Metaheuristic algorithms for solving lot-sizing and scheduling problems in single and multi-plant environments / Maryam Mohammadi - Mohammadi, Maryam (2015)
Economic lot scheduling problem (ELSP) is related to lot-sizing and scheduling several items in a single production facility. This project addresses the ELSP where multiple items have shelf life restrictions and planned backorders. For some products, shelf life might be less than the production cycle time, which leads to product spoilage before the end of the cycle. In order to achieve a feasible schedule, the production cycle time needs to be reduced to less than or equal to the shelf life duration. While the cost-minimization cycle time causes the spoilage of products, due to shelf life restrictions, appropriate decisions can be made based on one of three options: production rate reduction, cycle time reduction, or the simultaneous production rate and cycle time reduction. For each option, the optimal cycle time and production rate are appraised, which satisfy the shelf life constraints. On the other hand, backorders incur shelf life constraint alteration, which affects the corresponding inventory models. Accordingly, appropriate modifications are applied to the related mathematical inventory models. Further, a mixed integer non-linear model for the ELSP is developed which allows each product to be produced more than once per cycle. However, production of each item more than one time may result in an infeasible schedule due to the overlapping production times of various items. To eliminate the production time conflicts, adjustments must be made through advancing or delaying the production start time of some or all the items. The objective is to find the optimal production rate, lot size, production frequency, cycle time, as well as a feasible manufacturing schedule for the family of items, in addition to minimizing the total cost including production, setup, holding, backordering, and adjustment costs. Lot-sizing problems are more complicated in multi-facility systems because of interdependency between facilities. Therefore, the multi-item multi-period capacitated lot-sizing problem in a multi-stage system composed of multiple suppliers, plants, and distribution centers is addressed in order to investigate the effectiveness of coordinating production and distribution planning. Combinations of several functions such as purchasing, production, storage, backordering, and transportation between suppliers, plants and distribution centers are considered. The objective is to simultaneously determine the optimal raw material order quantity, production and inventory levels, and the transportation amount so that the demand can be satisfied with the lowest possible cost over a given planning horizon without violating the capacity restrictions of the plants and suppliers. Transfer decisions between plants are made when demand observed at a plant can be satisfied by other production sites to cope with under-capacity of a given plant. Furthermore, the model also allows for sales at distribution centers. Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed models. Metaheuristic approaches namely genetic algorithm, particle swarm optimization, artificial bee colony, simulated annealing, and imperialist competitive algorithm are adopted for the optimization procedures. To offer more efficiency, Taguchi method is utilized to calibrate the various parameters of the proposed algorithms. The statistical optimization results show the efficiency, effectiveness and robustness of the applied methods in solving the proposed optimization models.