An integrated production-marketing planning model With Cubic production cost function and imperfect production process

The basic assumption in the traditional inventory model is that all outputs are perfect items. However, this assumption is too simplistic in the most real-life situations due to a natural phenomenon in a production process. From this it is deduced that the system produces non-perfects items which can be classified into four groups of perfect, imperfect, reworkable defective and non-reworkable defective items. In this paper, compared with classic model, a new integrated imperfect quality economic production quantity problem is proposed where demand can be determined as a power function of selling price, advertising intensity, and customer services volume. Furthermore, as novelty way the unit cost is defined as a cubic function of outputs which is similar to real world. Also, a geometric programming modeling procedure is employed to formulate the problem. Finally, a numerical example is illustrated to study and analysis the behavior and application of the model.