The problem of maximizing the weighted number of just-in-time jobs in a two-machine ‡ow shop scheduling system is known to be NP-hard [4]. However, the question of whether this problem is strongly or ordinary NP-hard remains an open question. We provide a pseudo-polynomial time algorithm to solve this problem, proving that it is NP-hard in the ordinary sense. Moreover, we show how the pseudo-po...

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...