Narrow Results

Resource constrained scheduling problems are concerned with the allocation of limited resources to tasks over time. The solution to these problems is often a sequence, resource allocation, and schedule. When human workers are incorporated as a renewable resource, the allocation is defined as the number of workers assigned to perform each task. In practice, however, this solution does not adequately address how individual workers are to be assigned to tasks. This paper, therefore, provides mathematical models and heuristic techniques for solving this multi-period precedence constrained assignment problem. Results of a significant numerical investigation are also presented.

In this paper, we propose an assignment-based local search method for solving vehicle routing problems. This method is a multi-route improvement algorithm that can operate on several routes at a time. To evaluate the performance of the proposed method, extensive computational experiments on the proposed method applied to a set of benchmark problems are carried out. The results show that the proposed method, when coupled with metaheuristics such as simulated annealing, is comparable with other efficient heuristic methods proposed in the literature.

Information of sensitivity analysis, in a linear programming problem, is usually more important than the optimal solution itself. However, traditional sensitivity analysis, which perturbs exactly one coefficient and then determines the range preserving the optimality of the current optimal base, is impractical for the assignment problem. An optimal basic solution of the assignment problem is inherently degenerate, so it may be that the optimal base has changed but the optimal assignment remains unchanged. Furthermore, elements of a column (or row) in a cost matrix of assignment problem are usually closely related and change simultaneously, not uniquely. This paper focuses on two kinds of sensitivity analyses for the assignment problem. One is to determine the sensitivity range, over which the current optimal assignment or all the optimal assignments remain optimal, while perturbing the elements of one column (or row) in a cost matrix of the assignment problem simultaneously but dependently. The other is to perturb elements of one column (or row) in a cost matrix of the assignment problem simultaneously but independently. Numerical illustrations are presented to demonstrate that the approaches are useful in practice.

Alternative optimal solutions can give more choice for practical decision making. Therefore, the provision of methods for finding alternative optimal solutions is an important component part of the solution techniques for optimization models. The aim of this paper is to present a branch-and-bound algorithm for finding all optimal solutions of the linear assignment problem. Numerical experimental results are also given.

We are concerned with a variation of the assignment problem, where the assignment costs differ under different scenarios. We give a surrogate relaxation approach to derive a lower bound and an upper bound quickly, and show that the pegging test known for zero–one programming problems is also applicable to this problem. Next, we discuss how the computation time for pegging can be shortened by taking the special structure of the assignment problem into account. Finally, through numerical experiments we show that the developed method finds exact solutions for instances with small number of scenarios in relatively small CPU time, and good approximate solutions in case of many scenarios.

In this paper, we study the problem of unrelated parallel machine scheduling with controllable processing times and deteriorating maintenance activity. The jobs are nonresumable. The processing time of each job is a linear function of the amount of a continuously divisible resource allocated to the job. During the planning horizon, there is at most one maintenance activity scheduled on each machine. Additionally, if the starting time of maintenance activity is delayed, the length of the maintenance activity required to perform will increase. Considering the total completion times of all jobs, the impact of maintenance activity in the form of the variation in machine load and the amounts of compression, we need to determine the job sequence on each machine, the location of maintenance activities and processing time compression of each job simultaneously. Accordingly, a polynomial time solution to the problem is provided.

We focus on a single-machine scheduling problem with common and slack due-window assignment methods. Both the job sequence and due-windows are decision variables to be determined by the decision maker. We consider the following performance criterion: the total weighted number of early and late jobs plus the total weighted of earliness, tardiness and due-window assignment cost, where the weights depend on the position in which a job is scheduled. Some properties are established, and it is shown that the problem can be solved in $O(n^5)$ time, where $n$ is the number of jobs. The extensions of the model are to cases of general position-dependent processing times and time-dependent processing times.

Graphs provide us with a flexible and powerful way to represent objects in various areas of computer science. One of the main drawbacks is, however, that many standard algorithms on graphs have a high computational complexity. The present paper considers the problem of graph isomorphism, i.e. checking two graphs for identity. A novel approach for the efficient computation of graph isomorphism is presented. The proposed algorithm is based on bipartite graph matching by means of an assignment algorithm. The algorithmic framework is suboptimal in the sense of possibly rejecting pairs of graphs without making a decision. As an advantage, however, it offers polynomial runtime. In experiments on diverse graph data sets we demonstrate substantial speedups of our proposed method over several standard procedures for graph isomorphism. Furthermore, although the computational framework for isomorphism is suboptimal, we show that the proposed algorithm rejects only very few pairs of graphs and otherwise returns correct results.

