Abstract
In this paper, a new problem of job sequences in a workshop is presented, taking into account non-unit demands for the jobs and whose objective is to minimize the total completion time for all the jobs ({C}_{max}) satisfying a set of restrictions imposed on the problem to preserve the production mix. Two procedures are proposed to solve the new problem: Mixed Integer Linear Programming and a Metaheuristic based on Multistart and Local Search. The two proposed procedures are tested using instance set Nissan-9Eng.I, in both cases giving rise to highly satisfactory performance both in quality of solutions obtained and in the CPU times required. Through a case study of the Nissan engine manufacturing plant in Barcelona, our economic-productive analysis reveals that it is possible to save an average of € 1162.83 per day, manufacturing 270 engines, when we transform the current assembly line into a Heijunka-Flow Shop.
Highlights
The Flow Shop Scheduling Problem (FSP) is a sequencing problem that has received considerable attention from professionals and researchers in recent decades due in part to the wide range of production environments it can model [19]
The main contributions of this work are: (i) description and formulation of a new problem that we call Hejunka − Fm/prmu/Cmax/di ; (ii) design and implementation of a Metaheuristic based on Multistart and Local Search (MS-Q) to solve the new problem; (iii) a computational analysis of MS-Q and Mixed Integer Linear Programming (MILP) (CPLEX solver) performance in CPU time and quality of solutions using real-dimension instances related to case study; and (iv) an economic-productive feasibility study to implement the solutions on a production line
The proposed metaheuristic is based on a Multistart procedure with Local Search similar to Bautista and Alfaro [2]
Summary
The problem of the construction of a Quota sequence, which we will call Quota-Product Rate Variation Problem (Q-PRV), can be formulated as a Binary Linear Programming (BLP) representing maximum constraints satisfaction problem, as follows. To generate Quota sequences in accordance with the Maxsat Q-PRV model, an enumerative deterministic procedure can be designed based on the branching and cutting of partial solutions; in this work we have chosen to use random to promote the diversity of the initial solutions generated in Phase 1, allowing them to belong to different regions of the feasible solutions space Another indirect way of constructing sequences that satisfy all or a large part of the Quota constraints (14) is to determine integer values for the real production variables Xi, t as close as possible to their ideal values it and that, in addition, these values are consistent with the rest of the restrictions of the Maxsat Q-PRV model. The CPU time efficiency of the MAXSAT procedure is higher the lower the number of Quota constraints violated by the initial sequence (T) ; for this reason, the sequences provided by the A1 algorithm are used, since they comply with the Upper Quota property and tend to comply with the Lower Quota property when the values of the admission factor are small
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