Permutation based decision making under fuzzy environment using Tabu search

One of the techniques, which are used for Multiple Criteria Decision Making (MCDM) is the permutation. In the classical form of permutation, it is assumed that weights and decision matrix components are crisp. However, when group decision making is under consideration and decision makers could not agree on a crisp value for weights and decision matrix components, fuzzy numbers should be used. In this article, the fuzzy permutation technique for MCDM problems has been explained. The main deficiency of permutation is its big computational time, so a Tabu Search (TS) based algorithm has been proposed to reduce the computational time. A numerical example has illustrated the proposed approach clearly. Then, some benchmark instances extracted from literature are solved by proposed TS. The analyses of the results show the proper performance of the proposed method

Adjusted permutation method for multiple attribute decision making with meta-heuristic solution approaches

The permutation method of multiple attribute decision making has two significant deficiencies: high computational time and wrong priority output in some problem instances. In this paper, a novel permutation method called adjusted permutation method (APM) is proposed to compensate deficiencies of conventional permutation method. We propose Tabu search (TS) and particle swarm optimization (PSO) to find suitable solutions at a reasonable computational time for large problem instances. The proposed method is examined using some numerical examples to evaluate the performance of the proposed method. The preliminary results show that both approaches provide competent solutions in relatively reasonable amounts of time while TS performs better to solve APM

Scheduling flow lines with buffers by ant colony digraph

This work starts from modeling the scheduling of n jobs on m machines/stages as flowshop with buffers in manufacturing. A mixed-integer linear programing model is presented, showing that buffers of size n - 2 allow permuting sequences of jobs between stages. This model is addressed in the literature as non-permutation flowshop scheduling (NPFS) and is described in this article by a disjunctive graph (digraph) with the purpose of designing specialized heuristic and metaheuristics algorithms for the NPFS problem. Ant colony optimization (ACO) with the biologically inspired mechanisms of learned desirability and pheromone rule is shown to produce natively eligible schedules, as opposed to most metaheuristics approaches, which improve permutation solutions found by other heuristics. The proposed ACO has been critically compared and assessed by computation experiments over existing native approaches. Most makespan upper bounds of the established benchmark problems from Taillard (1993) and Demirkol, Mehta, and Uzsoy (1998) with up to 500 jobs on 20 machines have been improved by the proposed ACO

Non-permutation flowshop scheduling in a supply chain with sequence-dependent setup times

In this paper, we consider a flowshop scheduling problem with sequence-dependent setup times and a bicriteria objective to minimize the work-in-process inventory for the producer and to maximize the customers' service level. The use of a bicriteria objective is motivated by the fact that successful companies in today's environment not only try to minimize their own cost but also try to fulfill their customers' need. Two main approaches, permutation and non-permutation schedules, are considered in finding the optimal schedule for a flowshop. In permutation schedules the sequence of jobs remains the same on all machines whereas in non-permutation schedule, jobs can have different sequence on different machines. A linear mathematical model for solving the non-permutation flowshop is developed to comply with all of the operational constraints commonly encountered in the industry, including dynamic machine availabilities, dynamic job releases, and the possibility of jobs skipping one or more machines, should their operational requirements deem that it was necessary. As the model is shown to be NP-hard, a metasearch heuristic, employing a newly developed concept known as the Tabu search with embedded progressive perturbation (TSEPP) is developed to solve, in particular, industry-size problems efficiently. The effectiveness and efficiency of the search algorithm are assessed by comparing the search algorithmic solutions with that of the optimal solutions obtained from CPLEX in solvable small problem instances.Keywords: Sequence-dependent setup time, Mixed-integer linear programming, Non-permutation scheduling, Flowshop, Tabu search with embedded progressive perturbations, Bicriteri

Diseño y desarrollo de estructuras de planificación eficientes a través de técnicas de simulación y optimización aplicables a entornos productivos complejos

