Sequencing, lot sizing and scheduling in job shops: the common cycle approach

This paper deals with the multi-product, finite horizon, static demand, sequencing, lot sizing and scheduling problem in a job shop environment where the objective is to minimize the sum of setup and inventory holding costs while satisfying the demand with no backlogging. To solve this problem, we assume a common cycle for all products and divide the planning horizon into an integer number of identical production cycles. The problem is formulated as a mixed non-linear program which simultaneously determines sequencing, lot sizing and scheduling decisions. Unfortunately, for medium or large problems, the solution of this model may require an excessive amount of computational time. To solve such problems, we propose an adaptation of the simulated annealing algorithm and a tabu search algorithm. Within these two methods, a neighbouring solution is obtained by altering the production sequence of one of the machines. The modified set of sequences is then used as an input to another mixed non-linear program to determine lot sizes and starting dates. Some computational results are given to help assess the performance of the proposed heuristics

The impact of sequencing decisions on multi-item lot sizing and scheduling in flow shops

The problem of sequencing, lot sizing and scheduling a number of products in flow shops has been studied by several authors. It has been reported by some of them that the sequence to be used has a negligible impact on total cost. Consequently, little attention was given to the sequencing sub-problem. The purpose of this paper is to study the impact of sequencing decisions and to suggest some methods to determine the sequence to be used. We propose a mathematical programming based heuristic as well as some construction and local search heuristics. The proposed heuristics are compared and computational results for 360 test problems are reported. These results reveal that sequencing decisions may have a non-negligible impact on total cost and may allow us to identify the best among the heuristics tested

The economic lot scheduling problem under extended basic period and power-of-two policy

10.1007/s11590-009-0154-5Optimization Letters42157-17