Applying tabu search to the job-shop scheduling problem

In this paper, we apply the tabu-search technique to the job-shop scheduling problem, a notoriously difficult problem in combinatorial optimization. We show that our implementation of this method dominates both a previous approach with tabu search and the other heuristics based on iterative improvements.Partially supported by research contracts MPI 40% and 60% of the Italian Ministry of University and Scientific Research.     

Solving an integrated job-shop problem with human resource constraints

We propose two exact methods to solve an integrated employee-timetable and job-shop-scheduling problem. The problem is to find a minimum cost employee-timetable, where employees have different competences and work during shifts, so that the production, that corresponds to a job-shop with resource availability constraints, can be achieved. We introduce two new exact procedures: (1) a decomposition and cut generation approach and (2) a hybridization of a cut generation process with a branch and bound strategy. We also propose initial cuts that strongly improve these methods as well as a standard MIP approach. The computational performances of those methods on benchmark instances are compared to that of other methods from the literature.     

A polynomial algorithm for a two-machine no-wait job-shop scheduling problem

This paper considers the no-wait scheduling of n jobs, where each job is a chain of unit processing time operations to be processed alternately on two machines. The objective is to minimize the mean flow time. We propose an O(n⁶)-time algorithm to produce an optimal schedule. It is also shown that if zero processing time operations are allowed, then the problem is NP-hard in the strong sense.     

A repairing technique for the local search of the job-shop problem

The local search technique has become a widely used tool for solving many combinatorial optimization problems. In the case of the job-shop the implementation of such a technique is not straightforward at all due to the existence of the technological constraints among the operations that belong to the same job. Their presence renders a certain set of schedules infeasible. Consequently, special attention is required when defining optimization algorithms to prevent the possibility of reaching an infeasible schedule during execution. Traditionally, the problem is tackled on the neighborhood level by using only a limited set of moves for which feasibility inherently holds. This paper proposes an alternative way to avoid infeasibility by incorporating a repairing technique into the mechanism for applying moves to a schedule. Whenever an infeasible move is being applied, a repairing mechanism rearranges the underlying schedule in such a way that the feasibility of the move is restored. The possibility of reaching infeasible solutions is, therefore, eliminated on the lowest possible conceptual level. Consequently, neighborhood functions need not to be constrained to a limited set of feasible moves any more.     

The travelling salesperson problem with hotel selection

In this paper, we present the travelling salesperson problem with hotel selection (TSPHS), an extension of the TSP with a number of interesting applications. We present a mathematical formulation, explain the difference with related optimization problems and indicate what makes this problem inherently more difficult. We develop a simple but efficient heuristic that uses two constructive initialization procedures and an improvement procedure consisting of several neighbourhood search operators designed specifically for this problem, as well as some typical neighbourhoods from the literature. We generate several benchmark instances of varying sizes and compare the performance of our heuristic with CPLEX (10.0). We also generate some problems with known optimal solutions and use these to further demonstrate that our heuristic achieves good results in very limited computation times.     

A branch and bound method for the job-shop problem with sequence-dependent setup times

This paper deals with the job-shop scheduling problem with sequence-dependent setup times. We propose a new method to solve the makespan minimization problem to optimality. The method is based on iterative solving via branch and bound decisional versions of the problem. At each node of the branch and bound tree, constraint propagation algorithms adapted to setup times are performed for domain filtering and feasibility check. Relaxations based on the traveling salesman problem with time windows are also solved to perform additional pruning. The traveling salesman problem is formulated as an elementary shortest path problem with resource constraints and solved through dynamic programming. This method allows to close previously unsolved benchmark instances of the literature and also provides new lower and upper bounds.     

