Modelling and solving a bi-objective single period problem with incremental and all unit discount within stochastic constraints: NSGAII and MOPSO

One of the perennial problems in inventory control is the single-period problem which is called the newsboy problem. In this paper, a single-period problem is developed. The problem is presented by a bi-objective multi-product with multiple constraints to maximise the expected profit as well as minimising the whole warehouse space. Incremental and total discount policies are considered in purchasing the items. In order to optimise the objectives, three types of constraint are presumed for each product which are the service level, budget and required warehouse space. In addition, the decision variables are real and the problem will be modelled with a type of mixed integer nonlinear programming. Moreover, meta-heuristic algorithms are utilised to solve the model. Non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective particle swarm optimisation are proposed to find the Pareto front as near-optima solutions. To achieve better results, RSM method is applied to calibrate the flexible parameters of both algorithms. Finally, Student t-tests are employed to compare the performances of proposed algorithms in terms of solution qualities.