Discrete parallel machine makespan ScheLoc problem

Abstract

Scheduling-Location (ScheLoc) Problems integrate the separate fields of scheduling and location problems. In ScheLoc Problems the objective is to find locations for the machines and a schedule for each machine subject to some production and location constraints such that some scheduling objective is minimized. In this paper we consider the Discrete Parallel Machine Makespan (DPMM) ScheLoc Problem where the set of possible machine locations is discrete and a set of n jobs has to be taken to the machines and processed such that the makespan is minimized. Since the separate location and scheduling problem are both NP-hard, so is the corresponding ScheLoc Problem. Therefore, we propose an integer programming formulation and different versions of clustering heuristics, where jobs are split into clusters and each cluster is assigned to one of the possible machine locations. Since the IP formulation can only be solved for small scale instances we propose several lower bounds to measure the quality of the clustering heuristics. Extensive computational tests show the efficiency of the heuristics.

A comparison of evolutionary and simulated annealing algorithms for bi-criteria location-scheduling problem

“…Constraints ( 3) and ( 4) ensure that each job is performed on one position of a single machine in a launched location. The job j assigned to a single machine cannot start before its release date or completion time of the job scheduled to the same machine before j, what ensure constraints (5) and (6).…”

“…The constraint (6) guarantees that the number of launched locations is between 1 and µ. To limit the number of equivalent solutions represented by matrix x, (8) is present.…”

“…I N RECENT years, the location-scheduling problem, referred to as ScheLoc, and its applications have attracted attention of many researchers (see e.g. [3], [5], [6], [10], [15], [20], [22]) The ScheLoc has been considered for the first time in [5]. Then it has been discussed and developed in many works.…”

“…They differ depending on a kind of location area, type and number of machines, criterion evaluating a schedule of jobs, as well as used solution algorithms. A majority of works deals with a discrete area for the deployment of machines where a finite set of available positions for machines is known and given a priori, and a non-empty subset of this set is to be selected, (e.g., [6], [17], [15]). The evaluation of job schedule, noticed in the literature, is based on the makespan C max and the sum of completion times C j (see [21]).…”

Integrated approach in solving parallel machine scheduling and location (ScheLoc) problem

“…While in many scheduling problems, the locations of machines are fixed it is possible to show how to consider location and scheduling problems simultaneously. Obviously, this integrated method enhances the modeling power of scheduling for different real-life problems (Heßler & Deghdak, 2015). Hennes and Hamacher (2002) are believed to be the first who introduced the idea of scheduling and layout planning.…”