A general approach for optimizing regular criteria in the job-shop scheduling problem

Even though a very large number of solution methods has been developed for the job-shop scheduling problem, a majority has been designed for the makespan criterion. In this paper, we propose a general approach for optimizing any regular criterion in the job-shop scheduling problem. The approach is a local search method that uses a disjunctive graph model and neighborhoods generated by swapping critical arcs. The connectivity property of the neighborhood structure is proved and a novel efficient method for evaluating moves is presented. Besides its generality, another prominent advantage of the proposed approach is its simple implementation that only requires to tune the range of one parameter. Extensive computational experiments carried out on various criteria (makespan, total weighted flow time, total weighted tardiness, weighted sum of tardy jobs, maximum tardiness) show the efficiency of the proposed approach. Best results were obtained for some problem instances taken from the literature.     

A hybrid shifting bottleneck procedure algorithm for the parallel-machine job-shop scheduling problem

In practice, parallel-machine job-shop scheduling (PMJSS) is very useful in the development of standard modelling approaches and generic solution techniques for many real-world scheduling problems. In this paper, based on the analysis of structural properties in an extended disjunctive graph model, a hybrid shifting bottleneck procedure (HSBP) algorithm combined with Tabu Search (TS) metaheuristic algorithm is developed to deal with the PMJSS problem. The original-version shifting bottleneck procedure (SBP) algorithm for the job-shop scheduling (JSS) has been significantly improved to solve the PMJSS problem with four novelties: (i) a topological-sequence algorithm is proposed to decompose the PMJSS problem in a set of single-machine scheduling (SMS) and/or parallel-machine scheduling subproblems; (ii) a modified Carlier algorithm based on the proposed lemmas and the proofs is developed to solve the SMS subproblem; (iii) the Jackson rule is extended to solve the PMS subproblem; (iv) a TS metaheuristic algorithm is embedded under the framework of SBP to optimise the JSS and PMJSS cases. The computational experiments show that the proposed HSBP is very efficient in solving the JSS and PMJSS problems.     

The bidding selection and assignment problem with minimum quantity commitment

This paper studies the bidding selection and assignment problem with a novel constraint, namely minimum quantity commitment (MQC), motivated by the Royal Philips Electronics Company. Responding to the stipulations by the US Federal Maritime Commission, any shipping agent transporting to the US must satisfy a minimum quantity of containers. To insure this MQC for shipping agents, the Royal Philips Electronics Company, with a large number of shipping needs, has to assign enough containers to each selected shipping agent to transport cargos to the US. This restriction creates difficulties for Philips as the company seeks to satisfy its shipping needs with minimum total costs. To solve this problem, we first formulate it by a mixed-integer programming model. In order for both linear programming relaxation and Lagrangian relaxation to provide good lower bounds, we then strengthen the model by a few valid inequalities. Furthermore, a Lagrangian-based heuristic and a branch and cut solver are applied to solve the problem. Extensive experiments show the effectiveness of all the models and methods.     

The mean-absolute deviation portfolio selection problem with interval-valued returns

In real-world investments, one may care more about the future earnings than the current earnings of the assets. This paper discusses the uncertain portfolio selection problem where the asset returns are represented by interval data. Since the parameters are interval valued, the gain of returns is interval valued as well. According to the concept of the mean-absolute deviation function, we construct a pair of two-level mathematical programming models to calculate the lower and upper bounds of the investment return of the portfolio selection problem. Using the duality theorem and applying the variable transformation technique, the pair of two-level mathematical programs is transformed into a conventional one-level mathematical program. Solving the pair of mathematical programs produces the interval of the portfolio return of the problem. The calculated results conform to an essential idea in finance and economics that the greater the amount of risk that an investor is willing to take on the greater the potential return.     

On interval portfolio selection problem

The future returns of each securities cannot be correctly reflected by the data in the past, therefore the expert’s judgements and experiences should be considered to estimate the security returns for the future. In this paper, we propose an interval portfolio selection model in which both the returns and the risks of assets are defined as intervals. By using interval and convex analysis, we solve this model and get the noninferior solution. Finally, an example is given to illustrate our results. The interval portfolio selection model improves and generalizes the Markowitz’s mean-variance model and the results of Deng et al. (Eur J Oper Res 166(1):278–292, 2005).     

