SUMMARY
A multi-period production and inventory control problem for a multi-grade, multi-supplier petrochemical product is formulated and optimally solved. Raw materials are available from several suppliers, and several plants (chemical reactors) are used for making the petrochemical product. Several grades of the petrochemical product can be produced by changing the conditions inside each reactor. During transition from one grade to another, a certain amount is produced of off-spec material. The quantity of off-spec production is sequence dependent, i.e. it depends on the two grades that the transition takes place between. The problem is formulated and solved by means of a graphical network model as well as a mixed-integer programming (MIP) model. The MIP model determines, for each time period, the sequence and quantities of different grades produced in each plant, the amounts of raw materials purchased from each supplier, and the inventory levels of each grade. The objective is to maximize the total profit, which is equal to the sale revenue of all regular grades and off-spec materials, minus the raw material costs and inventory holding costs.