Improved Scheduling for the Three-Machine Proportionate Open Shop and Mixed Shop Minimum Makespan Problems

Abstract

Open shop scheduling problems have many practical applications, in which the jobs can be in any order with the only restriction that their durations do not overlap with each other. In some cases, the order of a subset of jobs dictates the flow shop model while the remaining jobs can be processed in any order according to the open shop model, and the corresponding problem is called mixed shop scheduling. For every job, if its processing times on all machines are the same, then the shop is called proportionate shop. In this paper we investigate the three-machine proportionate open shop and mixed shop minimum makespan problems proposed by Koulamas and Kyparisis. Our result improves the previous work in three ways. First, for both the open shop and the mixed shop scheduling problems, we derive additional sufficient conditions under which the corresponding problems are solvable in polynomial time. Second, for the non-solvable cases of the open shop scheduling problem we present an improved 13/12-approximation algorithm. Third, for the non-solvable cases of the mixed shop scheduling problem we present an improved approximation algorithm with the worst-case ratio bound of (7/6 +). All the algorithms proposed in this paper run in polynomial time. INDEX TERMS scheduling; open shop; mixed shop; proportionate shop; minimum makespan

Random-guided optimizer: a metaheuristic that shifts random search to guided search through iteration

“…According to (3), the selected unit is picked randomly from the population. In (4) states that the candidate is generated by moving the corresponding unit toward or surpassing the selected unit only if this selected unit is better than the corresponding unit. If not, the candidate is formed between the selected unit and the virtual unit that is distinct from the unit corresponding to the selected unit.…”

“…Optimization is a famous and essential study. Its importance and popularity make optimization has been implemented in many areas, such as in computing system [1], transportation [2], mobile communication [3], production and manufacturing [4], healthcare [5], power system [6], home appliance [7], and so on. In production and manufacture, some study need optimization, such as in flow shop scheduling in multi factory environment [8], nozzle assignment in printed circuit board assembly [9], and job assignment in manufacture where there are several parallel machines [10], and so on.…”