Solving a multi objective inventory control problem under budget constraint using a particle swarm optimization

In this paper, we extend a multi item multi period inventory control problem under budget constrain which demands are deterministic and known but variable in each period. The shortage in combination of backorder and lost sale is considered. In each period, shortages possible occur or not, where a binary variable is applied for representation it. We assume that order quantity is more that shortage quantity when shortage occurs in a period. The order should be placed in batch size, furthermore, decision variables are assumed integer type. In this research, all unit discount (AUD) for a number of items and incremental quantity discount (IQD) for other are considered. Here the model has been formulated as a multi-criteria decision making (MCDM) problem. The objectives are minimization of total inventory cost and minimization of total storage space. The model of this problem is shown to be a mixed integer nonlinear programming type and in order to solve it, a multi objective particle swarm optimization (MOPSO) approach is applied. A set of compromise solution including optimum and near optimum ones via MOPSO has been derived and the results are compared with that obtained from a weighting approach