as ABC % of Inventory Items % Annual $ UsageA B C Class% $ Vol% Items A8015 B 30 C 555

8 ABC Analysis Policies then established for each class after analysis Policies based on ABC analysis could include Focus more on development of class A suppliers Have tighter physical control of A items Forecast A items more carefully

9 Independent versus Dependent Demand Independent demand - demand for item is independent of demand for any other item Demand for cars is independent of demand for TV’s Dependent demand - demand for item is dependent upon the demand for some other item Demand for car tires is dependent on demand for cars

10 Inventory Costs Holding costs - associated with holding or “carrying” inventory over time Ordering costs - associated with costs of placing order and receiving goods Setup costs - cost to prepare a machine or process for manufacturing an order

11 Inventory Models When to order and how much to order Fixed order-quantity models Economic order quantity Production order quantity Quantity discount Probabilistic models

12 EOQ Assumptions Known, constant and independent demand Known and constant lead time Instantaneous and complete receipt of material No quantity discounts Only order (setup) cost and holding cost considered

13 Inventory Usage Over Time Time Inventory Level Average Inventory (Q*/2) 0 Minimum inventory Order quantity = Q (maximum inventory level) Usage Rate

14 EOQ Model How Much to Order? Order quantity Annual Cost Holding Cost Curve Total Cost Curve Order (Setup) Cost Curve Optimal Order Quantity (Q*) Minimum total cost

15 Deriving an EOQ 1. Develop an expression for setup or ordering costs 2. Develop an expression for holding cost 3. Set setup cost equal to holding cost 4. Solve the resulting equation for the best order quantity

16 EOQ Model When To Order Reorder Point (ROP) Time Inventory Level Average Inventory (Q*/2) Lead Time Optimal Order Quantity (Q*)

17 The Reorder Point (ROP) Curve Q* ROP (Units) Slope = units/day = d Lead time = L Time (days) Inventory level (units)

18 Production Order Quantity Model Answers how much to order and when to order Allows partial receipt of material – no instantaneous receipt of materials Other EOQ assumptions apply Suited for production environment Material produced, used immediately Provides production lot size Lower holding cost than EOQ model

19 POQ Model Inventory Levels Time Inventory Level Production Portion of Cycle Max. Inventory Q· (1- d/p) Q* Supply Begins Supply Ends Inventory level with no demand Demand portion of cycle with no supply

Production Order Quantity Model Answers how much to order and when to order Allows partial receipt of material – no instantaneous receipt of materials Other EOQ assumptions apply Suited for production environment Material produced, used immediately Provides production lot size Lower holding cost than EOQ model

21 POQ Model Inventory Levels Time Inventory Level Production Portion of Cycle Max. Inventory Q· (1- d/p) Q* Supply Begins Supply Ends Inventory level with no demand Demand portion of cycle with no supply

Quantity Discount Model Answers how much to order & when to order Allows quantity discounts Reduced price when item is purchased in larger quantities Other EOQ assumptions apply Trade-off is between lower price & increased holding cost

Quantity Discount Schedule Discount Number Discount QuantityDiscount (%)Discount Price (P) 1 0 to 999No discount $ ,000 to 1,9994$ ,000 and over5$4.75

Quantity Discount Model Compute the common EOQ and identify the feasible range. If the feasible EOQ is on the lowest price range, that is the optimal order quantity. If the EOQ is below the allowable range, adjust the EOQ to the lowest price break qty of that rangebelow If the EOQ is above the allowable range, discard that EOQabove Compare the total costs (including total cost of product) for the feasible EOQ and price break quantity. Select the quantity that yields the lowest total costs.

Probabilistic models When demand is not known, but can be expressed as a probabilistic distribution Uncertain demand raises possibility of stock out Service level – complement of probability of stock out