geometric programming

In recent years researchers have been interested in inventory models for deteriorating items along with determining the price of these items; given that in many real-world problems, changing the price can affect the demand level. Meanwhile, there are some other demand stimulation like advertising, multiple post-payments and discounting which can change and control the demand level of the items. In this paper, a new deteriorating inventory model was developed that considers these three demand stimulation along with pricing. The model has been converted and solved using geometric programming approach. Meanwhile, genetic algorithm was used as an alternative method to test the performance of GP approach. The model was implemented in real case study of food industry and numerical results and sensitivity analyses demonstrate the superiority of developed approach.

One of the primary assumptions in most optimal pricing methods is that the production cost is a non-increasing function of lot-size. This assumption does not hold for many real-world applications since the cost of unit production may have non-increasing trend up to a certain level and then it starts to increase for many reasons such as an increase in wages, depreciation, etc. Moreover, the production cost will eventually have a declining trend. This trend curve can be demonstrated in terms of cubic function and the resulted optimal pricing model can be modeled in Geometric Programming (GP). In this paper, we present a new optimal pricing model where the cost of production has different trends depending on the production size. The resulted problem is formulated as a parametric GP with five degrees of difficulty and it is solved using the recent advances of optimization techniques. The paper is supported with various numerical examples and the results are analyzed under different scenarios.

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.

A very useful multi-objective technique is goal programming. There are many methodologies of goal programming such as weighted goal programming, min-max goal programming, and lexicographic goal programming. In this paper, weighted goal programming is reformulated as goal programming with logarithmic deviation variables. Here, a comparison of the proposed method and goal programming with weighted sum method is presented. A numerical example and applications on two industrial problems have also enriched this paper.