4OR-Q J Oper ResDOI 10.1007/s10288-014-0263-6

PHD THESIS

Combinatorial optimization approaches for multi-partcyclic hoist scheduling problem

Adnen El Amraoui

Received: 30 May 2014© Springer-Verlag Berlin Heidelberg 2014

This is a summary of the author’s PhD thesis, supervised by Marie-Ange Manier,Abdellah El Moudni and Mohamed Benrejeb and defended on 12 July 2011 at the“Université de Technologie de Belfort-Montbéliard”. The thesis is written in Frenchand is available on web (http://www.theses.fr/16144587X). This work deals with thecyclic schedule of hoist activities in automated electroplating lines with a very specificvariant, called the heterogeneous multi-part jobs, where, during a cycle, differentpart jobs have to be treated simultaneously. The objective function of the consideredproblem, commonly labeled: Cyclic Hoist Scheduling Problem (CHSP), consists onthe minimization of the cycle time duration.

In recent years, scheduling problem with transportation resources has gained muchattention in the literature. Despite the differences between the numerous proposedmodels, they all deal with the coordination of material handling devices and classicalproblem scheduling decisions. Several researchers have been interested in the HoistScheduling Problem (HSP) and a large number of mathematical programming modelshave been developed. Nevertheless, the cyclic problem, and more precisely the single-job cyclic schedule was the most studied case in literature due to the strong complexityof the problem, even with a simple line configuration. The physical system of suchproblems, like electroplating lines, is composed of a row of tanks containing chemicalbaths and a handling system. Jobs (e.g. printed circuit board) have to be soaked inseveral baths according to their processing sequences. They are moved from one tankto another by a single hoist, which is moving along the tanks row on a single track. Theprocessing time of each job is confined within a minimum and a maximum durations(called time window). Any delay in it can make the job defective. One of the mainspecificities of such system is that the transport durations cannot be ignored as theirvalues are similar to the processing times.

In this work, the CHSP is presented as a branch steaming of Valued Constraint Sat-isfaction Problems (VCSPs). These problems are characterized by a valued constraintlanguage and a fixed set of cost function on a finite domain. Thus, a precise algebraiccharacterization of the multi-part CHSP problem for some existing line configura-tions in electroplating industry (i.e. multi-tank, multi-function, associated loading-

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unloading buffers) is proposed. This analysis is supported by several elaborated lemmaand theorems. Therefore, for each considered electroplating line configuration, newconstraints and variables bounds are added to the Mixed Integer Linear Programming(MILP) model. Thus, the solution feasibility is guaranteed and the research domainis restricted. Then, the optimal solution is quickly reached. The elaborated modelsare solved using ILOG Cplex Solver of IBM and several examples are considered toillustrate the satisfaction of the considered constraints system.

To solve large sized problems and to reduce the problem complexity by decreasingthe computational time unit, a first heuristic optimizing approach, labelled OptimizedCyclic Multi-Part Earliest Starting Time (OCMPEST), is elaborated. It derives itsoriginality from the fact that the cycle degree is not fixed in advance. The schedule isprogressively built by selecting at each step, a new hoist move operation, accordingto its starting time and resources availability (i.e. tanks and hoist). One of the keyparameter, in the design of a heuristic, is the neighborhood operator. In this sense,a backtrack procedure, which gives priority to the operation with the lowest startingtime, is integrated in the OCMPEST heuristic. This procedure traduces the policyof how the proposed heuristic acts on the dynamic of the search. Moreover, severalMinimum Part Set (MPS) job configurations (i.e. the sequence of how to introducejobs on the line) are considered, in a judicious way. This aims to quickly browsethe search space and find the optimal solution. Nevertheless, to address the problemof non-fixed cycle degree, a new Genetic Algorithm (GA) optimizing approach isproposed with several novelties: direct coding of the schedule, correcting algorithmsand polynomial computing procedure based on graph theory. While, the correctingalgorithms are developed to improve the solutions quality and to reduce the solutioninfeasibility, the polynomial computing procedure is proposed to evaluate the solutioncriteria.

Computational results show the effectiveness of the proposed MILP models. Where,more than 180 benchmark instances from literature (i.e. for lines with ten soaking tanksand two-part jobs) are solved to optimality, in no more than fifteen minutes. Besides,the OCMPEST heuristic shows its effectiveness in comparison with previous existingEarliest Starting Time (EST) heuristic and MILP model, in term of average cycle time.Thus, the following general result has been obtained from these comparisons and hasbeen checked by the GA approach: the cycle degree has a big impact on the problemcomplexity (the bigger it is, the more complex the problem is) but, often the averagecycle time is improved with high degrees.

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