A Multi-objective Multi-item Capacitated Lot-sizing Model with Safety Stock and Shortage Costs based on Just-in-time Approach

Lot-sizing problem is a class of production planning problems in which the availability amounts of the production plan are always considered as decision variable. Goal of this paper is to propose a new multi-item capacitated lot-sizing problem (MICLSP) with setup times, safety stock deficit costs, demand shortage costs both backorder and lost sale states, and different production manners. Although a considerable amount of researches concentrates on model development and solution procedures in the terms of single-objective problems in the past decade, to make the model more realistic, this paper develops a multi-objective mathematical programming model with three conflicting objectives. First objective attempts to minimize the total cost considered by the production plans including production costs with different production manners, inventory costs, safety stock deficit costs, shortage costs, and setup costs. Second objective is for leveling the production volume in different production periods. Third objective follow to force the model to produce as near as possible to just-in-time (JIT). The proposed model was indicated to be strongly NP-hard; hence a random search algorithm namely multi-objective simulated annealing (MOSA) has been proposed based on Lp-metric technique. At the end, results analysis on different sizes of problems demonstrates the intelligence and efficiency of the proposed methodology.