The parameters of the problem are as follows:
• - unit variable production cost for mode s at plant ispci
• - unit transportation cost for product from plant i to customer ijttctj
• - quantity of product produced at plant i by mode s itsat
• - demand for product by customer jtbtj
The decision variables of the problem are:
• - the intensity of using mode by plant i being part of the planning period, which is taken to be 1 iszs
• - the amount of product shipped from plant i to customer ijtutj
The PTP can now be formulated as the following linear programming problem: