Multi-objective optimisation of continuous review inventory system under mixture of lost sales and backorders within different constraints

This paper presents a continuous review stochastic inventory control system. The demand of each product assumed stochastic. In inventory models, it is common to assume that unsatisfied demand is backordered. We considered mixture of lost sales and backorders for shortages. We optimised inventory system with finding fraction of demand backordered. Also, we considered service level in model to improve customer satisfaction and compete better in retail environment. We considered two conflicting objectives: 1) minimising the total cost; 2) maximising the service level. The goal is to generate more diverse and better non-dominated solutions of reorder point, order size and fraction of demand backordered such that the total inventory cost is minimised and the service level is maximised. We considered constraints such as warehouse space, order quantity and restriction on available budget. Constraints are stochastic and follow normal distribution. Two multi-objective optimiser multi-objective particle swarm optimisation (MOPSO) and non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the problem. We compared the performance of two proposed algorithms with TOPSIS and statistical method. In this comparison, the optimum values of the NSGA-II parameters were obtained using regression analysis.