Abstract
Purpose: The aims of this article are to develop a new mathematical formulation and a new heuristic for the problem of preemptive two-agent scheduling in open shops subject to machine maintenance and eligibility constraints. Design/methodology: Using the ideas of minimum cost flow network and constraint programming, a heuristic and a network based linear programming are proposed to solve the problem. Findings: Computational experiments show that the heuristic generates a good quality schedule with a deviation of 0.25% on average from the optimum and the network based linear programming model can solve problems up to 110 jobs combined with 10 machines without considering the constraint that each operation can be processed on at most one machine at a time. In order to satisfy this constraint, a time consuming Constraint Programming is proposed. For n = 80 and m = 10, the average execution time for the combined models (linear programming model combined with Constraint programming) exceeds two hours. Therefore, the heuristic algorithm we developed is very efficient and is in need. Practical implications: Its practical implication occurs in TFT-LCD and E-paper manufacturing wherein units go through a series of diagnostic tests that do not have to be performed in any specified order. Originality/value: The main contribution of the article is to split the time horizon into many time intervals and use the dispatching rule for each time interval in the heuristic algorithm, and also to combine the minimum cost flow network with the Constraint Programming to solve the problem optimally.
Highlights
Consider two agents who have to schedule two sets of jobs on an m-machine open shop
Sedeno-Noda, Pablo and Gonzalez-Martin (2009) extended the same problem by considering performance costs including resource and personnel involvement. This two-agent problem under consideration arises in TFT-LCD and E-Paper manufacturing wherein units go through a series of diagnostic tests that do not have to be performed in any specified order
Cheng and Chou (2013) revised their maximum flow model to the minimum cost flow model for the same problem with makespan and maximum lateness criteria. We further extend their network for the two-agent open shop problem to test the effectiveness of our heuristic algorithm
Summary
Consider two agents who have to schedule two sets of jobs on an m-machine open shop. Each job has k operations, k ≤ m, and each operation must be performed on the corresponding specialized machine. The order in which the operations of each job are performed is irrelevant. Operation preemption is allowed and the machine availability and eligibility constraints are considered. The machine eligibility constraints are imposed when the number of operations of each job i can be less than m. Each machine can handle at most one operation at a time and each operation can be processed on at most one machine at a time. Let n denote the total number of jobs, i.e., n = na + nb, and each job j of agent A (B) is denoted by
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