Two-machine flow shop with dynamic storage space

The publications on two-machine flow shop scheduling problems with job dependent storage requirements, where a job seizes a portion of the storage space for the entire duration of its processing, were motivated by various applications ranging from supply chains of mineral resources to multimedia systems. In contrast to the previous publications that assumed that the availability of the storage space remains unchanged, this paper is concerned with a more general case when the availability is a function of time. It strengthens the previously published result concerning the existence of an optimal permutation schedule, shows that the variable storage space availability leads to the NP-hardness in the strong sense even for unit processing times, and presents a polynomial-time approximation scheme together with several heuristic algorithms. The heuristics are evaluated by means of computational experiments.

Minimizing Makespan in Permutation Flow Shop Scheduling with Proportional Deterioration

The [Formula: see text]-job and [Formula: see text]-machine permutation flow shop scheduling problem with a proportional deterioration is considered in which all machines process the jobs in the same order, i.e., a permutation schedule. A proportional deterioration means that the job deterioration as an increasing function that is proportional to a linear function of time. The objective is to minimize the makespan, i.e., the maximum completion time. When some dominant relationships between [Formula: see text] machines can be satisfied, we show that some special cases of the problem can be polynomial solvable. For the general case, we also propose a heuristic algorithm and give the computational experiments.

A Novel Non-Decreasing Temperature Based Simulated Annealing for Flow Shop Problems

The permutation flow shop problem (PFSP) is an NP-hard permutation sequencing scheduling problem, many meta-heuristics based schemes have been proposed for finding near optimal solutions. A simple insertion simulated annealing (SISA) scheme consisting of two phases is proposed for solving PFSP. First, to reduce the complexity, a simple insertion local search is conducted for constructing the solution. Second, to ensure continuous exploration in the search space, two non-decreasing temperature control mechanisms named Heating SA and Steady SA are introduced in a simulated annealing (SA) procedure. The Heating SA increases the exploration search ability and the Steady SA enhances the exploitation search ability. The most important feature of SISA is its simple implementation and low computation time complexity. Experimental results are compared with other state-of-the-art algorithms and reveal that SISA is able to efficiently yield good permutation schedule.

Solving a Real-World Problem Using an Evolving Heuristically Driven Schedule Builder

This work addresses the real-life scheduling problem of a Scottish company that must produce daily schedules for the catching and transportation of large numbers of live chickens. The problem is complex and highly constrained. We show that it can be successfully solved by division into two subproblems and solving each using a separate genetic algorithm (GA). We address the problem of whether this produces locally optimal solutions and how to overcome this. We extend the traditional approach of evolving a “permutation + schedule builder” by concentrating on evolving the schedule builder itself. This results in a unique schedule builder being built for each daily scheduling problem, each individually tailored to deal with the particular features of that problem. This results in a robust, fast, and flexible system that can cope with most of the circumstances imaginable at the factory. We also compare the performance of a GA approach to several other evolutionary methods and show that population-based methods are superior to both hill-climbing and simulated annealing in the quality of solutions produced. Population-based methods also have the distinct advantage of producing multiple, equally fit solutions, which is of particular importance when considering the practical aspects of the problem.