We consider the open shop, job shop, and ow shop scheduling problems with integral processing times. We give polynomial-time algorithms to determine if an instance has a schedule of length at most 3, and show that deciding if there is a schedule of length at most 4 is N P-complete. The latter result implies that, unless P = N P, there does not exist a polynomial-time approximation algorithm for...

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.

We consider the ow-shop scheduling problem. The objective is to schedule the jobs on the machines so that we minimize the time by which all jobs are completed. We studied and implemented diierent versions of the algorithm of Sevast'yanov based on linear programming to solve this problem. Using CPLEX, we did computational tests with random instances having up to 1000 jobs and 100 machines. If th...

This paper addresses a multiprocessor generalization of the preemptive open-shop scheduling problem. The set of processors is partitioned into two groups and the operations of the jobs may require either single processors in either group or simultaneously all processors from the same group. We consider two variants depending on whether preemptions are allowed at any fractional time point or onl...

We consider a scheduling problem, which we call the Scheduling and Wavelength Assignment (SWA) problem, arising in optical networks that are based on the Wavelength Division Multiplexing (WDM) technology. We prove that the SWA problem is NP-hard for both the preemptive and the non-preemptive cases. Furthermore, we propose two eÆcient approximation algorithms. The rst is for the preemptive case ...

This paper studies the problem of scheduling Job shops in robotic cells with no intermediate buffers, called No Wait Blocking Transport Job Shop Scheduling Problem (NWBT JSSP). This problem is an extension of the classical job shop problem. No Wait Blocking Transport job shop problems arise in many realistic production environments. To tackle this problem, we developed a Mixed Integer Linear Pr...

This paper studies the problem of scheduling Job shops in robotic cells with no intermediate buffers, called No Wait Blocking Transport Job Shop Scheduling Problem (NWBT JSSP). This problem is an extension of the classical job shop problem. No Wait Blocking Transport job shop problems arise in many realistic production environments. To tackle this problem, we developed a Mixed Integer Linear Pr...

We consider a scheduling problem, which we call the scheduling and wavelength assignment (SWA) problem, arising in optical networks that are based on the wavelength-divisionmultiplexing (WDM) technology. We prove that the SWA problem is -complete for both the preemptive and the nonpreemptive cases. Furthermore, we propose two efficient approximation algorithms. The first is for the preemptive c...