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## Solution for Supply Chain Network Design: Applying Optimization and Analytics to the Global Supply Chain 1st Edition Chapter 5, Problem 1

by Michael Watson Sara Lewis Peter Cacioppi Jay Jayaraman
106 Solutions 14 Chapters 25295 Studied ISBN: 9780133017373 5 (1)

# Chapter 5, Problem 1 : 1. For this problem, let’s consider a simplified...

1. For this problem, let’s consider a simplified version of the problem similar to the distributor in Brazil. The firm we are considering has three facilities, each with the capacity to serve 20 million units of demand. Assume that there are nine demand regions and that a demand region must be served by only one facility. If the demand (in millions) for the nine regions is 9, 7, 6, 6, 7, 6, 6, 7, and 6, explain why this problem has no feasible solution.

## Step-By-Step Solution

1. The total demand and total supply adds up to exactly 60 each. So, in theory, it could work out. But, the constraint that allows each demand to be served by one facility is causing us problems.

In this case, the demand with 9 cannot be combined with any of the other demand numbers to add up to 20 exactly.

For this question, it would be a good discussion point to ask what do you think would happen in reality? (They may short demand, capacity may not really be as tight as they claim, they may open up other facilities and try to grow demand to fill it, and so on—in other words, they will probably do something, and if they set up the problem like this, they are making it mathematically hard.)