Last year’s Final John Vande Vate Fall, 2009

Question 1 Project similar to ABL but for Alternative Apparel One issue they addressed was identifying the appropriate reorder point The question asked about the teams calculations

Review of Projects DV method Calculating the reorder point for the end of May assuming the forecast for July is also 550 and the lead time is 2 months: They considered two methods DA method ROP = 550 + 550 + 2.5*(0.47)(550 + 550)  2400 Note 2.5 here refers to 2.5 standard deviations in the Std. Normal distribution and is designed to ensure a 1% chance of stocking out in a given month DV method ROP = 550 + 550 + 2.5*(267.71)  2050

Question Just based on the information here and assuming the ratios of actual demand to firecasted demands are normally distributed and stationary (don’t change with time), is the DA ROP A. Too high B. About right C. Too low Explain your answer

Answer Too high. Reason: There are two problems. A. Forecasts have been historically high so the expected value of demand in the next two months is more like 0.92*(550 + 550) B. The standard deviation in demand during the two month is not the sum of the standard deviations. Assuming independence, the variances add to a more appropriate formula for the safety stock would be 2.5*0.47* *550

Follow On An analyst proposed that we significantly simplify the process by focusing on the top 10 styles. Tract the ratios of actual monthly demand for this group over the forecast for this group rather than build and track the 10 separate forecasts. We could use the distribution of these ratios when we set the reorder points for each of the 10 styles Good Idea? Why offer flexibility ? Why personalize?

Question 2 One project looked at routing wind towers to job sites One aspect of that project was the issue of “liquidated damages” -- if components are delivered late, GE must pay a penalty for each wind tower day of delay. Two suppliers provide r towers per week and will hold at most I towers in inventory We have two projects Project 1 requires p1 towers per week for 4 weeks starting immediately Project 2 requires p2 towers per week for 3 weeks starting in week 2 Develop a model that over the next four weeks delivers all the towers with minimum transportation and liquidated damages. There are currently no tower in inventory.

Model Inventory at Supplier s Inv[s, i-1]+r – Ship[s, 1, i] – Ship[s, 2, i] = Inv[s, i] LD’s at Customer c Late[c, i-1]-Early[c, i-1]+Demand[c, i]-Ship[1, c, i-lead time] -Ship[2, c, i-lead time] = Late[c, i] – Early[c, i]

Question 3 Another project was with Coca Cola Brazil and focused on deciding on the size and composition of the delivery fleet. Previously, the company only determined the size of the fleet and kept the composition constant, i.e., same fraction of 4, 6, 8, 10 and 12 pallet trucks In this question I propose that the company has signed a long term contract with a truck manufacturer to provide vehicles in this fixed proportion . There are more specific tools: push-pull interface, frozen period, demand management etc…

Question 2 Daily demand for both traditional and modern customers for cases and stops is a bivariate normal with mean 70K cases/day and 1700 stops per day and covariance matrix How many vehicles of each type should the company order? 1,036,840,000 1,674,400 640,000 There are more specific tools: push-pull interface, frozen period, demand management etc…

Answer This is a newsvendor question Think of Q as the capacity we bring to the market The benefit the last unit of capacity brings is that we don’t have to pay for a unit of (expensive) 3rd party capacity. That’s the variable cost of 3pl capacity minus the full cost (fixed plus variable) of owned capacity (340 – 214 – 88)(1-P) = 38 (1-P) The risk the last unit poses is that we will pay the fixed cost unnecessarily – it will be idle. 214P So P – the fraction of time we cover demand with our own fleet should be 0.1508 = 38/(214+38) Now we look up the fleet size that gets us close to this value There are more specific tools: push-pull interface, frozen period, demand management etc…

Here’s the bivariate normal Stops across the top Cases down the side 50 trucks = 30,000 cases 1600 stops. Too few. Here’s the bivariate normal Stops across the top Cases down the side Find n so that The probability of being less than (600n, 32n) is about 0.15 70 trucks = 42,000 cases 2,240 stops. About right

The Answer So we need 20 more trucks evenly divided between the 5 sizes or 4 additional trucks of each size.

Question 4 A company manufactures 3 models of high value electronics for distribution to customers in the US. The products are currently produced in Dalian and shipped to Los Angeles for distribution. The products costs roughly $200 per unit and we sell 400K annually. To fly the product from Dalian takes 2 days and costs $0.40 per unit. To ship the product by ocean takes 20 days and costs $0.04 per unit. Our inventory holding charges is 25%/year Question A. Use air or ocean?

Answer Freight Costs: Pipeline Costs: Simplify be getting the 400K out 400K*0.04 vs 400K*0.40 Pipeline Costs: 400K/365*25%*$200*20 vs 400K/365*25%*$200*2 Simplify be getting the 400K out 0.04 + 4000*.25/356 = 0.04 + 1000/356 vs 0.4 + 400*.25/365= 0.4 + 100/365 Clearly the latter is cheaper. Fly

Question The company maintains a fill rate of 98% (2 standard deviations) and relies on a carrier who provides two flights per week that reliably require 2 days. An alternative is to ship undifferentiated modules to LA and transform them there. This has no impact on manufacturing costs in Dalian but does at $0.15/unit in manufacturing cost in LA. The work is done by a third party so there’s no fixed appreciable fixed cost involved. Should we use the postponement strategy and if so, for which models?

Answer Model Sales/Wk Std. Dev. 1 5,000 1,000 2 4,000 3 10,000 200 Compute the safety stock required to maintain the fill rates. If the “pooled” inventory is sufficiently lower then paying the $0.15 in additional mfg costs saves capital. If postponement makes sense, it makes sense for…? Model Sales/Wk Std. Dev. 1 5,000 1,000 2 4,000 3 10,000 200

Models 1 & 2 The savings will come from safety stock Std dev on a daily basis Model 1: 378 = 1000/Sqrt(7) Model 2: 1512 = 4000/Sqrt(7) Models 1 & 2 combined 1558 = Sqrt(3782 + 15122) Safety Inventory: Separate: 2*Sqrt(2)*(378+1512) = 5,345 Combined: 2*Sqrt(2)*(1558) = 4,407 At $50 = 25%*200 per unit per year, the difference is about $47K per year. Mfg costs are $0.15*520,000 = $78K. So postponement probably isn’t a good strategy here.