Approximation algorithms for solving multi-objective optimization problems

This paper tries to cover the main aspects/properties related to scheduling problems, approximation algorithms, and multi-objective combinatorial optimization. Then, we try to describe the main techniques that can be used to solve such problems. In this paper, the reviews results relate to multi-objective optimization problems, exact and approximation search, with the aim of getting all Pareto optimal solutions for some NP-hard problems

Extended classification for flowshops with resequencing

Este trabajo presenta una clasificación extendida de líneas de flujo no-permutación. Se consideran las múltiples opciones que se presentan al incluir la posibilidad de resecuenciar piezas en la línea. Se ha visto que en la literatura actual no se ha clasificado con profundidad este tipo de producción. Abstract This paper presents an extended cassification for non-permutation flowshops. The versatile options which occur with the possibility of resequencing jobs within the line are considered. The literature review shows that no classification exists which considers extensively this type of flowshop

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Two-machine flowshop scheduling with flexible operations and controllable processing times

Ankara : The Department of Industrial Engineering and the Graduate School of Engineering and Science of Bilkent University, 2011.Thesis (Master's) -- Bilkent University, 2011.Includes bibliographical references leaves 77-84.In this study, we consider a two-machine flowshop scheduling problem with identical jobs. Each of these jobs has three operations, where the first operation must be performed on the first machine, the second operation must be performed on the second machine, and the third operation (named as flexible operation) can be performed on either machine but cannot be preempted. Highly flexible CNC machines are capable of performing different operations as long as the required cutting tools are loaded on these machines. The processing times on these machines can be changed easily in albeit of higher manufacturing cost by adjusting the machining parameters like the speed of the machine, feed rate, and/or the depth of cut. The overall problem is to determine the assignment of the flexible operations to the machines and processing times for each job simultaneously, with the bicriteria objective of minimizing the manufacturing cost and minimizing makespan. For such a bicriteria problem, there is no unique optimum but a set of nondominated solutions. Using ǫ constraint approach, the problem could be transformed to be minimizing total manufacturing cost objective for a given upper limit on the makespan objective. The resulting single criteria problem is a nonlinear mixed integer formulation. For the cases where the exact algorithm may not be efficient in terms of computation time, we propose an efficient approximation algorithm.Uruk, ZeynepM.S

Efficient Heuristics for Scheduling Tasks on a Flo Shop Environment to Optimize Makespan

In modern manufacturing the trend is the development of Computer Integrated Manufacturing, CIM technologies which is a computerized integration of manufacturing activities (Design, Planning, Scheduling and Control) produces right products at right time to react quickly to the global competitive market demands. The productivity of CIM is highly depending upon the scheduling of Flexible Manufacturing System (FMS). Shorting the make span leads to decreasing machines idle time which results improvement in CIM productivity. Conventional methods of solving scheduling problems based on priority rules still result schedules, sometimes, with significant idle times. To optimize these, this paper model the problem of a flow shop scheduling with the objective of minimizing the makes pan. The work proposed here deal with the production planning problem of a flexible manufacturing system. This paper model the problem of a flow shop scheduling with the objective of minimizing the makes pan. The objective is to minimize the make span of batch-processing machines in a flow shop. The processing times and the sizes of the jobs are known and non-identical. The machines can process a batch as long as its capacity is not exceeded. The processing time of a batch is the longest processing time among all the jobs in that batch. The problem under study is NP-hard for makespan objective. Consequently, comparison based on Gupta’s heuristics, RA heuristic’s, Palmer’s heuristics, CDS heuristics are proposed in this work. Gantt chart was generated to verify the effectiveness of the proposed approaches

A common framework and taxonomy for multicriteria scheduling problems with Interfering and competing Jobs: Multi-agent scheduling problems

Most classical scheduling research assumes that the objectives sought are common to all jobs to be scheduled. However, many real-life applications can be modeled by considering different sets of jobs, each one with its own objective(s), and an increasing number of papers addressing these problems has appeared over the last few years. Since so far the area lacks a uni ed view, the studied problems have received different names (such as interfering jobs, multi-agent scheduling, mixed-criteria, etc), some authors do not seem to be aware of important contributions in related problems, and solution procedures are often developed without taking into account existing ones. Therefore, the topic is in need of a common framework that allows for a systematic recollection of existing contributions, as well as a clear de nition of the main research avenues. In this paper we review multicriteria scheduling problems involving two or more sets of jobs and propose an uni ed framework providing a common de nition, name and notation for these problems. Moreover, we systematically review and classify the existing contributions in terms of the complexity of the problems and the proposed solution procedures, discuss the main advances, and point out future research lines in the topic

