A Graph-Theoretic Decomposition of the Job Shop Scheduling Problem to Achieve Scheduling Robustness

Abstract

In this paper we study the weighted tardiness job-shop scheduling problem, taking into consideration the presence of random shop disturbances. A basic thesis of the paper is that global scheduling performance is determined primarily by a subset of the scheduling decisions to be made. By making these decisions in an a priori static fashion, which maintains a global perspective, overall performance efficiency can be achieved. Further, by allowing the remaining decisions to be made dynamically, flexibility can be retained in the schedule to compensate for unforeseen system disturbances. We develop a decomposition method that partitions job operations into an ordered sequence of subsets. This decomposition identifies and resolves a “crucial subset” of scheduling decisions through the use of a branch-and-bound algorithm. We conduct computational experiments that demonstrate the performance of the approach under deterministic cases, and the robustness of the approach under a wide range of processing time perturbations. We show that the performance of the method is superior, particularly for low to medium levels of disturbances.

Computational Science and Its Applications – ICCSA 2007

“…We show that the problem of computing the worse completion time of an operation in all feasible semi-active schedules can be done by finding an elementary longest path in the disjunctive graph representing the problem with additional constraints. This gives a general framework integrating previous studies [1,3,5,6,7,12].…”

“…We obtain the 6 schedules displayed in Figure 2. Note that such restriction cannot be modeled by the group of permutable operation representation used in [1,5,6,7,12]. The solution of problem SP is 20 which is the worst-case makespan value of the 6 semi-active schedules.…”

“…Another class of related work in the context of flexibility generation for online scheduling is linked to the concept of groups of permutable operations [5,6], also called ordered group assignment [3,12]. A group of permutable operations is a restriction of the sequential flexibility considered here in such a way that each operation is assigned to a group and, there is a complete order between the groups of operations performed on the same machine.…”

“…This paper addresses the problem of providing more flexibility than the classical temporal one in disjunctive scheduling problems where the objective is to minimize a regular minmax objective function. As already considered in previous studies [2,3,5,6,7,12], this can be achieved by defining only a partial order of the operations on each machine, leaving to the end-user the possibility to make the remaining sequencing decisions. This is the principle of the groups of permutable operations model that has been studied by several authors [3,5,6,7,12].…”

Parallel Machine Scheduling with Uncertain Communication Delays

“…Kouvelis and Yu [13] might be a good introduction. Remark that Wu et al [21] apply to the job shop (criterion: weighted tardiness) ideas similar to those we independently present in this paper, that is fixing off line a partial order among the tasks.…”