Chapter 6 Inventory Analysis 1

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? Buffer Operation Waiting Processing

5 Flow Times in White Collar Processes Source: J. Blackburn

6 6.1: Operational Flows Throughput R Inventory I I = R T Flow time T = Inventory I / Throughput R FLOW TIME T I avg total inv = I input + I in-process + I output I = I i + I p + I o

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 costRate of returnCost/flow unit Example 6.2

9 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 Q Time t Inventory Profile : # of jackets in inventory over time. R = Demand rate Inventory T = T i + T p = (Q/2)/R + I p /R Example 6.3

10 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. Batch Size Q Total annual costs H Q/2: Annual holding cost S R /Q:Annual setup cost EOQ Total Cost = S(R/Q) + H(Q/2) + CR

11 Economies of Scale: R = unitsC = $ / unit r = %/yrS = $ / order Example 6.4 Example 6.5 Total annual cost under current plan EOQ Total annual cost under current plan I cycle = Q*/2 TC* T i = I cycle / R

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

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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 I th = R * T th 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.