Topic 6. INVENTORY MANAGEMENT

1. Topic 6. INVENTORY MANAGEMENT

2. I. Introduction • What is inventory? • stored resource used to satisfy current or future demand • Types of Inventories: • Raw Materials/Components • In-Process Goods (WIP) • Finished Goods • Supplies

3. Introduction • Inventory Related Costs: • Holding Cost -- cost to carry a unit in inventory for a length of time (annual), includes interest opportunity cost, insurance, taxes, depreciation, obsolescence, deterioration, May be expressed as a percentage of unit price or as a dollar amount per unit

4. Introduction • Inventory Related Costs (continued): • Order Cost -- Cost of ordering and receiving inventory, Include determining how much is needed, preparing invoices, shipping costs, inspecting goods upon receipt for quantity and quality, Generally expressed as a fixed dollar amount, regardless of order size • Inventory may also influence purchasing cost • Inventory is costly

5. Introduction • Inventory Related Costs (continued): • Shortage Cost-- result when demand exceeds the inventory on hand, Include the opportunity cost of not making a sales, loss of customer goodwill, late charges, and in the case of internal customers, the cost of lost production or downtime, difficult to measure, thus may have be subjectively estimated

6. Introduction • Why Hold Inventories? • Meet anticipated demand • Lead time – the time period between place an order until receive the order • Average lead time demand is considered as anticipate demand • Protect against stock-out • Safety stock – more than average lead time demand inventory

7. Introduction • Why Hold Inventories (continued)? • De-couple successive operations - separate production from distribution • Wine production and inventory • Smooth production process • Snowmobile production and inventory • Buy/Produce in economic lot sizes - take advantage of quantity discounts • Hedge against price increases

8. Introduction • JIT Inventory – minimum inventory needed to keep a system running, small lot sizes • Advantages • lower inventory costs • easy to identify problems and potential problems • Disadvantages • requires accurate timing and cooperation • breakdowns stop everything

9. High A Annual $ volume of items B C Low Few Many Number of Items Introduction • Inventory Classification • Identify important Items and more inventory control on important items • Measure of importance: • ABC analysis: • A = 70-80% of total inventory value, but only 15% of items • B = 15-25% of total inventory value, but 30% of items • C = 5% of total inventory value, but 55% of items

10. 0 214800 232087768 Introduction • Monitor Inventory • As important as demand forecast for decision making • Universal Product Code - Bar code printed on a label that hasinformation about the item to which it is attached • Cycle counting: taking physical counts of items and reconciling with records on a continual rotating basis, regular inventory audits, ABC approach

11. Introduction • Inventory Systems • Objective: minimize annual total inventory cost and maintain satisfied service level. • service level: probability of no shortage Total Inventory Cost is not Inventory Cost • Annual total inventory cost (TC) = annual product cost + annual inventory cost • Annual product cost = annual demand * unit price • Annual inventory cost = annual holding cost + annual setup (order) cost + annual shortage cost

12. Introduction • Possible performance measures • customer satisfaction • number of backorders/lost sales • number of customer complaints • inventory turnover • ratio of annual cost of goods sold to average inventory investment • days of inventory • expected number of days of sales that can be supplied from existing inventory

13. Introduction • Requirements for Effective Inventory Management : • A system to keep track of the inventory on hand and on order • A classification system for inventory items • A reliable forecast of demand that includes an measure of forecast error • Reasonable estimates of inventory holding costs, ordering costs, and shortage costs • Knowledge of lead times and lead time variability

14. Introduction • 1. Continuous (Perpetual) Review System: (event-triggered) • Monitor the inventory level all the time, order a fixed quantity (Q) when the inventory level drops to the reorder point (ROP) • Calculate: Q and ROP • Re-Order Point (ROP) – an inventory level when actual inventory drops to it will trigger an activity of re-order.

15. Introduction • 2. Periodic Review System: (time-triggered) • Place an order every fixed period T. Each time bring the current inventory to a target level M • Calculate: T and M • 3. Advantages and Disadvantages?

