Carl Esswein

Maximization of solution flexibility for robust shop scheduling

We consider the problem of introducing flexibility in the schedule determination phase, for shop scheduling problems with release dates and deadlines. The flexibility is provided by generating a family of schedules, instead of a unique one. We represent a family of schedules by an ordered group assignment defining for each machine a sequence of groups where the operations within a group are totally permutable. We propose a polynomial time algorithm to evaluate the worst case completion time of operations in an ordered group assignment. We then consider the single machine problem with heads and deadlines associated to operations, as a sub-problem of the job shop problem. We propose polynomial time dynamic programming algorithms for minimizing the number of groups and for maximizing the number of characterized sequences, under specific constraints. Finally, computational experiences on job shop benchmarks, show the impact of grouping operations on the solution makespan value.

Two-machine shop scheduling: Compromise between flexibility and makespan value

In this paper, we consider the problem of providing flexibility to solutions of two-machine shop scheduling problems. We use the concept of group-scheduling to characterize a whole set of schedules so as to provide more choice to the decision-maker at any decision point. A group-schedule is a sequence of groups of permutable operations defined on each machine where each group is such that any permutation of the operations inside the group leads to a feasible schedule. Flexibility of a solution and its makespan are often conflicting, thus we search for a compromise between a low number of groups and a small value of makespan. We resolve the complexity status of the relevant problems for the two-machine flow shop, job shop and open shop. A number of approximation algorithms are developed and their worst-case performance is analyzed. For the flow shop, an effective heuristic algorithm is proposed and the results of computational experiments are reported.

Revisiting Branch and Bound Search Strategies for Machine Scheduling Problems

In the design of exact methods for NP-hard machine scheduling problems, branch and bound algorithms have always been widely considered. In this work we revisit the classic search strategies for branch and bound schemes. We consider a systematic application of the well known dynamic programming dominance property for machine scheduling problems. Several conditions concerning the application of the proposed property with respect to best first, depth first, breadth first search strategies and problem characteristics are presented. Computational testing on single machine and flow shop problems validate in practice the efficiency of the considered approach and suggest that the traditional choice of depth first search with respect to best first and breadth first is strongly questionable.

A Genetic Algorithm For A Bicriteria Flexible Job Shop Scheduling Problem

The problem we consider in this paper is a flexible job shop scheduling problem. The aim is to minimize two criteria: the makespan and the maximum lateness and we are interested in finding an approximation of the Pareto front. The method that we propose is a genetic algorithm. The initial population is partially generated by using a tabu search algorithm which minimizes a linear combination of the two criteria. The method is tested on benchmark instances from literature

Counting and enumeration complexity with application to multicriteria scheduling

Abstract.In this paper we tackle an important point of combinatorial optimisation: that of complexity theory when dealing with the counting or enumeration of optimal solutions. Complexity theory has been initially designed for decision problems and evolved over the years, for instance, to tackle particular features in optimisation problems. It has also evolved, more or less recently, towards the complexity of counting and enumeration problems and several complexity classes, which we review in this paper, have emerged in the literature. This kind of problems makes sense, notably, in the case of multicriteria optimisation where the aim is often to enumerate the set of the so-called Pareto optima. In the second part of this paper we review the complexity of multicriteria scheduling problems in the light of the previous complexity results.

Scheduling batches in flowshop with limited buffers in the shampoo industry

In this paper we address the problem of planning a temporary storage area in a real production system. This temporary storage area is composed of parallel temporary storage units with distinct capacities. The storage operation of a job, also called a batch, has to answer time restrictions such as release dates, due dates, restricted family dependent setup times and time lags, and also a space constraint which is the capacity of the temporary storage unit. The goal is to schedule the batches on the storage units in order to minimize the total setup times and the maximum lateness. First, we model the problem on a single storage unit as a two-machine flowshop problem with a limited buffer capacity and we show that it is NP-hard. We also show that the particular case in which no lateness is allowed is solvable in polynomial time under special conditions on the buffer capacity, both for single or parallel temporary storage units. Next we provide three heuristics: a greedy algorithm, a hybrid heuristic based on Ant Colony Optimization and Simulated Annealing and finally a dedicated heuristic. The latter strongly exploits the structural properties shown in this paper. We provide experimental results which highlight the efficiency of the dedicated heuristic in comparison with the two other heuristics.

Solution Algorithms for Storage Facilities Usage Optimization

Abstract In this work we address the problem of planning a temporary storage area in a shampoo production system. Here, the production process consists of three successive steps: the making, the temporary storage and the packing. This temporary storage area consists of parallel temporary storage units with distinct capacities. The storage operation of a job, also called a batch, has to answer time restrictions such as release dates, due dates, family dependent setup times and time lags, and also a space constraint which is the capacity of the temporary storage unit. The goal is to schedule the batches on the storage units in order to minimize the total setup times and the maximum lateness. First, we model the problem on a single storage unit a two-machine flowshop with a limited buffer capacity. Next we provide three heuristics: a greedy algorithm, a hybrid heuristic based on Ant Colony Optimization and Simulated Annealing and finally a dedicated heuristic. The latter strongly exploits the structural properties shown in this paper. We provide experimental results of the evaluation on wide range instances of these heuristics. The results highlight the efficiency of the dedicated heuristic by comparison to the two others.

A TABU SEARCH ALGORITHM FOR SOLVING A BICRITERIA FLEXIBLE JOB SHOP SCHEDULING PROBLEM

Abstract We consider in this paper a scheduling problem issued from an industrial context. This problem can be seen as a flexible job shop scheduling problem. Solutions are evaluated using two criteria: the makespan and the maximum lateness. We propose a Tabu search algorithm that finds a solution with minimum makespan, respecting a given bound for the maximum lateness. This approach is called the epsilon-constraint approach in multicriteria literature and it can be used for finding the whole set of dominant criteria vectors. The Tabu search algorithm is tested on benchmark instances of the literature and results are discussed.