Overview on: sequencing in mixed model flowshop production line with static and dynamic context

In the present work a literature overview was given on solution techniques considering basic as well as more advanced and consequently more complex arrangements of mixed model flowshops. We first analyzed the occurrence of setup time/cost; existing solution techniques are mainly focused on permutation sequences. Thereafter we discussed objectives resulting in the introduction of variety of methods allowing resequencing of jobs within the line. The possibility of resequencing within the line ranges from 1) offline or intermittent buffers, 2) parallel stations, namely flexible, hybrid or compound flowshops, 3) merging and splitting of parallel lines, 4) re-entrant flowshops, to 5) change job attributes without physically interchanging the position. In continuation the differences in the consideration of static and dynamic demand was studied. Also intermittent setups are possible, depending on the horizon and including the possibility of resequencing, four problem cases were highlighted: static, semi dynamic, nearly dynamic and dynamic case. Finally a general overview was given on existing solution methods, including exact and approximation methods. The approximation methods are furthermore divided in two cases, know as heuristics and methaheuristic

Minimizing the sum of flow times with batching and delivery in a supply chain

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The aim of this thesis is to study one of the classical scheduling objectives that is of minimizing the sum of flow times, in the context of a supply chain network. We consider the situation that a supplier schedules a set of jobs for delivery in batches to several manufacturers, who in tum have to schedule and deliver jobs in batches to several customers. The individual problem from the viewpoint of supplier and manufacturers will be considered separately. The decision problem faced by the supplier is that of minimizing the sum of flow time and delivery cost of a set of jobs to be processed on a single machine for delivery in batches to manufacturers. The problem from the viewpoint of manufacturer is similar to the supplier's problem and the only difference is that the scheduling, batching and delivery decisions made by the supplier define a release date for each job, before which the manufacturer cannot start the processing of that job. Also a combined problem in the light of cooperation between the supplier and manufacturer will be considered. The objective of the combined problem is to find the best scheduling, batching, and delivery decisions that benefit the entire system including the supplier and manufacturer. Structural properties of each problem are investigated and used to devise a branch and bound solution scheme. Computational experience shows significant improvements over existing algorithms and also shows that cooperation between a supplier and a manufacturer reduces the total system cost of up to 12.35%, while theoretically the reduction of up to 20% can be achieved for special cases

