A comment on the formulation of an aggregate production planning problem

Conventionally, a revenue function, a cost function and a profit function are selected to be the objective function for Aggregate Production Planning (APP) problems. The theory of constraints (TOC) alternative consideration argues that instead of measuring by cost, factory should evaluate their performance by throughput. Even though, there are a lot of research works on formulations of APP problems, there has been no investigation, which formulation is the most appropriate for APP problems. In this research, the investigation of the formulation of existing APP problems is done. In order to clarify the difference of each objective function, a simple case study has been used to compare the performances of the APP problem with revenue, cost, and profit objective functions when resource constraints (limited processing time) are not included and included in the model. For the profit objective function, two formulations are also compared: profit objective function by TOC and profit objective function by linear programming. From the results, it can be shown that setting the objective function of an APP problem is very important because it may lead to a wrong decision in production planning.