Adjustment of Variables and Constraints in a Model

You have been asked to assist in the distribution design for Santa Insulators- the Brazilian’s premiere source for porcelain insulators used in electrical lines. Santa Insulatorsoperates two plants (Plant 1 in Lorena, SPand Plant 2 in Sorocaba, SP). The plants produce a range of insulatortypes and sizes, but you have determined that the most relevant flow unit is simply each insulator. Because the insulators are quite fragile, they are transported directly from the plants to the three DCs located in Sao Paulo, SP; Campinas, SP and Rio de Janeiro, RJ. Each DC has a different demand forinsulators:

Sao Paulo, SP: 6,000insulators perweek
Campinas, SP: 550insulators perweek
Rio de Janeiro, RJ: 3,160insulators perweek
The cost of transporting an insulatorfrom each plant to each DC ($/insulator) is shown below :

$/insulatorSao Paulo, SPCampinas, SPRio de Janeiro, RJPlant 1 (Lorena, SP)1.902.492.50Plant 2 (Sorocaba, SP)1.010.865.27

The plants have their differences, but they have the same capacity of 5,000 insulators/week.

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The Chief Financial Officer for Santa Insulators, Paulo Silva, believes that the models are not including the cost of running a production line at a plant. He tells you that to manage a production line of one product type costs $5,000 per week. So, if a plant is producing both Type A and Type B insulators, they incur a $10,000 fixed cost.

How should we adjust the variables and constraints in the model to implement the changes requested by the CFO?