We consider the open shop scheduling problem with uncertain durations modelled as fuzzy numbers. We define the concepts of necessary and possible β-robustness of schedules and set as our goal to maximise them. Additionally, we propose to assess solution robustness by means of Monte Carlo simulations. Experimental results using a genetic algorithm illustrate the proposals.

In this paper we consider a generalized version of the classical preemptive open shop problem with sum of weighted job completion times objective. The main result is a (2 + ε)-approximation algorithm for this problem. In the last section we also discuss the possibility of improving our algorithm.

This paper aims to prove the efficiency of an adapted computationally intelligence-based behavior of cats called the cat swarm optimization algorithm, that solves the open shop scheduling problem, classified as NP-hard which its importance appears in several industrial and manufacturing applications. The cat swarm optimization algorithm was applied to solve some benchmark instances from the lit...

In this paper, a new approach to overlapping operations in job shop scheduling is presented. In many job shops, a customer demand can be met in more than one way for each job, where demand determines the quantity of each finished job ordered by a customer. In each job, embedded operations can be performed due to overlapping considerations in which each operation may be overlapped with the other...

One of the main restrictions in scheduling problems are the machine (resource) restrictions: each machine can perform at most one job at a time. We explore machine dependencies is shop scheduling problems representing them as graphs. Our study shows that the structure of machine dependency graphs is important in the complexity analysis of shop scheduling problems. We call acyclic a shop schedul...

We can reformulate a vehicle routing problem (VRP) as an open shop scheduling problem (SSP) by representing visits as activities, vehicles as resources on the factory floor, and travel as set up costs between activities. In this paper we present two reformulations: from VRP to open shop, and the inverse, from SSP to VRP. Not surprisingly, VRP technology performs poorly on reformulated SSP’s, as...

in this paper, an exact geometric algorithm is presented for solving two-job sequencing and scheduling problems in flexible flow shop and job shop environments while the resources are (un)available in some time periods and processors (un)availability is the same in all work centers. this study seems utterly new and it is applicable to any performance measure based on the completion time. the in...

In this paper we study both the nonpreemptive and preemptive versions of the popular unit-time open shop scheduling problem. For the set of feasible schedules, we construct the linear description of the convex hull of the vectors of the job completion times. Based on the properties of the resulting scheduling polyhedron, we show that the problem of constructing an optimal schedule minimizing an...

The concept of irreducibility in shop scheduling problems withdifferent objectives has proven one of the most fertile research topics as theset of all irreducible sequences in a given shop contains at least one optimalsequence for arbitrary processing times. Recently, a number of equivalent for-mulations of the reducibility in open-shop problem with Makespan objectivesare pr...

The general job-shop scheduling problem is known to be extremely hard. We describe a GA approach which produces reasonably good results very quickly on standard benchmark job-shop scheduling problems, better than previous eeorts using genetic algorithms for this task, and comparable to existing conventional search-based methods. The representation used is a variant of one known to work moderate...