Inventory Planning Problem

This is an inventory planning problem. A manufacturing firm makes two versions of a video game console, “Fast” and “Really Fast”. The main components that go into each console are a (1) motherboard, including a CPU and RAM chips; and a (2) graphics card.

The two consoles use the same motherboard, which costs $50 per unit. The “Fast” console requires the “Fast” graphics card which costs $80; the “Really Fast” console requires a different graphics card, namely the “Really Fast” graphics card which costs $100.

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These consoles sell primarily in the Holiday season. The marketing department has developed a demand forecast for the two consoles for the upcoming season; in particular, they have identified five possible demand scenarios, which are equally likely outcomes. The scenarios are given in table below.

Scenario Demand for Fast Console Demand for Really Fast Console Probability
1 200 1000 0.20
2 300 800 0.20
3 500 700 0.20
4 700 600 0.20
5 800 400 0.20

Suppose that the Fast Console sells for $201, while the Really Fast Console sells for $300.

The firm must order the components (the mother board; and the two graphic cards) prior to the Holiday season, before it knows the demand scenario.After ordering, by the start of the Holiday season, the firm will know what the demand scenario is for the season. It can then determine how to allocate its components to the production of the two consoles to meet the demand as best as possible. Its objective is to maximize its expected revenue, net of the cost of the components.(The cost of assembly is assumed to be negligible.) Any leftover components that cannot be used to meet demand in the season have zero value.

The problem is to determine how many of each component to order.You should formulate this as a stochastic linear program, and solve.

NOTE: We have provided an optional spreadsheet template you can use to help formulate your solution. It will be available in the solution to part c.

Based on the set up and Stochastic LP solution, answer the following questions: