The Mixed Disc Packing Problem: Part I: Some Bounds on Density

Packing problems in general constitute a difficult set of problems which still defy solution The determination of bounds on the solution of such problems can, however, provide insight concerning the problem and can help in the development of new solution procedures. This paper, Part I, develops some bounds on the density of packing mixed discs on a circular plate. A methodology is proposed which formulates the problem as a linear program and requires the generation of feasible packings. The procedure for testing feasible packings, the solution algorithm, and results of experimentation are discussed in Part II, to appear in the next issue.     

All-terminal network reliability optimization via probabilistic solution discovery

This paper presents a new algorithm that can be readily applied to solve the all-terminal network reliability allocation problems. The optimization problem solved considers the minimization of the network design cost subject to a known constraint on all-terminal reliability by assuming that the network contains a known number of functionally equivalent components (with different performance specifications) that can be used to provide redundancy. The algorithm is based on two major steps that use a probabilistic solution discovery approach and Monte Carlo simulation to generate the quasi-optimal network designs. Examples for different sizes of all-terminal networks are used throughout the paper to illustrate the approach. The results obtained for the larger networks with unknown optima show that the quality of the solutions generated by the proposed algorithm is significantly higher with respect to other approaches and that these solutions are obtained from restricted solution search space. Although developed for all-terminal reliability optimization, the algorithm can be easily applied in other resource-constrained allocation problems.     

Solving Fixed Charge Location-Allocation Problems with Capacity and Configuration Constraints

Location-allocation problems involve the selection of locations that will be used as sources to satisfy a demand at various destinations. Associated with each potential source is a capacity limitation on output and a cost function which is broken down into a fixed charge plus an output dependent variable cost. Linear distribution costs comprise the remaining part of the total system cost. Configuration constraints which rule that specific source combinations are infeasible may be included for consideration. A solution procedure is presented that finds the minimal cost solution. The procedure utilizes a new enumerative search scheme in conjunction with adaptive bounds on the fixed costs, and constraints based on the dual variables to reduce the feasible solution set to a manageable size. For each of the small number of enumerated source configurations that pass all fixed cost and duality tests, a transportation problem is optimized to determine the minimum cost allocation. An experimental computer code was developed and numerical results are presented.     

A variable-depth search algorithm for the recursive bipartitioning of signal flow graphs

We discuss the use of local search techniques for mapping video algorithms onto programmable high-performance video signal processors. The mapping problem is very complex due to many constraints that need to be satisfied in order to obtain a feasible solution. The complexity is reduced by decomposing the mapping problem into three subproblems, namely delay management, partitioning, and scheduling. We present the partitioning problem and the representation of video algorithms by signal flow graphs. Furthermore, we propose a solution strategy that is based on recursive bipartitioning of these graphs. The bipartitions are generated using a variable-depth search algorithm. The results demonstrate that the frequently cited flexibility of local search techniques can be successfully exploited in handling complicated problems.     

A GRASP algorithm for flexible job-shop scheduling with maintenance constraints

In most realistic situations, machines may be unavailable due to maintenance, pre-schedules and so on. The availability constraints are non-fixed in that the completion time of the maintenance task is not fixed and has to be determined during the scheduling procedure. In this paper a greedy randomised adaptive search procedure (GRASP) algorithm is presented to solve the flexible job-shop scheduling problem with non-fixed availability constraints (FJSSP-nfa). The GRASP algorithm is a metaheuristic algorithm which is characterised by multiple initialisations. Basically, it operates in the following manner: first a feasible solution is obtained, which is then further improved by a local search technique. The main objective is to repeat these two phases in an iterative manner and to preserve the best found solution. Representative FJSSP-nfa benchmark problems are solved in order to test the effectiveness and efficiency of the proposed algorithm.     

A genetic algorithm heuristic approach to general outsourcing capacitated production planning problems

This paper addresses a dynamic capacitated production planning (CPP) problem with consideration of outsourcing. Specifically, the outsourcing problem considered in this paper has the following features: (1) all demands are met by production or outsourcing without postponement or backlog, (2) production, inventory, and outsourcing levels all have a limit, and (3) the cost functions are considered arbitrarily and time-varying. These features come together, leading to a so-called general outsourcing CPP problem. In our previous work, an algorithm with pseudo-polynomial time complexity was developed, which includes a formation of a feasible solution region and then a search procedure using dynamic programming techniques. Due to the computational complexity with such an approach, only small and medium problems can be solved in a practical sense. In this paper, we present a genetic algorithm (GA) approach to the same problem. The novelty of this GA approach is that the idea of the feasible solution region is used as a heuristic to guide the searching process. We present a computational experiment to show the effectiveness of the proposed approach.     