16. Introduction • Dependent and Independent Demand: • Dependent demand: derived demand, lumpy (subassemblies and components) • cars • Independent demand: from customer side, smooth (end items and finished goods) • tires

17. II. Inventory Models On Order Quantity • Model Basics (consider as annual) • Total Cost (TC) = Product Cost + Inventory Cost Inventory Cost = Holding Cost + Setup (Order) Cost + Shortage Cost TC = Product Cost + Holding Cost + Setup (Order) Cost + Shortage Cost

18. Inventory Models On Order Quantity • Product Cost = Annual Demand * Unit Price • Holding Cost = average inventory level * Holding Cost per unit per year • Ordering Cost = # of orders * Setup Cost per order • # of orders = annual demand / order quantity • Shortage Cost = Shortage Cost per unit * average # of shortage per year Best Order Quantity = a quantity that minimizes TC

19. Inventory Models On Order Quantity EOQ Model (Economic Order Quantity), Fixed-Order-Quantity Model • Assumptions • There is one product type • Demand is known and constant • Lead time is known and constant • Receipt of inventory is instantaneous (one batch, same time) • Shortage is not allowed

20. EOQ Model (continued) Q Reorder point Place order Receive order Receive order Place order Receive order Lead time

21. EOQ Model (continued) • Notation and Terminology • Q = order quantity(# of pieces per order) • Q0 = Economic Order Quantity (EOQ) • D = demand for the time period considered (units per year) • S = setup/order cost ($ per order) • H= holding cost per unit per year ($ per unit per year) • in general proportional to the price, H = I*P

22. EOQ Model (continued) • Notation and Terminology (continued) • I = Interest rate (expanded) (% per year) • P= unit price ($ per unit) • IC = inventory cost = setup cost + holding cost • TC = IC+ product cost Find Out EOQ

23. EOQ Model (continued) • Average Inventory Level = • Holding Cost = • Number of orders per year = • Setup (Order) Cost = • Shortage Cost = 0, why?

24. EOQ Model (continued) • Product Cost = • IC = • Total Cost (TC) = • Minimize TC Minimize IC, why?

25. EOQ Model (continued) • Observation: at the best order quantity EOQ (Q0), holding cost = setup cost Solve Q0, we have

26. EOQ Model (continued) The Inventory Cost Curve is U-Shaped Annual Cost Annual Carrying Costs Annual Ordering Costs QO (EOQ) Order Quantity (Q)

27. EOQ Model (continued) • Example: Annual demand = 10,000 unit/year, ordering cost = $50/order, unit cost (price) = $4/unit, expanded interest rate = 25%/year. EOQ? TC at EOQ?

28. EOQ Model (continued) • Sensitivity of IC with related to Q -- Example (continued)

29. EOQ Model (continued) • Conclusion: • 1. Inventory cost curve is flat around EOQ • 2. Flatter when Q increases than when Q decreases from EOQ • Thinking Challenge: • If the order quantity Q = 2*EOQ, by how much IC will increase?

30. EOQ Model (continued) • Sensitivity of EOQ with related to D, H, S, P, I • 1. Insensitive to parameter change • 2. Directions?

31. EPQ Model EPQ (Economic Production Quantity) Model: Fixed Order Quantity Model with Incremental Replenishment • Problem description: • Assumptions • There is one product type • Demand is known and constant • Receipt of inventory is gradual and at a constant replenishment (production) rate • Shortage is not allowed

32. EPQ Model (continued) Production rate - usage rate Q Quantity on hand Usage rate Reorder point Time Start to produce Start to produce Finish production Production run length

33. EPQ Model (continued) • Notation and Terminology • Qp = production quantity(# of pieces/production run) • Qp0 = Best production quantity (EPQ) • p = daily production rate (units per day) • d = daily demand rate (units per day) • D = demand rate (units per year) • S = production setup (order) cost($ per setup) • H = holding cost per unit per year (again H = I*P in general) • T= production run length = Q/p

34. EPQ Model (continued) • Maximum Inventory Level = • Average Inventory Level = • Annual Holding Cost =

35. EPQ Model (continued) • Number of production runs per year = • Order Cost = • IC = • TC = • Minimize TC Minimize IC, why?

