Procedural Optimization Models for Multiobjective Flexible JSSP

Abstract

The most challenging issues related to manufacturing efficiency occur if the jobs to be sched-uled are structurally different, if these jobs allow flexible routings on the equipments and mul-tiple objectives are required. This framework, called Multi-objective Flexible Job Shop Scheduling Problems (MOFJSSP), applicable to many real processes, has been less reported in the literature than the JSSP framework, which has been extensively formalized, modeled and analyzed from many perspectives. The MOFJSSP lie, as many other NP-hard problems, in a tedious place where the vast optimization theory meets the real world context. The paper brings to discussion the most optimization models suited to MOFJSSP and analyzes in detail the genetic algorithms and agent-based models as the most appropriate procedural models.Keywords: JSSP, Multiobjective, Optimization, Genetic Algorithm, Agent-Based Model1 IntroductionOptimization is a requirement for a very wide spectrum of real world applications. Regarding the theory of optimization, this is very well developed in certain areas (such as linear programming and, generally speaking, exact methods), but still an open research topic in other areas (as heuristic approaches). Whatever the theoretical method chosen to solve a certain class of real problem, an op-timization model for that context is initially needed. For many problems, it is implicitly included in the optimization method and practitioners do not handle it as a separate stage in problem solving.An optimization model has three compo-nents: variables, objective(s) and constraints and, based on these and problem specific in-put data it generates as output optimal values for the variables and the associated objective value(s). In other words, an optimization model recommends actions to obtain the best solution(s); it is an optimization prescription.Optimization models have many advantages and limits as well. We could mention here a more or less rigidity in model the reality, an inherent simplification of reality (selection over all the actual interacting factors), difficulties in best specification the objective function, partial parameter accuracy, omit-ting delays in the complex systems, biases of the modeler, time pressure constraints, model simplifying, assumption adopted when ap-proaching the complex systems [1], [2]. All these emerge when the optimization theory meet the real world context. A very good support in this direction is [3], where an en-gineering point of view of optimization theo-ry is presented. A possible solution could be the usage of a two level repetitive simulation to obtain suboptimal but feasible solutions [4].In manufacturing, the most critical optimiza-tion aspect is time efficiency. Around this concept, for the manifold production contexts various scheduling problems frameworks were designed: flow shop scheduling, job shop scheduling, open shop scheduling [5], [6], [7].A Job Shop Scheduling Problem (JSSP) states that a finite set of heterogeneous jobs composed by many operations have to be op-timally scheduled on a set of finite machines (resources) such that the precedence con-straint, the non-preemption constraint and the resource capacity constraint are satisfied. This means that operations of every job must be processed in a predetermined order, every operation must not be interrupted and a ma-chine processes only an operation at a time. The objective is to minimize the make span for the entire set of jobs. The output of the JSSP is therefore a time-optimal allocation of the limited machines to the operations of jobs, named optimal schedule. The most part of theoretical and practical background in JSSP concerns the non-flexible uniobjective condition [8], [9], [10].If moreover the routes of the jobs on the re-sources are flexible, or the structure of the jobs varies, or the resource set varies during the scheduling, Flexible JSSP (FJSSP) is the right framework to use [11]. …