A review and evaluation on constructive heuristics to optimise product mix based on the Theory of Constraints

In this paper, we address the problem of defining the product mix in order to maximise a system's throughput. This problem is well known for being NP-Complete and therefore, most contributions to the topic focus on developing heuristics that are able to obtain good solutions for the problem in a short CPU time. In particular, constructive heuristics are available for the problem such as that by Fredendall and Lea, and by Aryanezhad and Komijan. We propose a new constructive heuristic based on the Theory of Constraints and the Knapsack Problem. The computational results indicate that the proposed heuristic yields better results than the existing heuristic.

Generating unconstrained two-dimensional non-guillotine cutting patterns by a Recursive Partitioning Algorithm

In this study, a dynamic programming approach to deal with the unconstrained two-dimensional non-guillotine cutting problem is presented. The method extends the recently introduced recursive partitioning approach for the manufacturer's pallet loading problem. The approach involves two phases and uses bounds based on unconstrained two-staged and non-staged guillotine cutting. The method is able to find the optimal cutting pattern of a large number of pro blem instances of moderate sizes known in the literature and a counterexample for which the approach fails to find known optimal solutions was not found. For the instances that the required computer runtime is excessive, the approach is combined with simple heuristics to reduce its running time. Detailed numerical experiments show the reliability of the method. Journal of the Operational Research Society (2012) 63, 183-200. doi: 10.1057/jors.2011.6 Published online 17 August 2011

Simple heuristics for the assembly line worker assignment and balancing problem

We propose simple heuristics for the assembly line worker assignment and balancing problem. This problem typically occurs in assembly lines in sheltered work centers for the disabled. Different from the well-known simple assembly line balancing problem, the task execution times vary according to the assigned worker. We develop a constructive heuristic framework based on task and worker priority rules defining the order in which the tasks and workers should be assigned to the workstations. We present a number of such rules and compare their performance across three possible uses: as a stand-alone method, as an initial solution generator for meta-heuristics, and as a decoder for a hybrid genetic algorithm. Our results show that the heuristics are fast, they obtain good results as a stand-alone method and are efficient when used as a initial solution generator or as a solution decoder within more elaborate approaches.

Column generation for a multitrip vehicle routing problem with time windows, driver work hours, and heterogeneous fleet

This study addresses a vehicle routing problem with time windows, accessibility restrictions on customers, and a fleet that is heterogeneous with regard to capacity and average speed. A vehicle can performmultiple routes per day, all starting and ending at a single depot, and it is assigned to a single driverwhose totalwork hours are limited.Acolumn generation algorithmis proposed.The column generation pricing subproblem requires a specific elementary shortest path problem with resource constraints algorithm to address the possibility for each vehicle performingmultiple routes per day and to address the need to set the workday’s start time within the planning horizon. A constructive heuristic and a metaheuristic based on tabu search are also developed to find good solutions.

An algorithm for the strip packing problem using collision free region and exact fitting placement

The irregular shape packing problem is approached. The container has a fixed width and an open dimension to be minimized. The proposed algorithm constructively creates the solution using an ordered list of items and a placement heuristic. Simulated annealing is the adopted metaheuristic to solve the optimization problem. A two-level algorithm is used to minimize the open dimension of the container. To ensure feasible layouts, the concept of collision free region is used. A collision free region represents all possible translations for an item to be placed and may be degenerated. For a moving item, the proposed placement heuristic detects the presence of exact fits (when the item is fully constrained by its surroundings) and exact slides (when the item position is constrained in all but one direction). The relevance of these positions is analyzed and a new placement heuristic is proposed. Computational comparisons on benchmark problems show that the proposed algorithm generated highly competitive solutions. Moreover, our algorithm updated some best known results. (C) 2012 Elsevier Ltd. All rights reserved.

Heuristic methods for the single machine scheduling problem with different ready times and a common due date

The single machine scheduling problem with a common due date and non-identical ready times for the jobs is examined in this work. Performance is measured by the minimization of the weighted sum of earliness and tardiness penalties of the jobs. Since this problem is NP-hard, the application of constructive heuristics that exploit specific characteristics of the problem to improve their performance is investigated. The proposed approaches are examined through a computational comparative study on a set of 280 benchmark test problems with up to 1000 jobs.

Hybrid heuristic-waterfilling game theory approach in MC-CDMA resource allocation

This paper discusses the power allocation with fixed rate constraint problem in multi-carrier code division multiple access (MC-CDMA) networks, that has been solved through game theoretic perspective by the use of an iterative water-filling algorithm (IWFA). The problem is analyzed under various interference density configurations, and its reliability is studied in terms of solution existence and uniqueness. Moreover, numerical results reveal the approach shortcoming, thus a new method combining swarm intelligence and IWFA is proposed to make practicable the use of game theoretic approaches in realistic MC-CDMA systems scenarios. The contribution of this paper is twofold: (i) provide a complete analysis for the existence and uniqueness of the game solution, from simple to more realist and complex interference scenarios; (ii) propose a hybrid power allocation optimization method combining swarm intelligence, game theory and IWFA. To corroborate the effectiveness of the proposed method, an outage probability analysis in realistic interference scenarios, and a complexity comparison with the classical IWFA are presented. (C) 2011 Elsevier B.V. All rights reserved.

Multi-objective evolutionary algorithm for single and multiple fault service restoration in large-scale distribution systems

Network reconfiguration for service restoration (SR) in distribution systems is a complex optimization problem. For large-scale distribution systems, it is computationally hard to find adequate SR plans in real time since the problem is combinatorial and non-linear, involving several constraints and objectives. Two Multi-Objective Evolutionary Algorithms that use Node-Depth Encoding (NDE) have proved able to efficiently generate adequate SR plans for large distribution systems: (i) one of them is the hybridization of the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) with NDE, named NSGA-N; (ii) the other is a Multi-Objective Evolutionary Algorithm based on subpopulation tables that uses NDE, named MEAN. Further challenges are faced now, i.e. the design of SR plans for larger systems as good as those for relatively smaller ones and for multiple faults as good as those for one fault (single fault). In order to tackle both challenges, this paper proposes a method that results from the combination of NSGA-N, MEAN and a new heuristic. Such a heuristic focuses on the application of NDE operators to alarming network zones according to technical constraints. The method generates similar quality SR plans in distribution systems of significantly different sizes (from 3860 to 30,880 buses). Moreover, the number of switching operations required to implement the SR plans generated by the proposed method increases in a moderate way with the number of faults.