Neighborhood search algorithms with restricted infeasible solution sets–application to a transportation project evaluation problem

Abstract

Using a transportation project evaluation problem as an example, in this paper we employ the local search method, the threshold accepting method, together with the combination of feasible and restricted infeasible solution sets in neighborhood searches, to develop four solution algorithms. The test results indicate that the threshold accepting algorithm and the local search algorithm, that combine feasible and restricted infeasible solution sets, can improve the conventional threshold accepting algorithm and local search algorithm, which are confined to feasible solution sets.     

A flow-based tabu search algorithm for the RCPSP with transfer times

In this paper, we propose a tabu search algorithm for the resource-constrained project scheduling problem with transfer times. Solutions are represented by resource flows extending the disjunctive graph model for shop scheduling problems. Neighborhoods are defined by parallel and serial modifications rerouting or reversing flow on certain arcs. This approach is evaluated from a theoretical and experimental point of view. Besides studying the connectivity of different neighborhoods, computational results are presented for benchmark instances with and without transfer times.     

A GRASP algorithm for flexible job-shop scheduling problem with limited resource constraints

A greedy randomised adaptive search procedure (GRASP) is an iterative multi-start metaheuristic for difficult combinatorial optimisation. The GRASP iteration consists of two phases: a construction phase, in which a feasible solution is found and a local search phase, in which a local optimum in the neighbourhood of the constructed solution is sought. In this paper, a GRASP algorithm is presented to solve the flexible job-shop scheduling problem (FJSSP) with limited resource constraints. The main constraint of this scheduling problem is that each operation of a job must follow an appointed process order and each operation must be processed on an appointed machine. These constraints are used to balance between the resource limitation and machine flexibility. The model objectives are the minimisation of makespan, maximum workload and total workload. Representative benchmark problems are solved in order to test the effectiveness and efficiency of the GRASP algorithm. The computational result shows that the proposed algorithm produced better results than other authors’ algorithms.     

Flexible job-shop scheduling problems with ‘AND’/‘OR’ precedence constraints

The purpose of this research is to solve flexible job-shop scheduling problems with ‘AND’/‘OR’ precedence constraints in the operations. We first formulate the problem as a Mixed-Integer Linear Program (MILP). The MILP can be used to compute optimal solutions for small-sized problems. We also developed a heuristic algorithm that can obtain a good solution for the problem regardless of its size. Moreover, we have developed a representation and schedule builder that always produces a legal and feasible solution for the problem, and developed genetic and tabu search algorithms based on the proposed schedule builder. The results of the computational experiments show that the developed meta-heuristics are very effective.     

A method for scheduling in parallel manufacturing systems with flexible resources

We address the Parallel-Machine Flexible-Resource Scheduling (PMFRS) problem of simultaneously allocating flexible resources, and sequencing jobs, in cellular manufacturing systems where the cells are configured in parallel. We present a new solution methodology for the PMFRS problem called the Nested Partitions (NP) method. This method combines global sampling of the feasible region and local search heuristics. To efficiently apply the NP method we reformulate the PMFRS problem, develop a new sampling algorithm that can be used to obtain good feasible schedules, and suggest a new improvement heuristic. Numerical examples are also presented to illustrate the new method.     

An artificial bee colony algorithm for the economic lot scheduling problem

In this study, we present an artificial bee colony (ABC) algorithm for the economic lot scheduling problem modelled through the extended basic period (EBP) approach. We allow both power-of-two (PoT) and non-power-of-two multipliers in the solution representation. We develop mutation strategies to generate neighbouring food sources for the ABC algorithm and these strategies are also used to develop two different variable neighbourhood search algorithms to further enhance the solution quality. Our algorithm maintains both feasible and infeasible solutions in the population through the use of some sophisticated constraint handling methods. Experimental results show that the proposed algorithm succeeds to find the all the best-known EBP solutions for the high utilisation 10-item benchmark problems and improves the best known solutions for two of the six low utilisation 10-item benchmark problems. In addition, we develop a new problem instance with 50 items and run it at different utilisation levels ranging from 50 to 99% to see the effectiveness of the proposed algorithm on large instances. We show that the proposed ABC algorithm with mixed solution representation outperforms the ABC that is restricted only to PoT multipliers at almost all utilisation levels of the large instance.     

A reliability/availability approach to joint production and maintenance scheduling with multiple preventive maintenance services

In classical scheduling problems, it is often assumed that the machines are available during the whole planning horizon, while in realistic environments, machines need to be maintained and therefore may become unavailable within production periods. Hence, in this paper we suggest a joint production and maintenance scheduling (JPMS) with multiple preventive maintenance services, in which the reliability/availability approach is employed to model the maintenance aspects of a problem. To cope with the suggested JPMS, a mixed integer nonlinear programming model is developed and then a population-based variable neighbourhood search (PVNS) algorithm is devised for a solution method. In order to enhance the search diversification of basic variable neighbourhood search (VNS), our PVNS uses an epitome-based mechanism in each iteration to transform a group of initial individuals into a new solution, and then multiple trial solutions are generated in the shaking stage for a given solution. At the end of the local search stage, the best obtained solution by all of the trial solutions is recorded and the worst solution in population is replaced with this new solution. The evolution procedure is continued until a predefined number of iterations is violated. To validate the effectiveness and robustness of PVNS, an extensive computational study is implemented and the simulation results reveal that our PVNS performs better than traditional algorithms, especially in large size problems.     

