Graduate Program in Business Information Systems

1. Graduate Program in Business Information Systems Inventory Decisions with Certain Factors Aslı Sencer

2. A Retailer’s Plea If I order too little, I make no profit. If I order too much, I may go broke. Every product is different. Help me! Aslı Sencer

3. Why do we control inventory? • Inventories represent a vast segment of total economic activity. • Even minor improvements can create large savings. How do we control inventory? • Application of optimization techniques • Information processing and retrieval techniques Aslı Sencer

4. Decisions of an inventory policy • If there is no production, i.e., pure inventory system • How much to order? Order quantity • When to order? Reorder quantity Ex:Order Q=100 units when the inventory level drops to r=15 units. • If there is also production • When to start/stop production? Aslı Sencer

5. An inventory system Aslı Sencer

6. Elements of Inventory Decisions • Costs: • Ordering and Procurement costs • Inventory holding or carrying costs • Inventory shortage costs • Demand structure • How does it vary? Certain, uncertain? • Supply structure • Any capacity limitations, defectives, number of suppliers? • Lead times: • Certain, uncertain? Aslı Sencer

7. Ordering and Procurement Costs • Represent all expenses incurred in ordering or manufacturing items related to • Acquisition • Transportation • Collecting, sorting, placing the items in the storage • Managerial and clerical costs associated with order placement. • Ordering costs are fixed, independent of the order size. • Procurement costs depend on the order size. Aslı Sencer

8. Holding or Carrying Costs • Expenses incurred during the storage of items. • Physical Costs: Warehouse operation costs, insurence, property taxes. • Pilferage, spoilage, obsolescence • Opportunity cost of investing in inventory rather than investing somewhere else, ex. in a bank. • Inventory costs are variable costs that depend on the order size. Aslı Sencer

9. Shortage Costs • Occur whenever the demand is not satisfied. Order is either “backordered” or “lost”. • Backordering Costs: • Fixed cost of extra managerial work. • Loss of customer goodwill: Variable cost that depends on duration of backorder. • Lost Sales Costs: • Marginal profit that the item would have earned. • Loss of customer goodwill. Aslı Sencer

10. Demand Structure • Continuous versus discrete demand Ex: Natural gas consumption in houses Detergent consumption in houses • Deterministic (certain) versus stochastic (uncertain) demand Ex: Order quantities for the next months are 20,30,10,50. Order quantities in a month are normally distributed with mean 25 and variance 4. • Constant versus dynamic demand Ex: Demand quantities for the next months are 20, 21, 20, 19 Demand quantities for the next months are 20, 50, 10, 2 Aslı Sencer

11. Supply Structure • Any defectives? If the received lot includes defective items this brings uncertainty • Any capacity limitations? Do we fully receive what we order? • Number of suppliers, fixed or variable? Aslı Sencer

12. Lead time • Time elapsed between the order delivery and order receipt. • Can be constant or stochastic. Ex: Lead time is 10 days. Lead time is between 8-12 days. Aslı Sencer

13. The Economic Order QuantityEOQ-Model • Decision variable:Q = Order Quantity • Parameters: k = Fixed cost per order ($/order) A = Annual number of items demanded (unit/year) c = Unit cost of procuring an item ($/unit) h = Annual cost of holding a dollar in inventory ($/$/year) • Objective is to “minimize total annual cost”. Aslı Sencer

14. EOQ Inventory Policy Average Inv. Level Aslı Sencer

15. Assumptions of Classical EOQ Model • Demand rate is constant or stable. • There is infinite supply availability. • Lead time is constant or zero. • No quantity discounts are made. • All demand is met on time, no backordering, no stockout. Aslı Sencer

16. Costs of EOQ Model • Total ordering cost is the number of orders times the cost per order: • Total holding cost is the cost per item held 1year times the average inventory: • The annual procurement cost is the product of annual demand and unit cost: Procurement cost = Ac Aslı Sencer

17. Annual Cost of EOQ-Model • HereAcis not a relevant cost and thus dropped. • Minimize Total Annual Inventory Cost: Aslı Sencer

