An oil refinery pumps thousands of barrels of crude and refines it to produce fuels. The refinery must plan its production for the next four months to meet its expected demand. The monthly production capacity of the oil refinery is 12 barrels. It does not have any stock of oil at the beginning of the first month. The refinery has a tank to stock a maximum of 5 barrels. The demand forecast for oil for the next four months are 7, 4, 9, and 6 barrels, respectively. The refinery must be stopped once in a month for maintenance. Whenever the plant is started from complete closure, the plant incurs a set up cost of €400 and a holding cost €2 per month per barrel. If the refinery produces in month 2, then it should produce in month 4. The refinery wants to determine its production rate per month to minimize its cost of setup and inventory holding. (Note: For computational simplicity, refinery’s volumes and costs are given in smaller units.)
a. Formulate an integer programming model for this problem.
b. Solve this model by using the computer.