An improved branch and bound procedure for scheduling a flow line manufacturing cell

This paper presents a new branch and bound procedure for scheduling a flow-line manufacturing cell. This procedure and an existing procedure are tested on several problem sets with varying numbers of families, jobs and machines, and varying setup time distributions. The results show that the new procedure solves small problems dramatically faster than the existing procedure. Three heuristic procedures, based on the new branch and bound procedure, are developed. These heuristic procedures as well as a tabu search procedure are tested on problem sets with larger problem sizes. The results show that one of the new procedures generates solutions with improved makespans compared to the tabu search procedure.     

A scatter search approach to sequence-dependent setup times job shop scheduling

Scheduling jobs on multiple machines is a difficult problem when real-world constraints such as the sequence setup time, setup times for jobs and multiple criteria are used for solution goodness. It is usually sufficient to obtain a near-optimal solution quickly when an optimal solution would require days or weeks of computation. Common scheduling heuristics such as Shortest Processing Time can be used to obtain a feasible schedule quickly, but are not designed for multiple simultaneous objectives. We use a new meta-heuristic known as a scatter search (SS) to solve these types of job shop scheduling problems. The results are compared with solutions obtained by common heuristics, a tabu search, simulated annealing, and a genetic algorithm. We show that by combining the mechanism of diversification and intensification, SS produces excellent results in a very reasonable computation time. The study presents an efficient alternative for companies with a complicated scheduling and production situation.     

Tabu search algorithm for flexible flow path design of unidirectional automated-guided vehicle systems

The unidirectional flow path design problem is one of the most important but difficult problems for the efficient design of automated-guided vehicle systems. As the problem was first formulated by Gaskins and Tanchoco, many researchers have studied the problem. However, the existing solution methods fail to provide an efficient solution approach. In this paper, a mathematical model for the unidirectional flow path design problem is developed. To obtain a near-to-optimal solution in reasonable computation time, a tabu search algorithm is presented. A fast construction algorithm first obtains a feasible initial solution, and a long-term memory structure and a neighbor solution generation approach are adapted to the problem characteristics and embedded in the proposed tabu search algorithm. Computational experiments show that the developed tabu search algorithm outperforms the Ko and Egbelu’s algorithm, Int J Prod Res, 41:2325–2343, (2003).     

Imposing precedence constraints on NC punch press sequences

A few years ago D. Dornfeld, R. Gil and I addressed the problem of numerically controlled punch press sequencing, but did not formally treat the obstacle of how to impose precedence constraints on the sequences (Svestka et al. 1981). This has been accomplished by partitioning the problem into smaller problems and patching them together to satisfy the constraints, or by direct construction of such sequences, usually involving the closest unvisited city (CUC) heuristic. However, these approaches do have some difficulties. For example, the CUC heuristic can fail to generate a feasible solution for such problems even though solutions can be shown to exist. Here, we introduce a new method for imposing precedence constraints, which either finds a feasible solution or shows that there are none. The method can also be more efficient that CUC, for problems with more than 30 hits.     

A meta-heuristic approach for solving the no-wait flow-shop problem

No-wait flow-shop scheduling problems refer to the set of problems in which a number of jobs are available for processing on a number of machines in a flow-shop context with the added constraint that there should be no waiting time between consecutive operations of the jobs. The problem is strongly NP-hard. In this paper, the considered performance measure is the makespan. In order to explore the feasible region of the problem, a hybrid algorithm of Tabu Search and Particle Swarm Optimisation (PSO) is proposed. In the proposed approach, PSO algorithm is used in order to move from one solution to a neighbourhood solution. We first employ a new coding and decoding technique to efficiently map the discrete feasible space to the set of integer numbers. The proposed PSO will further use this coding technique to explore the solution space and move from one solution to a neighbourhood solution. Afterwards, the algorithm decodes the solutions to its respective feasible solution in the discrete feasible space and returns the new solutions to the TS. The algorithm is tested by solving a large number of problems available in the literature. Computational results show that the proposed algorithm is able to outperform competitive methods and improves some of the best-known solutions of the considered test problems.     

Response to Al-Hakim's note

Storage location assignment and interleaving policy are two closely related problems in warehousing management. This paper addresses the location assignment and interleaving problem at the same time in an automated storage/retrieval system with duration-of-stay based shared storage policy. Based on the heuristics for single command operation, a two-step procedure is developed to solve the problem. A tabu search algorithm is proposed to improve the solution for medium and large sized problems. The computational results indicate that the tabu search algorithm is effective in finding high quality solutions, and efficient in solving large sized problems.