Portfolio selection problem with interval coefficients

We investigate the portfolio selection problem with interval objective function coefficients as a multiple objective problem including uncertainties. Robust efficient solutions, Pareto optimal for all possible perturbation of coefficients within given intervals, are secure and conservative solutions. Using preference cones we show that the robust efficient solutions can be identified by working with only a finite subset of the possible perturbations of the coefficients.     

A discrete firefly algorithm for solving the flexible job-shop scheduling problem in a make-to-order manufacturing system

Central European Journal of Operations Research - This work presents a multi-objective discrete firefly algorithm (MO-DFFA) for solving the flexible job-shop scheduling problem (FJSP) in a...     

Stochastic linear knapsack programming problem and its application to a portfolio selection problem

In this paper a probability maximization model of a stochastic linear knapsack problem is considered where the random variables consist of several groups with mutually correlated ones. We propose a solution algorithm to the equivalent nonlinear fractional programming problem with a simple ranking method. This approach will be effectively applied to one of the portfolio selection problems.     

A discrete artificial bee colony algorithm for the multi-objective flexible job-shop scheduling problem with maintenance activities

This paper presents a novel discrete artificial bee colony (DABC) algorithm for solving the multi-objective flexible job shop scheduling problem with maintenance activities. Performance criteria considered are the maximum completion time so called makespan, the total workload of machines and the workload of the critical machine. Unlike the original ABC algorithm, the proposed DABC algorithm presents a unique solution representation where a food source is represented by two discrete vectors and tabu search (TS) is applied to each food source to generate neighboring food sources for the employed bees, onlooker bees, and scout bees. An efficient initialization scheme is introduced to construct the initial population with a certain level of quality and diversity. A self-adaptive strategy is adopted to enable the DABC algorithm with learning ability for producing neighboring solutions in different promising regions whereas an external Pareto archive set is designed to record the non-dominated solutions found so far. Furthermore, a novel decoding method is also presented to tackle maintenance activities in schedules generated. The proposed DABC algorithm is tested on a set of the well-known benchmark instances from the existing literature. Through a detailed analysis of experimental results, the highly effective and efficient performance of the proposed DABC algorithm is shown against the best performing algorithms from the literature.     

On correct selection for a ranking problem

Givenk populations which belong to the exponential class, and having specified two positive constants (δ ^*,P ^*), an experimenter wishes to selectt populations which (a) exclude all those populations with a parameter value not greater than thetth largest parameter value minusδ ^*, and (b) include all those populations with a parameter value not smaller than the (t+1)th largest parameter value plusδ ^*. This paper shows that the probability of successfully making such a selection, called aδ ^*-correct selection, is at leastP ^* if the basic sequential procedure,P _B ^* , of Bechhofer, et al. [3] is used. This result includes the corresponding old result of their book (p. 129) as a particular case.     

A note on a journal selection problem

This note explores the convergence properties of certain sequences of conditional probabilities arising in a journal selection problem, where the probabilities of interest are decreasing in either a deterministic or stochastic fashion. We prove the convergence to a nonextreme value of the probability of an eventual event for any choice of problem parameters within the open unit interval. Computational results illustrate the convergence properties.     

A global optimization problem in portfolio selection

This paper deals with the issue of buy-in thresholds in portfolio optimization using the Markowitz approach. Optimal values of invested fractions calculated using, for instance, the classical minimum-risk problem can be unsatisfactory in practice because they lead to unrealistically small holdings of certain assets. Hence we may want to impose a discrete restriction on each invested fraction y _i such as y _i >  y _min or y _i =  0. We shall describe an approach which uses a combination of local and global optimization to determine satisfactory solutions. The approach could also be applied to other discrete conditions—for instance when assets can only be purchased in units of a certain size (roundlots).     

A heuristic for the routing and carrier selection problem

We consider the problem of simultaneously selecting customers to be served by external carriers and routing a heterogeneous internal fleet. Very little attention was devoted to this problem. A recent paper proposed a heuristic solution procedure. Our paper shows that better results can be obtained by a simple method and corrects some erroneous results presented in the previous paper.