This exercise illustrates some of the tradeoffs involved in determining the location and concentration of production.

A multinational corporation is considering three different production sites (P1, P2, P3) to manufacture a product that serves two markets M1 and M2, which have demands of 900 and 800 units respectively. The total volume of production equals the demand. In other words, the total production in all three sites should be 1,700 units. The maximum capacities for P1, P2, and P3 are 500, 500, and 1,000 units respectively (that means you have to use at least two production sites) and the question is how many units should the company manufacture in each location in order to minimize the cost?

Two elements have to be taken into account: the production cost and the transportation cost.

TOTAL COST = PRODUCTION COST + TRANSPORTATION COST

For the former, the economies of scale play an important role in determining the total cost of production: different ways of distributing the production among the three sites (the firm can also use two sites only) result in different production costs.

Once a certain distribution is considered, the transportation costs should also be calculated (in real life these costs are much more complex since they would include potential tariffs, customs clearance procedures, …): a production site could be very efficient from an economies of scale standpoint but far from the markets. The costs of shipping one unit of production from each production site to each market are shown in the table below:

 

P1 P2 P3 M1 1.5 0.5 3.5 M2 2 1.8 6