We show that several decision problems originating from max-plus or tropical convexity are equivalent to zero-sum two player game problems. In particular, we set up an equivalence between the external representation of tropical convex sets and zero-sum stochastic games, in which tropical polyhedra correspond to deterministic games with finite action spaces. Then, we show that the winning initial positions can be determined from the associated tropical polyhedron. We obtain as a corollary a game theoretical proof of the fact that the tropical rank of a matrix, defined as the maximal size of a submatrix for which the optimal assignment problem has a unique solution, coincides with the maximal number of rows (or columns) of the matrix which are linearly independent in the tropical sense. Our proofs rely on techniques from non-linear Perron–Frobenius theory.

Moving object databases (MOD) are being used in a wide range of location-based services that are of growing interest in many application areas. In the literature, several query types such as nearest neighbor, reverse nearest neighbor, k-nearest neighbor, and proximity queries have been considered in MOD. In this paper, we propose a novel operator called the assignment operator as a query type for MOD. The assignment operator is an operator used in a query to solve the assignment problem (also known as the weighted bipartite graph-matching problem). Assignment operator finds a perfect match between two sets of objects in a manner that minimizes a total cost. For instance, a set of moving objects such as taxi cabs are assigned to a set of customers in a manner that minimizes the total cost of traveling for the taxis. A possible implementation of the assignment operator in MOD and its performance evaluation are given.

In this paper, a mixed integer programming (MIP) mathematical model was formulated for the quay crane scheduling and assignment problem (QCSAP) in container terminals with the aim of minimizing the total cost of activities. With the assumption that due to the uncertain nature of the ship’s activities and operations, we have considered most of the parameters of the problem to be indeterminate in order to bring the optimal solution closer to the real world. In this paper, the uncertain nature of the parameters was investigated by using uncertainty theory and in the form of indeterminate quantities. These uncertainties might be subject to the conditions, such as the failure of cranes, container terminal transportation means, congestion in the dockyard, adverse weather conditions, etc. Further, considering the large dimensions of such real problems and the complexity of solving them in terms of processing time, the simulated annealing (SA) meta-heuristic optimization algorithm was utilized to solve the above model. The proposed algorithm has been coded by MATLAB software and its efficiency was put on test by comparing its results for a low-dimensional problem with the accurate solution from GAMS software is compared in terms of computational times for small sizes. The proposed algorithm exhibited promising potentials for quick approximation of usable solutions to high-dimensional QCSAPs. The calculations show that, nondeterministic model with the help of the above proposed algorithm can be one of the basic factors in increasing the productivity of container terminals and the main purpose and advantage of this research is compared to the basic model presented by Tavakkoli-Moghaddam et al. in 2009 which has been analyzed and investigated with definitive data and optimized with the help of genetic algorithm. In addition, some restrictions were added to the basic model in order to make the above crane assignment scheduling problem more practical.

The pattern matching with wildcards and length constraints problem is an interesting problem in the literature whose computational complexity is still open. There are polynomial time exact algorithms for its special cases. There are heuristic algorithms, and online algorithms that do not guarantee an optimal solution to the original problem. We consider two special cases of the problem for which we develop offline solutions. We give an algorithm for one case with provably better worst case time complexity compared to existing algorithms. We present the first exact algorithm for the second case. This algorithm uses integer linear programming (ILP) and it takes polynomial time under certain conditions.

Decision rules for stabilization policy in an open economy arc examined under alternative specifications of the balance of payments. In particular, distinction between interest-sensitive debt capital and equity capital which responds to an activity variable alters the comparative static properties of instrument assignment. Various aspects of dynamic adjustment are further investigated in a context in which time is endogenous and in which the decision process minimizes a criterion function. It is shown that traditional one-to-one pairing of targets and controls may be inferior to assignment of clusters of instruments to some targets for specified time intervals.