1 1 Slide Inventory Management Professor Ahmadi

2 2 Slide The Functions of Inventory n To ”decouple” or separate various parts of the production process n To provide a stock of goods that will provide a “selection” for customers n To take advantage of quantity discounts n To hedge against inflation and upward price changes

3 3 Slide Types of Inventory n Raw material n Work-in-progress n Maintenance/repair/operating supply n Finished goods

4 4 Slide n Divides on-hand inventory into 3 classes A class, B class, C classA class, B class, C class n Basis is usually annual $ volume $ volume = Annual demand x Unit cost$ volume = Annual demand x Unit cost n Policies based on ABC analysis Develop class A suppliers moreDevelop class A suppliers more Give tighter physical control of A itemsGive tighter physical control of A items Forecast A items more carefullyForecast A items more carefully ABC Analysis

5 5 Slide % of Inventory Items Example of Classifying Items as ABC % Annual $ UsageA B C Class% $ Vol% Items A8015 B 30 C 555

6 6 Slide n Physically counting a sample of total inventory on a regular basis n Used often with ABC classification A items counted most often (e.g., daily)A items counted most often (e.g., daily) Advantages of cycle counting Eliminates shutdown and interruption of production necessary for annual physical inventoriesEliminates shutdown and interruption of production necessary for annual physical inventories Eliminates annual inventory adjustmentsEliminates annual inventory adjustments Allows the cause of errors to be identified and remedial action to be takenAllows the cause of errors to be identified and remedial action to be taken Maintains accurate inventory recordsMaintains accurate inventory records Cycle Counting

7 7 Slide Independent versus Dependent Demand n Independent demand - demand for item is independent of demand for any other item n Dependent demand - demand for item is dependent upon the demand for some other item

8 8 Slide Inventory Costs n Holding costs - associated with holding or “carrying” inventory over time (Such as Obsolescence, Insurance, Extra staffing, Interest, Pilferage, Damage, Warehousing, Etc.) n Ordering costs - associated with costs of placing order and receiving goods (Such as: Supplies, Forms, Order processing, Clerical support, Etc.) n Setup costs - cost to prepare a machine or process for manufacturing an order (Such as Clean-up costs, Re-tooling costs, Adjustment costs, Etc.)

9 9 Slide 1. Economic order quantity models (EOQ) 2. Production order quantity models (POQ) 3. Quantity discount 4. Probabilistic models (Normal Demand) 5. Probabilistic models (Discrete demand) Inventory Models

10 Slide n Known and constant demand n Known and constant lead time n Instantaneous receipt of material n No quantity discounts n Only order (setup) cost and holding cost n No stockouts EOQ Assumptions

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

12 Slide 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

13 Slide 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

14 Slide Optimal Order Quantity Expected Number of Orders Expected Time Between Orders Working Days/Year Working Days/Year == × × == == = =× Q* DS H N D Q*Q* T N d D ROPdL 2 D = Demand per year S = Setup (order) cost per order H = Holding (carrying) cost d = Demand per day L = Lead time in days EOQ Model Equations

15 Slide n Answers how much to order and when to order n Allows partial receipt of material Other EOQ assumptions applyOther EOQ assumptions apply n Suited for production environment Material produced, used immediatelyMaterial produced, used immediately Provides production lot sizeProvides production lot size n Lower holding cost than EOQ model Production Order Quantity Model (POQ)

16 Slide D = Demand per year S = Setup cost H = Holding cost d = Demand per day p = Production per day POQ Model Equations Optimal Order Quantity Setup Cost Holding Cost == - = * = * = Q H* d p Q D Q S p * 1 ( 0.5 * H * Q - d p 1 ) - d p 1 () 2*D*S () Maximum inventory level

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

18 Slide n Answers how much & when to order n Allows demand to vary Follows normal distributionFollows normal distribution Other EOQ assumptions applyOther EOQ assumptions apply n Consider service level & safety stock Service level = 1 - Probability of stockoutService level = 1 - Probability of stockout Higher service level means more safety stockHigher service level means more safety stock More safety stock means higher ROPMore safety stock means higher ROP Probabilistic Models