- In this research, the comparative performance of permutation and non-permutation schedules is investigated in an assembly flow shop (AFS) with shift production, where a limited buffer storage is available between two machines. Most of the traditional scheduling problems consider continuous production, i.e., production occurs for 24 hours (3 * 8-hour shifts) each day, seven days a week. However, some companies operate only one or two shifts each day, which creates a limited availability constraint on the machines. This causes a discontinuity in production between end and start of two successive production days. To mimic real-life industry practice, dynamic job release and dynamic machine availability times have been considered. Each job considered in a problem can have different weight assigned based on customers’ preferences. The setup times between jobs are assumed to be machine- and sequence-dependent. However, at the start of each production day, setup times are not sequence-dependent but depend on machine startup times such as preheating time, pressure build up, etc. The objective of the problem is to minimize the linear combination of total setup time and weighted tardiness. The minimization of total setup time represents producer’s interest whereas the minimization of weighted tardiness represents customers’ interest. Since these two objectives are not evaluated on a commensurate basis, a normalization factor is used.
The problem is formulated as a mixed-integer linear programming (MILP) model, MILP-1 for permutation schedules and MILP-2 for non-permutation schedules. The MILP models for small-size problem instances are solved to optimality using CPLEX. However, the problem is shown to be NP-hard. As a result, it is not possible to find an optimal solution within a reasonable time, as the problem size increases. Hence, a meta-heuristic search algorithm based on short-term Tabu Search (TS) and Tabu Search/Path-Relinking (TS/PR) are developed. TS represents a local search algorithm, whereas TS/PR represents a hybridization of local search enhanced with population-based search algorithm. Two algorithms each, are developed for both, permutation (PN) and non-permutation (NPN) sequences. One of the algorithms is based on short term TS and the other is based on TS/PR. The developed heuristics are tested on sixteen small-size problems and their solution quality are compared with the optimal solution obtained from CPLEX. The evaluations show that the developed heuristics obtain good quality solutions within much less computational time. For PN sequence, the best algorithm obtained an average deviation of 0.49% compared with the optimal solution and for NPN sequence, the deviation is 0.13%. In addition, a slight improvement of 2.68% was obtained by adopting an NPN sequence over PN sequence for these problem instances.
A statistical designed experiment is conducted to evaluate the difference in performance of the developed heuristics, and permutation and non-permutation schedules. The results show that the TS/PR algorithms outperform short-term TS, in the case of both PN and NPN sequences. The comparison between the solutions from the best PN algorithm and the best NPN algorithm shows that an average improvement of 1.64% is obtained by implementing an NPN sequence over PN sequence. The statistical analysis shows that the improvement offered by NPN sequence is statistically significant for problems with large number of product types and small number of jobs in each product. In addition, it is also shown that the NPN sequence performs better for non-continuous production as compared to continuous production. The efficiency of the algorithms was analyzed using the computational time required by the algorithms. The results show that PN algorithms require a significantly less computational time as compared to NPN algorithms. Hence, it is recommended that NPN sequences be considered only for the problems with large number of product types and small number of jobs in each product. For other problems, only PN sequence should be considered. TS/PR algorithm is recommended for both, PN and NPN sequences.