36. EPQ Model (continued) • Observation: at EPO, holding cost = setup cost • Best Production Quantity (EPQ) formula:

37. EPQ Model (continued) • Remarks: EPQ > EOQ (why?) • Example: D=2000 unit/year, S=$5/setup, H=$0.4/unit/year, p=100 unit/day, 200 working days/year. Find the best production batch size and the # of production runs/year.

38. EOQ with discount EOQ with Discount Model: • Assumptions: same as with EOQ, plus discount on all units • Terminology • Price breaks: the smallest order quantity to receive a discount price • Feasibility: the order quantity matching the claimed price is feasible, otherwise infeasible.

39. EOQ with discount (continued) • Example: Order Price 0-399 $2.1/unit 400-699 $2.0 Great equal 700 $1.9 • Idea is to compare TC curves under different prices - why TC?

40. Total Cost Curve for Price 1 Total Cost Curve for Price 2 Total Cost Curve for Price 3 Order Quantity EOQ with discount (continued) $ cost 400 700

41. Total Cost Curve for Price 1 Total Cost Curve for Price 2 Total Cost Curve for Price 3 Order Quantity EOQ with discount (continued) $ cost 400 700

42. EOQ with discount (continued) • Observations: • EOQ with a lower price, if feasible, is better than any order quantity with the same or higher price. • Potential best order quantity: cheapest feasible EOQ, price breaks associated with lower prices.

43. EOQ with discount (continued) • Solution Procedure: • 1. Find the feasible EOQ with cheapest possible price. • 2. Calculate TCs of the EOQ (from Step 1) and price breaks above EOQ. • 3. Pick the order quantity with lowest TC

44. EOQ with discount (continued) • Example (continued) Annual demand = 10,000 unit/year, order cost = $5.5/order. Assuming holding costs are proportional to unit prices and annual interest rate = 20%. Find the best order quantity.

45. III. Models on Reorder Points - When to Order? • Models on Reorder Points - When to Order? • Find ROP (Re-Order Point) • ROP depends on: • Lead Time: time between placing and receiving an order • Demand Distribution: how uncertain • Desired Service Level: probability of no shortage = 1-P(s), where P(s) = probability of shortage

46. Models on Reorder Points - When to Order ? (continued) • Constant Demand Rate: • Constant daily demand rate = d, Lead time = L days ROP = d * L = Lead time demand • Remark: • no uncertainty in demand • service level = 100% • safety stock = 0

47. Models on Reorder Points - When to Order ? (continued) • Variable Demand with Stable Average Rate • How continuous review system works? • Lead time demand: demand during the lead time • ROP Lead time demand ==> • ROP < Lead time demand ==> • ROP = Average lead time demand + Safety Stock = m + SS

48. Models on Reorder Points - When to Order ? (continued) • Remarks: • Higher the desired service level ---> • More uncertain the demand ---> • Two methods to determine the SS

49. Models on Reorder Points - When to Order ? (continued) • 1. Determine SS and ROP based on shortage cost inf. (if available) • SS increases  Holding cost ? Shortage cost ? • Best SS minimizes total inventory cost

50. Models on Reorder Points - When to Order ? (continued) • 1. Determine SS and ROP based on shortage cost inf. (continued) -- Example: Consider a light switch carried by Litely. Litely sells 1,350 of these switches per year, and places order for 300 of these switches at a time. The carrying cost per unit per year is calculated as $5 while the stock out cost is estimated at $6 ($3 lost profit per switch and another $3 lost in goodwill, or future sales loss). Find the best SS level and ROP for Litely.