Bi-Criteria Batching and Scheduling in Hybrid Flow Shops

In this research, a bi-criteria batching and scheduling problem is investigated in hybrid flow shop environments, where unrelated-parallel machines are run simultaneously with different capacities and eligibilities in processing, in some stages. The objective is to simultaneously minimize a linear combination of the total weighted completion time and total weighted tardiness. The first favors the producer’s interest by minimizing work-in-process inventory, inventory holding cost, and energy consumption as well as maximizing machine utilization, while the second favors the customers’ interest by maximizing customers’ service level and delivery speed. In particular, it disregards the group technology assumptions (GTAs) by allowing for the possibility of splitting pre-determined groups of jobs into inconsistent batches in order to improve the operational efficiency. A comparison between the group scheduling and batch scheduling approaches reveals the outstanding performance of the batch scheduling approach. As a result, contrary to the GTAs, jobs belonging to a group might be processed on more than one machine as batches, but not all machines may be capable of processing all jobs. A sequence- and machine-dependent setup time is required between each of two consecutively scheduled batches belonging to different groups. Based on manufacturing company policy, the desired lower bounds on batch sizes are considered for the number of jobs assigned to batches. Although, the direction in which all jobs move through production line is the same, some jobs may skip some stages. Furthermore, to reflect real industry requirements, the job release times and the machine availability times are considered to be dynamic, which means not all machines and jobs are available at the beginning of the planning horizon.The problem is formulated with the help of four mixed-integer linear programming (MILP) models. Two out of four MILP models are formulated as two integrated phases, i.e., batching and scheduling phases, with respect to the precedence constraints between each pair of jobs batches and or the position concept within batches. The optimal combination between batch compositions of groups are determined in the batching phase, while the optimal assignment and sequence of batches on machines and sequence of jobs within batches are determined in the scheduling phase, with respect to a set of operational constraints. A batch composition of a group corresponding to a particular stage, determined in the batching phase of the MILP model, represents the number of batches assigned to the group as well as the number and type of jobs belonging to each batch of that group. Since the first and second MILP models lead to unmanageable solution space, the relaxed MILP model, which allocates one and only one job to each batch of each group in each stage, can be developed to focus on the non-dominated solution space. The optimal solutions of MILP models and relaxed MILP model are equal, if and only if the optimal solution of the relaxed MILP model does not violate the desired lower bounds on batch sizes. Since the relaxed MILP model cannot guarantee the optimal solution of the MILP models, a third MILP model is developed by integrating batching and scheduling phases. This MILP model eliminates an exhaustive combination enumeration between batch compositions of all groups in all stages. Although the third MILP model converges to the optimal solution slower than the relaxed MILP model, it guarantees finding the optimal solution of the first and second MILP models. A comparison between four MILP models shows the superior performance of the third MILP model. However, since the problem is strongly NP-hard, it is not possible to find its optimal solution within a reasonable time as the problem size increases from small to medium to large, even by the relaxed MILP model or the fourth MILP model. Therefore, several meta-heuristic algorithms based upon basic local search, basic population-based search, and hybridization of local search and population-based searches are developed, which move back and forth between batching and scheduling phases. Tabu Search (TS) is implemented as a basic local search algorithm, while Tabu Search Path-Relinking (TS PR) is implemented as a local search algorithm enhanced with a population-based structure. TS is incorporated into the framework of path-relinking to exploit the information on good solutions. The TS PR algorithm comprises several distinguishing features including relinking procedures to effectively explore trajectories connecting elite solutions and the methods used to choose the reference solution. Particle Swarm Optimization (PSO) is implemented as a basic population-based algorithm, while Particle Swarm Optimization enhanced with a local search algorithm (PSO LSA) is developed to realize the benefits of batching and, consequently, enhance the quality of solutions.Since there is interdependency between positions of a job in different stages of a hybrid flow shop in batch scheduling, a meta-heuristic algorithm is not capable of capturing these interdependencies and, subsequently, its efficacy can be diminished. In order to capture this interdependency, the non-, partial- complete-, and stage-based interdependency strategy are developed. In the stage-based-interdependency strategy, a complete sequence related to all of the stages is gradually determined, stage by stage. An initial solution finding mechanism is developed to trigger the search into the solution space and generate an initial population. The performances of these algorithms are compared to each other in order to identify which algorithm(s) outperforms the others. Nevertheless, the performances of the best algorithm(s) are evaluated with respect to a tight lower bound obtained from a branch-and-price (B&P) algorithm. The B&P algorithm uses Dantzig-Wolfe decomposition (DWD) to divide the original problem into a master problem and several sub-problems (SPs) corresponding to each stage. The original problem is decomposed into the SPs by three DWDs corresponding to the three MILP models. Although, by applying DWD technique in the first and second MILP models, an exhaustive combination enumeration between batch compositions of all groups in all stages is excluded and, as a result, the SPs are easier to solve than the original problem, they are still strongly NP-hard because of an enormous number of combinations between batch compositions of all groups in each stage. However, the DWD technique corresponding to the relaxed MILP model not only drastically reduces the number of variables and constraints in the SPs, but also eliminates the batching phase of the first and second MILP models. Decomposing the original problem based on the relaxed MILP model and implementing the B&P algorithm cannot guarantee optimal solutions or tight lower bounds of problems unless the number of violations in the desired lower bounds on batch sizes is not significant. Therefore, the third MILP model is decomposed by DWD so that the B&P algorithm is capable of finding tight lower bounds even for large-size instances of the problem. A comparison between the lower bounds obtained from the B&P algorithm and CPLEX reveals the impressive performance of the B&P algorithm, particularly for large-size problems. The evaluation of the best algorithms based upon these tight lower bounds developed by the B&P algorithm, uncovers the outstanding performance of hybrid algorithms compared to the results obtained from CPLEX.Keywords: Bi-Criteria Objective, Column Generation, Batch Scheduling, Tabu Search, Batching and Scheduling, Desired Lower Bounds on Batch Sizes, Path-Relinking, Branch-and-Price Optimization Algorithm, Particle Swarm Optimization, Group Scheduling, Hybrid Flow Shop, Dantzig-Wolfe Decomposition, Mixed-Integer Linear Programming Model, Sequence- and Machine-Dependent Setup Tim