La tesis aborda problemas de secuenciamiento en entornos productivos del tipo flow shop en los que se retira la condición de ordenamientos permutativos. Este tipo de problemas se encuentran inmersos dentro de los sistemas de Planificación y Control de la Producción que dan soporte en la toma de decisiones a las organizaciones o empresas que producen bienes del tipo manufactura. Como primera aproximación al problema se presenta una revisión exhaustiva de la literatura científica sobre problemas flow shop no permutativos (NPFS). De esta forma se pudo enmarcar la tesis doctoral en la literatura de la temática y se definió concretamente la contribución a la literatura del tema. Como resultado del estudio de la literatura se planteó abordar los problemas NPFS desde una perspectiva que permitiera estudiar la estructura de las soluciones para así poder compararlos con los resultados de los problemas flow shop permutativos (PFS). Primeramente, se propuso estudiar los problemas NPFS con makespan como función objetivo bajo un nuevo enfoque de planificación. Para ello se utilizará la metodología de lotes de transferencia o lot streaming, la cual modifica el problema clásico de secuenciamiento incorporando nuevas variables de decisión al problema a optimizar. Las nuevas variables de decisión van asociadas al dimensionamiento del tamaño del lote de producción. Este estudio reportó resultados para NPFS y PFS bastante similares, aunque el caso NPFS obtuvo leves mejoras para las instancias más grandes. No obstante, el esfuerzo computacional requerido para resolver el caso NPFS fue considerablemente mayor que requerido para PFS. A partir de estos resultados, se planteó un estudio conceptual de las soluciones NPFS y PFS para el caso de dos trabajos en términos de caminos críticos (conjunto de actividades que definen el makespan) que posibilitaron caracterizar ambos conjuntos de soluciones de forma no-paramétrica, es decir, independizarse de los parámetros que definen un escenario. De este estudio de caminos críticos, se pudieron analizar una serie de propiedades y definir criterios de dominancia entre las soluciones NPFS y PFS que permitirían reducir el espacio factible. A su vez, el estudio no-paramétrico permitió realizar una serie experimentaciones computacionales innovadoras, que dieron sustento al desarrollo de algunas hipótesis sobre la relación de las soluciones NPFS y PFS para el caso de que los problemas sean evaluados en escenarios paramétricamente definidos. Para evaluar estas hipótesis se implementaron experimentaciones paramétricas a través de programación matemática, las cuales validaron las hipótesis planteadas.This dissertation focuseson non-permutation scheduling problems in flow shop production settings. These problems, proper of systems of Production Planning and Control, are central to the decision making processes in organizations or firms producing manufactured goods. A first look into these problems requires a thorough review of the scientific literature on non-permutation flow shop (NPFS) problems. This review provides a background on this issue and defines precisely the contribution of this thesis to the literature. A novel and interesting approach to address NPFS problems is by studying the structure of the solutions, comparing it to the corresponding structure of permutation flow shop (PFS) problems. In this light, we study NPFS problems where makespan is minimized considering a special planning technique involving lot streaming. This technique modifies the regular scheduling problem adding new decision variables, related to production lot sizing. From the implementation of lot streaming on these problems we obtain new results. The main conclusion is that the makespans of NPFS and PFS problems are quite similar, although NPFS yields a better makespan for larger instances. The computational effort required by NPFS problems is much larger than that of solving PFS ones. Up from these results, we develop a new approach to the analysis of solutions to NPFS and PFS problems. We center on the two jobs case, and on the concept of critical path (enumerating the set of activities that defines makespan). This allows the non-parametric characterization of the solutions, freeing them from the dependence on particular parameters. We analyze a family of propertiesthat yield dominance criteria for the comparison between NPFS and PFS solutions, reducing, in general, the number of feasible solutions. In addition, this non-parametric method allows the design of novel computational experimental frameworks, yielding newinsights on the relation between NPFS and PFS solutions for parametric scenarios. To assess these hypotheses, we obtain via an application of mathematical programming a set of parametric results that we test in experiments that confirm the aforementioned hypotheses.Fil: Rossit, Daniel Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

Bi-criteria Scheduling in an Assembly Flow Shop with Limited Buffer Storage and Shift Production

