Article: Modelling and solving a bi-objective single period problem with incremental and all unit discount within stochastic constraints: NSGAII and MOPSO Journal: International Journal of Services and Operations Management (IJSOM) 2018 Vol.30 No.4 pp.520 - 541 Abstract: 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. Inderscience Publishers - linking academia, business and industry through research

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

Authors: Mahsa Najimi; Seyed Hamid Reza Pasandideh

Addresses: Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran ' Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

Abstract: 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.

Keywords: inventory control; bi-objective; single-period; incremental and total discount; meta-heuristic algorithms; non-dominated sorting genetic algorithm II; NSGA-II; MOPSO.

DOI: 10.1504/IJSOM.2018.093516

International Journal of Services and Operations Management, 2018 Vol.30 No.4, pp.520 - 541

Received: 20 Feb 2016
Accepted: 12 Nov 2016
Published online: 27 Jul 2018 *

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

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