6 An Optimizing Problem Version

In the previous Exercise 2, several tables have been given to specify a concrete production plan. They are as follows:

  1. Given 7 different products (p P)

  2. Manufactured in 4 identical factories (f F)

  3. By means of 5 identical machines in each factory (m M)

  4. Using 20 different raw products (r R)

  5. A table qp,m defining which product p can be manufactured on which machine m

  6. A table Rr,p saying how many units of raw materials r are used to manufacture a unit of product p

  7. A table Hp,mq(p,m) defining the hours of machine m that is taken to manufacture one unit of product p

  8. A table Rcr giving the cost of a unit of raw materials r

  9. A table Mcm specifying the cost of machine m per hour of work

  10. A table Sp giving the selling price of product p

  11. Finally, a table Qf,p,mqp,m saying how many unit of products p are manufactured in factory f by means of machine m.

Especially, the last table Q is a given table that specifies the production plan. It is a given arbitrary plan without asking the question whether this plan is optimal in any sense. Let us now ask the question whether this plan could be changed without changing the manufactured quantity of each product, just by switching the production quantity from one machine to another.

  6.1 Version 1: the easy problem
  6.2 Version 2: Limit Capacity
  6.3 Version 3: with Setup Costs