Determining the product mix in environments with multiple constraints, considering the priority of constraints

One of the problems in the production line is determining the product mix while paying attention to resources and customer demands. The theory of constraints is a philosophy that is decisive in determining the product mix according to the constraints of the system and the productivity of the system. This theory gives an optimal solution in environments with one constraint, but in systems with more constraints, the solution may become impossible. The present research examines the problem of determining the product mix in environments with more than one constraint. It is necessary to pay attention to the opinions of the decision maker regarding the priority of the bottlenecks in the environments with more constraints.
Three states for the theory of constraints method are envisioned according to the number and type of bottlenecks: the first is the state where the system has only one bottleneck and the solution of the theory of constraints is identical to the optimal method of linear programming. The second is the case where the system has more than one bottleneck and the theory of constraints maintains its efficiency and produces an optimal solution. The third is the case where the system has more than one bottleneck and the theory of constraints produces an impossible solution. It is worth noting that in all the three cases considered for the theory of constraints, the opinions of the decision makers have been ignored, which is considered in the proposed method. To prove the efficiency of the proposed model, various examples have been solved with the help of goal programming and WinQSB software. The computation results and the processing time show the efficiency of the proposed model in reaching the optimal solution in environments with multiple constraints by considering the opinions of the decision maker.