Simulated Annealing Algorithm for the Linear Ordering Problem: The Case of Tanzania Input Output Tables

Linear Ordering is a problem of ordering the rows and columns of a matrix such that the sum of the upper triangle values is as large as possible. The problem has many applications including aggregation of individual preferences, weighted ancestry relationships and triangulation of input-output tables in economics. As a result, many researchers have been working on the problem which is known to be NP-hard. Consequently, heuristic algorithms have been developed and implemented on benchmark data or specific real-world applications. Simulated Annealing has seldom been used for this problem. Furthermore, only one attempt has been done on the Tanzanian input output table data. This article presents a Simulated Annealing approach to the problem and compares results with previous work on the same data using Great Deluge algorithm. Three cooling schedules are compared, namely linear, geometric and Lundy & Mees. The results show that Simulated Annealing and Great Deluge provide similar results including execution time and final solution quality. It is concluded that Simulated Annealing is a good algorithm for the Linear Ordering problem given a careful selection of required parameters. Keywords: Combinatorial Optimization; Linear Ordering Problem; Simulated Annealing; Triangulation; Input Output table

Models and Strategies for Variants of the Job Shop Scheduling Problem

Recently, a variety of constraint programming and Boolean satisfiability approaches to scheduling problems have been introduced. They have in common the use of relatively simple propagation mechanisms and an adaptive way to focus on the most constrained part of the problem. In some cases, these methods compare favorably to more classical constraint programming methods relying on propagation algorithms for global unary or cumulative resource constraints and dedicated search heuristics. In particular, we described an approach that combines restarting, with a generic adaptive heuristic and solution guided branching on a simple model based on a decomposition of disjunctive constraints. In this paper, we introduce an adaptation of this technique for an important subclass of job shop scheduling problems (JSPs), where the objective function involves minimization of earliness/tardiness costs. We further show that our technique can be improved by adding domain specific information for one variant of the JSP (involving time lag constraints). In particular we introduce a dedicated greedy heuristic, and an improved model for the case where the maximal time lag is 0 (also referred to as no-wait JSPs).Comment: Principles and Practice of Constraint Programming - CP 2011, Perugia : Italy (2011

Heuristics for the dynamic facility layout problem with unequal area departments

The facility layout problem (FLP) is a well researched problem of finding positions of departments on a plant floor such that departments do not overlap and some objective(s) is (are) optimized. In this dissertation, the FLP with unequal area rectangular shaped departments is considered, when material flows between departments change during the planning horizon. This problem is known as the dynamic FLP. The change in material flows between pairs of departments in consecutive periods may require rearrangements of departments during the planning horizon in order to keep material handling costs low. The objective of our problem is to minimize the sum of the material handling and rearrangement costs. Because of the combinatorial structure of the problem, only small sized problems can be solved in reasonable time using exact techniques. As a result, construction and improvement heuristics are developed for the proposed problem. The construction algorithms are boundary search heuristics as well as a dual simplex method, and the improvement heuristics are tabu search and memetic heuristics with boundary search and dual simplex (linear programming model) techniques. The heuristics were tested on a generated data set as well as some instances from the literature. In summary, the memetic heuristic with the boundary search technique out-performed the other techniques with respect to solution quality

a fast heuristic for routing in post disaster humanitarian relief logistics

Abstract In the last decades, natural disasters have been affecting the human life of millions of people. The impressive scale of these disasters has pointed out the need for an effective management of the relief supply operations. One of the crucial issues in this context is the routing of vehicles carrying critical supplies and help to disaster victims. This problem poses unique logistics challenges, including damaged transportation infrastructure and limited knowledge on the road travel times. In such circumstances, selecting more reliable paths could help the rescue team to provide fast services to those in needs. The classic cost-minimizing routing problems do not properly reflect the relevant issue of the arrival time, which clearly has a serious impact on the survival rate of the affected community. In this paper, we focus specifically on the arrival time objective function in a multi-vehicle routing problem where stochastic travel times are taken into account. The considered problem should be solved promptly in the aftermath of a disaster, hence we propose a fast heuristic that could be applied to solve the problem

