Chapter 6

1. Chapter 6 Inventory Analysis

2. Accurately Matching Demand with Supply is the Key Challenge: Inventories • ... by 1990 Wal-Mart was already winning an important technological war that other discounters did not seem to know was on. “Wal-Mart has the most advanced inventory technology in the business and they have invested billions in it”. (NYT, Nov. 95). • WSJ, Aug. 93: Dell Computer stock plunges. The company was sharply off in forecast of demand resulting in inventory writedowns. • BW 1997:

3. Costs of not Matching Supply and Demand • Cost of overstocking • liquidation, obsolescence, holding • Cost of under-stocking • lost sales and resulting lost margin

4. Where is the Flow Time? Operation Buffer Processing Waiting

5. Flow Times in White Collar ProcessesSource: J. Blackburn

6. 6.1: Operational Flows I avg total inv = I input + I in-process + I output I = Ii + Ip + Io Throughput R Inventory I FLOW TIME T I = R T Flow time T = Inventory I / Throughput R

7. 6.2: Why do Buffers Build? Why hold Inventory? • Economies of scale • Fixed costs associated with batches • Quantity discounts • Trade Promotions • Uncertainty • Information Uncertainty • Supply/demand uncertainty • Seasonal Variability • Strategic • Flooding, availability Cycle/Batch stock Safety stock Seasonal stock Strategic stock

8. 6.3: Cost of Inventory • Physical holding cost (out-of-pocket) • Financial holding cost (opportunity cost) • Low responsiveness • to demand/market changes • to supply/quality changes Holding cost Inventory Unit Holding Cost = H = (h + r) C Physical holding cost Rate of return Cost/flow unit Example 6.2

9. Inventory Profile: # of jackets in inventory over time. Inventory Q R = Demand rate Time t 6.4: Economies of Scale: Inventory Build-Up Diagram R: Annual demand rate, Q: Number per replenishment order • Number of orders per year = R/Q. • I cycle = Q/2 T = Ti + Tp = (Q/2)/R + Ip/R Example 6.3

10. Total annual costs H Q/2: Annual holding cost S R /Q:Annual setup cost EOQ Batch Size Q Economies of Scale: Economic Order Quantity EOQ R : Demand per year, S : Setup or Order Cost ($/setup; $/order), H : Marginal annual holding cost ($/per unit per year), Q : Order quantity. C : Cost per unit ($/unit), r : Cost of capital (%/yr), h:Physical unit holding cost ($/unit,yr), H = (h + r) C. Total Cost = S(R/Q) + H(Q/2) + CR

11. Economies of Scale: Example 6.4 R= units C = $ / unit r = %/yr S = $ / order Total annual cost under current plan Example 6.5 EOQ Total annual cost under current plan Icycle = Q*/2 Ti = I cycle / R TC*

12. Find most economical order quantity: Spreadsheet (Table 6.2, p. 146)

14. 6.6: Role of Leadtime L • The two key decisions in inventory management are: • How much to order? • When to order? ROP = L * R = Lead Time * Throughput Example 6.8

15. 6.8: Levers Ith = R * Tth • Reducing critical activity time • Eliminating NVA activities • Redesigning the process to replace sequential with parallel processing

16. Learning Objectives: Batching & Economies of Scale • Increasing batch size of production (or purchase) increases average inventories (and thus cycle times). • Average inventory for a batch size of Q is Q/2. • The optimal batch size trades off setup cost and holding cost. • To reduce batch size, one has to reduce setup cost (time). • Square-root relationship between Q and (R, S): • If demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and produce (order) twice as often. • To reduce batch size by a factor of 2, setup cost has to be reduced by a factor of 4.