The single-period problem which is called newsboy problem, is one of the commonplace problem in inventory control. Using inventory control models in each stage of industry cycle has become commonly to determine the order quantities and commodity inventory. In this paper, optimizing a bi-objective, multi-product, multi-constraint, single-period problem is considered with incremental discount policy in purchasing commodity to find the order quantities which will be maximized both the expected profit and the minimized service level. The constraints are budget and the warehouse capacity. In addition, the decision variables are real and it is assumed that the holding and shortage costs occur at the end of the period. The formulation of the problem is presented and shown to be a mixed integer nonlinear programming model. Furthermore, Multi- Objective Decision Making (MODM) approaches are utilized to solve the model with meta-heuristic algorithms. The Genetic algorithm (GA) and the Particle swarm optimization (PSO) are provided to find an approximate optimum solutions of the problem. After applying the RSM method to calibrate the parameters of both algorithms, their performance in solving instances are compared in terms of the solution quality of both algorithms. In final, GAMS is applied for validating their solutions.

Keywords

Inventory control; single-period; incremental discount; MODM approaches; meta-heuristic algorithms.