Although it is only August, the Big View

(BV) electronics company is placing orders now for holiday shopping season sales of a new super-large, flat-screen TV. Orders will be delivered from the overseas manufacturer to the company’s sites in 3 regional shopping malls.

Due to the global nature of orders, this will be BV’s only buying opportunity until after the first of next year. The product is very new and different from competitors, which makes BV uncertain how well it will sell. The following table shows projected sales (if stock is available) at the 3 malls under 5 possible demand scenarios, along with the probability of each:

Demand Scenario Mall 1 2 3 4 5 1 200 400 500 600 800 2 320 490 600 475 900 3 550 250 400 550 650 Prob 0.10 0.20 0.40 0.20 0.10 BV will pay $500 per TV purchased and shipped to the 3 malls. Extra units may be obtained for one mall from another’s excess at a transfer cost of $150. Whatever the source, each TV sold during the season will bring $800. TV’s still available at the end of the season in any malls will all be sold at the clearance price of $300. BV wishes to find a plan that maximizes the total expected net profit over all the units purchased in August.

(a) Explain how BV’s planning task can be modeled as a Two-Stage Stochastic Program with recourse (definition 4.18 )?

Specifically, what will be decided in Stage 1, what scenarios s need to be treated in Stage 2, and what recourse decisions are available?

(b) Assuming it is satisfactory to treat numbers of TVs as continuous, formulate a Stochastic Linear Program in Extensive Format (Figure 4.4) to compute a maximum expected net-profit plan for BV.

Use Stage 1 decision variables xm !

the number TVs purchased for mall m.

Combine with Stage 2 decision variables wm,n 1s2 ! the number of units transferred from mall m to mall n under scenario s, ym 1s2 ! the number of TVs sold in mall m under scenario s, and zm 1s2 ! the number of overstock units sold at discount from mall m after the season.

(c) Use class optimization software to solve your model of

(b) and explain what decisions prove optimal.