PurposeThis paper presents a mixed-integer programming model for a single machine earliness/tardiness scheduling problem where the objective is to minimize total earliness/tardiness duration when the uncertainty of parameters such as processing times and due date is coded with grey numbers.Design/methodology/approachGrey theory and grey numbers are used for illustrating the uncertainty of parameters in processing times and common due date, where the objective is to minimize the total earliness/tardiness duration. The paper proposes a 0–1 mathematical model for the problem and an effective heuristic method for the problem by using expected processing times for ordering jobs.FindingsThe uncertainty of the processing times and common due date are encoded with grey numbers and a position-dependent mixed-integer mathematical programming model is proposed for the problem in order to minimize total grey earliness/tardiness duration of jobs having grey processing times and a common due date. By using expected processing times for ranking grey processing times, V-shaped property of the problem and an efficient heuristic method for the problem are proposed. Solutions obtained from the heuristic method show that the heuristic is effective. The experimental study also reveals that while differences between upper and lower bounds of grey processing times decrease, the proposed heuristic's performance decreases.Originality/valueThe grey theory and grey numbers have been rarely used as machine scheduling problems. Therefore, this study provides an important contribution to the literature.
This paper investigates permutation flow shop scheduling (PFSS) problems under the effects of position-dependent learning and linear deterioration. In a PFSS problem, there are n jobs and m machines in series. Jobs are separated into operations on m different machines in series, and jobs have to follow the same machine order with the same sequence. The PFSS problem under the effects of learning and deterioration is introduced with a mixed-integer nonlinear programming model. The time requirement for solving large-scale problems type of PFSS problem is exceedingly high. Therefore, wellknown metaheuristic methods for the PFSS problem without learning and deterioration effects such as iterated greedy algorithms and discrete differential evolution algorithm are adapted for the problem with learning and deterioration effects in order to find a faster and near-optimal or optimal solution for the problem. Furthermore, this paper proposes a hybrid solution algorithm that is called population-based Tabu search algorithm (TS POP) with evolutionary strategies such as crossover and mutation. The search algorithm is built on the basic structure of Tabu search and it searches for the best candidate from a solution population instead of improving the current best candidate at each iteration. Furthermore, the performances of these methods in view of solution quality are discussed in this paper by using test problems for 20, 50, and 100 jobs with 5, 10, 20 machines. Experimental results show that the proposed TS POP algorithm outperforms the other existing algorithms in view of solution quality.
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