Fast local search for fuzzy job shop scheduling

In the sequel, we propose a new neighbourhood structure for local search for the fuzzy job shop scheduling problem. This is a variant of the well-known job shop problem, with uncertainty in task durations modelled using fuzzy numbers and where the goal is to minimise the expected makespan of the resulting schedule. The new neighbourhood structure is based in changing the relative order of subsequences of tasks within critical blocks. We study its theoretical properties and provide a makespan estimate which allows to select only feasible neighbours while covering a greater portion of the search space than a previous neighbourhood from the literature. Despite its larger search domain, experimental results show that this new structure notably reduces the computational load of local search with respect to the previous neighbourhood while maintaining or even improving solution quality

Metaheuristic strategies for scheduling problems with uncertainty

Scheduling problems have formed an important body of research during the last decades. A scheduling problem consists in scheduling a set of jobs {J1, . . . , Jn} on a set of physical resources or machines {M1, . . . , Mm}. Each job Ji is composed of m tasks or operations {θi1, . . . , θim} with processing time pij . At the same time, we usually have constraints that establish that two task belonging to the same job cannot overlap their execution in time and that each task requires the uninterrupted and exclusive use of one of the machines for its whole processing time. Depending on the additional constraints we define, we may obtain different families of problems. The most popular in the literature are the job shop (JSP), the open shop (OSP) and the flow shop (FSP) but there exists also variants of them as the flexible job shop (FJSP) among others. Commonly, the objective function to optimise is the earliest time in which all jobs can be finished or makespan. However many other objectives may be optimised, being the most popular the tardiness, the idleness and the total flow time. In classical scheduling problems all input data are assumed to be well defined and all constraints are assumed to be hard, which is not so common in real-life applications. To reduce the gap between theory and practice, this thesis focuses on solving scheduling problems considering that uncertainty and vagueness. For instance, we shall consider uncertain task durations as well as flexible due-date constraint

MODELING, OPTIMISATION AND ANALYSIS OF RE-ENTRANT FLOWSHOP JOB SCHEDULING WITH FUZZY PROCESSING TIMES

This paper presents a makespan minimization of -jobs -machines re-entrant flow shop scheduling problem (RFSP) under fuzzy uncertainties using Genetic Algorithm. The RFSP objective is formulated as a mathematical programme constrained by number of jobs and resources availability with traditional scheduling policies of First Come First Serve (FCFS) and the First Buffer First Serve (FBFS). Jobs processing times were specified by fuzzy numbers and modelled using triangular membership function representations. The modified centroid defuzzification technique was used at different alpha-cuts to obtain fuzzy processing times (FPT) of jobs to explore the importance of uncertainty. The traditional GA schemes and operators were used together with roulette wheel algorithm without elitism in the selection process based on job fuzzy completion times. A test problem of five jobs with specified Job Processing and Transit Times between service centres, Job Start Times and Job Due times was posed. Results obtained using the deterministic and fuzzy processing times were compared for the two different scheduling policies, FCFS and FBFS. The deterministic optimal makespan for FBFS schedule was 61.2% in excess of the FCFS policy schedule.  The results also show that schedules with fuzzy uncertainty processing times provides shorter makespans than those for deterministic processing times and those under FCFS performing better than those under FBFS policy for early jobs while on the long run the FBFS policy performs better. The results underscore the need to take account of comprehensive fuzzy uncertainties in job processing times as a trade-off between time and costs influenced by production makespan. http://dx.doi.org/10.4314/njt.v36i3.2