A two-stage pricing and inventory optimization model for both ameliorating and deteriorating items in a competing environment

This paper develops a pricing and inventory model of a supply chain composing one supplier and two manufacturers in which the supplier sells its product to two competing manufacturers. each manufacturer faces a deterministic demand that depends on his/her own and the other competitor sale price. selling price for the supplier is time dependent and increment function. both amelioration and deterioration effects are seen simultaneously for this model. in this paper, it is assumed that shortages are not allowed in which the objective is maximizing the total profit of supplier and manufacturers in two stages. in first stage, the total profit of supplier is maximized and then in the second stage, two manufacturers maximize their total profits with regard to the optimal decision variables obtained in the first stage. a case study of trout fish breeding is presented and numerical example is solved by mathematica optimization tool. sensitivity analysis is conducted to study the effect of various parameters on the optimal solution.