18. Optimal Solution of EOQ • Optimal solution is theeconomic order quantity • Optimal Total Cost Aslı Sencer

19. Example:The House of Wines and Liquors Allex Mullen decides that the first task in utilizing inventory models is to determine the value of model parameters: • Annual demand 5200 cases of beer • $10 telephone charge for ordering • Purchase cost is $1.5/case beer+shipping cost $0.5/case • 10%bank interest, 5%state franchise tax, 5% theft insurance rate How many should he order, how often, and at what annual relevant inventory cost? Aslı Sencer

20. Solution: The economic order quantity is • The inventory cycle duration is T = Q/A = 510/5200 = 0.098 year or 36 days • The total annual relevant inventory cost is: Aslı Sencer

21. Robustness of EOQ Model • EOQ is a robust model with respect to the estimation errors in A, k, c or h. • Let Aactual=4 Aestimated Then EOQactual=2 Aestimated Since Aslı Sencer

22. Ex: The House of Wines and Liquors • Alex Mullen applies EOQ to another product, a particular variety of Chilean wine that sells 1000 cases annually. The cost is $20 per case. A telephone call to Chile to place an order costs $100. The holding costs are the same as for Tres Equis Beer. Aslı Sencer

23. Ex: T = Q/A = 24/1000 = .224 year or 82 days Aslı Sencer

24. Optimal Inventory Policywith Backordering Orders placed during shortages are backordered. Aslı Sencer

25. Optimal Inventory Policywith Backordering S: Quantity on hand when a shipment arrives. P:Cost of being one item short for a year Optimal order quantity and order level: Aslı Sencer

26. Example:The House of Wines and Liquors-Backorders The marketing department tells Alex that beer is a convenience product that can not be backordered, so sale is lost! However some wine customers are connoisseurs who are willing to order out-of-stock items. Nevertheless, the store owner will incur some penalty cost if there is a shortage of wine. Suppose that retailer suffers lost profit on future business equal to $0.01/unit each day that a wine is on backorder. What should be the optimal ordering policy if backordering is allowed? Solution: The order quantity is computed: p = $.01×365 = $3.65/unit/year. Aslı Sencer

27. Example: Solution • The order level S is • The relevant cost is smaller than before, why? Aslı Sencer

28. Is backordering better? • Fewer orders are placed when there is backordering. • Average inventory level is smaller. Backorders/cycle=Q* – S*=324 – 154 = 170 units/cycle. Proportion of demand not satisfied on time =(Q*-S*)/Q*=170/324= 52.5% • The results suggest that: Retailers will run short in each cycle. But can they get away with it? • So backordering must make sense! Aslı Sencer

29. Imputed Shortage Penalty An alternative approach for establishing an inventory policy is based on achieving a desired service level. Service Level, L is the proportion of demand met on time Imputed shortage penalty Aslı Sencer

30. As p increases EOQ is more robust A=1000 units/yr k=$100/order c=$20/unit h= $0.20/$/year L=47.5% 324 L=90% 236 Q* EOQ with no backordering 224 S* 212 154 P $3.65 $36 imputed shortage penalty Aslı Sencer

31. Economic Production-Quantity Model The inventory model may be extended to finding the optimal production quantity. Aslı Sencer

32. Economic Production-Quantity Model • B: Annual production rate • K:Production setup cost. • c: Variable production cost per unit. • Total Annual Cost: • Economic Production Quantity: Aslı Sencer

33. Example: Water Wheelies have annual demand of A=100,000 units and are made at the rate of B = 500,000 units. Production costs are k = $2,000/setup and c = $5/unit variable. It costs h = $.40/year to tie up a dollar. • Economic production quantity is • Total relevant cost is TC(8,944) Aslı Sencer

34. More Elaborate Models • Incorporate a second one-time shortage penalty. • Add additional products. • Incorporate uncertainty regarding: • Demand • Lead-time for delivery of order • Incorporate lost sales • Extend to single period products Aslı Sencer

35. Economic Order Quantity Model(Figure 15-3) Aslı Sencer

36. Sensitivity Analysis(Figure 15-6) Aslı Sencer

37. Graphing the Sensitivity Analysis (Figure 15-7) Aslı Sencer

38. Backordering Model(Figure 15-9) Aslı Sencer

39. Production Model(Figure 15-13) Aslı Sencer