A fast heuristic for routing in post-disaster humanitarian relief logistics

In the last decades, natural disasters have been affecting the human life of millions of people. The impressive scale of these disasters has pointed out the need for an effective management of the relief supply operations. One of the crucial issues in this context is the routing of vehicles carrying critical supplies and help to disaster victims. This problem poses unique logistics challenges, including damaged transportation infrastructure and limited knowledge on the road travel times. In such circumstances, selecting more reliable paths could help the rescue team to provide fast services to those in needs. The classic cost-minimizing routing problems do not properly reflect the relevant issue of the arrival time, which clearly has a serious impact on the survival rate of the affected community. In this paper, we focus specifically on the arrival time objective function in a multi-vehicle routing problem where stochastic travel times are taken into account. The considered problem should be solved promptly in the aftermath of a disaster, hence we propose a fast heuristic that could be applied to solve the problem

Optimal consignment stocking policies for a supply chain under different system constraints

The research aims are to enable the decision maker of an integrated vendor-buyer system under Consignment Stock (CS) policy to make the optimal/sub-optimal production/replenishment decisions when some general and realistic critical factors are considered. In the system, the vendor produces one product at a finite rate and ships the outputs by a number of equal-sized lots within a production cycle. Under a long-term CS agreement, the vendor maintains a certain inventory level at the buyer’s warehouse, and the buyer compensates the vendor only for the consumed products. The holding cost consists of a storage component and a financial component. Moreover, both of the cases that the unit holding costs may be higher at the buyer or at the vendor are considered. Based upon such a system, four sets of inventory models are developed each of which considers one more factor than the former. The first set of models allows a controllable lead-time with an additional investment and jointly determines the shipping size, the number of shipments, and the lead time, that minimize the yearly joint total expected cost (JTEC) of the system. The second set of models considers a buyer’s capacity limitation which causes some shipments to be delayed so that the arrival of these shipments does not cause the buyer’s inventory to go beyond its limitation. As a result, the number of delayed shipments is added as the fourth decision variable. A variable demand rate is allowed in the third set of models. Uncertainty caused by the varying demand are controlled by a safety factor, which becomes the fifth decision variable. Finally, the risk of obsolescence of the product is considered in the fourth model. The first model is solved analytically, whereas the rest are not, mainly because of the complexity of the problem and the number of variables being considered. Three doubly-hybrid meta-heuristic algorithms that combine two different hybrid meta-heuristic algorithms are developed to provide a solution procedure for the rest of models. Numerical experiments illustrate the solution procedures and reveal the effects of the buyer’s capacity limitation, the effects of the variable demand rate, and the effects of the risk of obsolescence, on the system. Furthermore, sensitivity analysis shows that some of the system parameters (such as the backorder penalty, the extra space penalty, the ratio of the unit holding cost of the vendor over that of the buyer) are very influential to the joint system total cost and the optimal solutions of the decision variables

Integration of production, maintenance and quality : Modelling and solution approaches