In this research, the comparative performance of permutation and non-permutation schedules is investigated in an assembly flow shop (AFS) with shift production, where a limited buffer storage is available between two machines. Most of the traditional scheduling problems consider continuous production, i.e., production occurs for 24 hours (3 * 8-hour shifts) each day, seven days a week. However, some companies operate only one or two shifts each day, which creates a limited availability constraint on the machines. This causes a discontinuity in production between end and start of two successive production days. To mimic real-life industry practice, dynamic job release and dynamic machine availability times have been considered. Each job considered in a problem can have different weight assigned based on customers’ preferences. The setup times between jobs are assumed to be machine- and sequence-dependent. However, at the start of each production day, setup times are not sequence-dependent but depend on machine startup times such as preheating time, pressure build up, etc. The objective of the problem is to minimize the linear combination of total setup time and weighted tardiness. The minimization of total setup time represents producer’s interest whereas the minimization of weighted tardiness represents customers’ interest. Since these two objectives are not evaluated on a commensurate basis, a normalization factor is used. The problem is formulated as a mixed-integer linear programming (MILP) model, MILP-1 for permutation schedules and MILP-2 for non-permutation schedules. The MILP models for small-size problem instances are solved to optimality using CPLEX. However, the problem is shown to be NP-hard. As a result, it is not possible to find an optimal solution within a reasonable time, as the problem size increases. Hence, a meta-heuristic search algorithm based on short-term Tabu Search (TS) and Tabu Search/Path-Relinking (TS/PR) are developed. TS represents a local search algorithm, whereas TS/PR represents a hybridization of local search enhanced with population-based search algorithm. Two algorithms each, are developed for both, permutation (PN) and non-permutation (NPN) sequences. One of the algorithms is based on short term TS and the other is based on TS/PR. The developed heuristics are tested on sixteen small-size problems and their solution quality are compared with the optimal solution obtained from CPLEX. The evaluations show that the developed heuristics obtain good quality solutions within much less computational time. For PN sequence, the best algorithm obtained an average deviation of 0.49% compared with the optimal solution and for NPN sequence, the deviation is 0.13%. In addition, a slight improvement of 2.68% was obtained by adopting an NPN sequence over PN sequence for these problem instances. A statistical designed experiment is conducted to evaluate the difference in performance of the developed heuristics, and permutation and non-permutation schedules. The results show that the TS/PR algorithms outperform short-term TS, in the case of both PN and NPN sequences. The comparison between the solutions from the best PN algorithm and the best NPN algorithm shows that an average improvement of 1.64% is obtained by implementing an NPN sequence over PN sequence. The statistical analysis shows that the improvement offered by NPN sequence is statistically significant for problems with large number of product types and small number of jobs in each product. In addition, it is also shown that the NPN sequence performs better for non-continuous production as compared to continuous production. The efficiency of the algorithms was analyzed using the computational time required by the algorithms. The results show that PN algorithms require a significantly less computational time as compared to NPN algorithms. Hence, it is recommended that NPN sequences be considered only for the problems with large number of product types and small number of jobs in each product. For other problems, only PN sequence should be considered. TS/PR algorithm is recommended for both, PN and NPN sequences

Hybrid flowshop scheduling with dual resources in a supply chain

This dissertation addresses a hybrid-flow shop scheduling problem with dual resource constraints in a supply chain. Most of the traditional scheduling problems deal with machine as the only resource. However, other resources such as labor is not only required for processing jobs but are often constrained. Considering the second resource (labor) makes the scheduling problems more realistic and practical to implement in industries. In this research labor has different skill levels and the skill level required to perform the setup could be different from that needed to perform the run. The setup time is sequence-dependent, and job release times and machine availability times are dynamic. Also machine skipping is allowed. In tactical supply chain decisions such as scheduling, the goal is to minimize the cost of producer. However, when looking at the whole network, minimizing the cost of the producer alone may not lead to minimizing the cost of the whole supply chain. In fact the coordination between the producer and other entities in the network can minimize the cost. In this dissertation coordination between producer and customers is considered in order to make effective scheduling decisions. The goal of this research is to minimize the work-in-process inventory for the producer and maximize customers' service level to maintain producer-customers coordination. A linear mixed-integer mathematical programming model is proposed and CPLEX solver is used to find solutions for generated example problems with branch-and-bound technique. As the problem is NP-hard in the strong sense three different meta-search heuristic algorithms based on tabu search are developed in order to quickly solve the scheduling problems. A total of 243 examples were generated in small, medium and large size problems. Search algorithms performance in small size problems can be assessed by comparing them with the optimal solution from branch-and-bound method. However, in medium and large size problems, branch-and-bound method cannot find the optimal solution and therefore for assessing the performance of search algorithms three different lower bounding methods are proposed. The first method is based on Logic-Based Benders Decomposition and the second and third methods are two different variations of iterative selective linear programming (LP) relaxation called fractional LP relaxation and positive LP relaxation. An experimental analysis based on a nested-factorial design with blocking is developed in order to identify statistically significant differences between the effectiveness and efficiency of the lower bounding methods and search algorithms. The results showed that the proposed search algorithms and lower bounding methods are very effective and efficient. On average the developed lower bounding methods tighten the lower bound found by branch-and-bound by 11.93%. The quality of search algorithms is the same as the upper bound found by branch-and-bound. However, the search algorithms are on average 3.8 times faster than the branch-and-bound method