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Assignment problems in logistics
Janez Povh, 2008, original scientific article

Abstract: We consider two classical problems from location theory which may serve as theoretical models for several logistic problems where one wants to assign elements of a set A to elements of a set B such that some linear or quadratic function attains its minimum. It turns out that linear objective function yields a linear assignment problem, which can be solved easily by several primal-dual methods like Hungarian method, Shortest augmenting path method etc. On the other hand, taking quadratic objective function into account makes the problem much harder. The resulting quadratic assignment problem is a very useful model but also very tough problem from theoretical and practical point of view. We list several well-known applications of these models and also the most effective methods to solve the problem. However, it is still a challenging task to solve this problem to optimality when the size of underlying sets A and B is greater than 25 and currently impossible task when the size is greater than 35.
Keywords: quadratic assignment problem, linear assignment problem, branch and bound algorithm, heuristics
Published: 05.06.2012; Views: 907; Downloads: 57
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Chinese postman problem with priority nodes
Tomaž Kramberger, Gregor Štrubelj, Janez Žerovnik, 2009, original scientific article

Abstract: A generalization of the Chinese Postman Problem is studied in which the delays at a subset of priority nodes are penalized in the cost function. As it is shown that the problem is NP-hard, two tour constructing heuristics are proposed, and their properties are studied. It is proved that one of the heuristics gives optimal solutions on a subset of instances with bounded cost of delays. The implementations of the heuristics are compared on several types of randomly generated instances.
Keywords: Chinese postman problem, ARP, heuristics, Eulerian graph
Published: 05.06.2012; Views: 1103; Downloads: 21
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Heuristic approach to inventory control with advance capacity information
Marko Jakšič, Borut Rusjan, 2009, original scientific article

Abstract: There is a growing trend of information sharing within modern supply chains. This trend is mainly stimulated by recent developments in information technology and the increasing awareness that accurate and timely information helps firms cope with volatile and uncertain business conditions. We model a periodic-review, single-item, capacitated stochastic inventory system, where a supply chain member has the ability to obtain advance capacity information (‘ACI’) about future supply capacity availability. ACI is used to reduce the uncertainty of future supply and thus enables the decision-maker to make better ordering decisions. We develop an easily applicable heuristic based on insights gained from an analysis of the optimal policy. In a numerical study we quantify the benefits of ACI and compare the performance of the proposed heuristic with the optimal performance. We illustrate the conditions in which the procedure is working well and comment on its practical applicability.
Keywords: inventories, supply, stochastic processes, operations research, heuristics
Published: 30.11.2017; Views: 247; Downloads: 162
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Multi-objective optimization algorithms with the island metaheuristic for effective project management problem solving
Christina Brester, Ivan Ryzhikov, Eugene Semenkin, 2017, original scientific article

Abstract: Background and Purpose: In every organization, project management raises many different decision-making problems, a large proportion of which can be efficiently solved using specific decision-making support systems. Yet such kinds of problems are always a challenge since there is no time-efficient or computationally efficient algorithm to solve them as a result of their complexity. In this study, we consider the problem of optimal financial investment. In our solution, we take into account the following organizational resource and project characteristics: profits, costs and risks. Design/Methodology/Approach: The decision-making problem is reduced to a multi-criteria 0-1 knapsack problem. This implies that we need to find a non-dominated set of alternative solutions, which are a trade-off between maximizing incomes and minimizing risks. At the same time, alternatives must satisfy constraints. This leads to a constrained two-criterion optimization problem in the Boolean space. To cope with the peculiarities and high complexity of the problem, evolution-based algorithms with an island meta-heuristic are applied as an alternative to conventional techniques. Results: The problem in hand was reduced to a two-criterion unconstrained extreme problem and solved with different evolution-based multi-objective optimization heuristics. Next, we applied a proposed meta-heuristic combining the particular algorithms and causing their interaction in a cooperative and collaborative way. The obtained results showed that the island heuristic outperformed the original ones based on the values of a specific metric, thus showing the representativeness of Pareto front approximations. Having more representative approximations, decision-makers have more alternative project portfolios corresponding to different risk and profit estimations. Since these criteria are conflicting, when choosing an alternative with an estimated high profit, decision-makers follow a strategy with an estimated high risk and vice versa. Conclusion: In the present paper, the project portfolio decision-making problem was reduced to a 0-1 knapsack constrained multi-objective optimization problem. The algorithm investigation confirms that the use of the island meta-heuristic significantly improves the performance of genetic algorithms, thereby providing an efficient tool for Financial Responsibility Centres Management.
Keywords: 0-1 multi-objective constrained knapsack problem, project management portfolio problem, multi-objective evolution-based optimization algorithms, collaborative and cooperative meta-heuristics
Published: 04.05.2018; Views: 449; Downloads: 149
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