Dans cette thèse, nous analysons le problème de l'intégration de la planification de production et de la maintenance préventive, ainsi que l'élaboration du système de contrôle de la qualité. Premièrement, on considère un système de production composé d'une machine et de plusieurs produits dans un contexte incertain, dont les prix et le coût changent d'une période à l'autre. La machine se détériore avec le temps et sa probabilité de défaillance, ainsi que le risque de passage à un état hors contrôle augmentent. Le taux de défaillance dans un état dégradé est plus élevé et donc, des coûts liés à la qualité s’imposent. Lorsque la machine tombe en panne, une maintenance corrective ou une réparation minimale seront initiées pour la remettre en marche sans influer ses conditions ou le processus de détérioration. L'augmentation du nombre de défaillances de la machine se traduit par un temps d'arrêt supérieur et un taux de disponibilité inférieur. D'autre part, la réalisation des plans de production est fortement influencée par la disponibilité et la fiabilité de la machine. Les interactions entre la planification de la maintenance et celle de la production sont incorporées dans notre modèle mathématique. Dans la première étape, l'effet de maintenance sur la qualité est pris en compte. La maintenance préventive est considérée comme imparfaite. La condition de la machine est définie par l’âge actuel, et la machine dispose de plusieurs niveaux de maintenance avec des caractéristiques différentes (coûts, délais d'exécution et impacts sur les conditions du système). La détermination des niveaux de maintenance préventive optimaux conduit à un problème d’optimisation difficile. Un modèle de maximisation du profit est développé, dans lequel la vente des produits conformes et non conformes, les coûts de la production, les stocks tenus, la rupture de stock, la configuration de la machine, la maintenance préventive et corrective, le remplacement de la machine et le coût de la qualité sont considérés dans la fonction de l’objectif. De plus, un système composé de plusieurs machines est étudié. Dans cette extension, les nombres optimaux d’inspections est également considéré. La fonction de l’objectif consiste à minimiser le coût total qui est la somme des coûts liés à la maintenance, la production et la qualité. Ensuite, en tenant compte de la complexité des modèles préposés, nous développons des méthodes de résolution efficaces qui sont fondées sur la combinaison d'algorithmes génétiques avec des méthodes de recherches locales. On présente un algorithme mimétique qui emploi l’algorithme Nelder-Mead, avec un logiciel d'optimisation pour déterminer les valeurs exactes de plusieurs variables de décisions à chaque évaluation. La méthode de résolution proposée est comparée, en termes de temps d’exécution et de qualités des solutions, avec plusieurs méthodes Métaheuristiques. Mots-clés : Planification de la production, Maintenance préventive imparfaite, Inspection, Qualité, Modèles intégrés, MétaheuristiquesIn this thesis, we study the integrated planning of production, maintenance, and quality in multi-product, multi-period imperfect systems. First, we consider a production system composed of one machine and several products in a time-varying context. The machine deteriorates with time and so, the probability of machine failure, or the risk of a shift to an out-of-control state, increases. The defective rate in the shifted state is higher and so, quality related costs will be imposed. When the machine fails, a corrective maintenance or a minimal repair will be initiated to bring the machine in operation without influencing on its conditions or on the deterioration process. Increasing the expected number of machine failures results in a higher downtime and a lower availability rate. On the other hand, realization of the production plans is significantly influenced by the machine availability and reliability. The interactions between maintenance scheduling and production planning are incorporated in the mathematical model. In the first step, the impact of maintenance on the expected quality level is addressed. The maintenance is also imperfect and the machine conditions after maintenance can be anywhere between as-good-as-new and as-bad-as-old situations. Machine conditions are stated by its effective age, and the machine has several maintenance levels with different costs, execution times, and impacts on the system conditions. High level maintenances on the one hand have greater influences on the improvement of the system state and on the other hand, they occupy more the available production time. The optimal determination of such preventive maintenance levels to be performed at each maintenance intrusion is a challenging problem. A profit maximization model is developed, where the sale of conforming and non-conforming products, costs of production, inventory holding, backorder, setup, preventive and corrective maintenance, machine replacement, and the quality cost are addressed in the objective function. Then, a system with multiple machines is taken into account. In this extension, the number of quality inspections is involved in the joint model. The objective function minimizes the total cost which is the sum of maintenance, production and quality costs. In order to reduce the gap between the theory and the application of joint models, and taking into account the complexity of the integrated problems, we have developed an efficient solution method that is based on the combination of genetic algorithms with local search and problem specific methods. The proposed memetic algorithm employs Nelder-Mead algorithm along with an optimization package for exact determination of the values of several decision variables in each chromosome evolution. The method extracts not only the positive knowledge in good solutions, but also the negative knowledge in poor individuals to determine the algorithm transitions. The method is compared in terms of the solution time and quality to several heuristic methods. Keywords : Multi-period production planning, Imperfect preventive maintenance, Inspection, Quality, Integrated model, Metaheuristic