Modelling And optimal lot-sizing of the replenishments in constrained, multi-product and bi-objective EPQ models with defective products: Generalised Cross Decomposition

The optimal lot-sizing of the replenishments has a cumulative effect on practical Economic Production Quantity (EPQ) models with the aim of inventory system management. In this paper, an EPQ model of the replenishment is proposed by taking into account the real-world conditions. A bi-objective inventory model is designed in order to minimise the total inventory cost and to maximise the profit, simultaneously. Realistic and practical stochastic constraints are imposed on the procurement cost, the screening cost, the disposal cost, and the space cost. The objective of the present study is to optimise the lot-sizing of the replenishment, while the stochastic constraints are satisfied and the optimum number of lots and optimum volume of each lot are calculated. Responding to the inconsistency of objective functions, an Lp-metric method is utilised to integrate and gain a single objective function. The mathematical formulation of the model is stochastic, Mix Integer Nonlinear Programming (MINLP), large-scale and hard to solve. In this regards, Generalised Cross Decomposition (GCD) is utilised to optimise the MINLP model of this research. The results of numerical examples and sensitivity analyses give us a complete insight into the applicability and accuracy of the suggested model and the solution method.