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Boaz Golany Konstantin Kogan Uriel G. Rothblum 《Journal of Optimization Theory and Applications》2011,148(2):336-363
We generalize a static two-agent location problem into dynamic, asymmetric settings. The dynamics is due to the ability of
the agents to move at limited speeds. Since each agent has its own objective (demand) function and these functions are interdependent,
decisions made by each agent may affect the performance of the other agent and thus affect the overall performance of the
system. We show that, under a broad range of system’s parameters, centralized (system-wide optimal) and non-cooperative (Nash)
behavior of the agents are characterized by a similar structure. The timing of these trajectories and the intermediate speeds
are however different. Moreover, non-cooperative agents travel more and may never rest and thus the system performance deteriorates
under decentralized decision-making. We show that a static linear reward approach, recently developed in Golany and Rothblum
(Nav. Res. Logist. 53(1):1–15, 2006), can be generalized to provide coordination of the moving agents and suggest its dynamic modification. When the reward scheme
is applied, the agents are induced to choose the system-wide optimal solution, even though they operate in a decentralized
decision-making mode. 相似文献
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Robust optimization (RO) is a distribution-free worst-case solution methodology designed for uncertain maximization problems via a max-min approach considering a bounded uncertainty set. It yields a feasible solution over this set with a guaranteed worst-case value. As opposed to a previous conception that RO is conservative based on optimal value analysis, we argue that in practice the uncertain parameters rarely take simultaneously the values of the worst-case scenario, and thus introduce a new performance measure based on simulated average values. To this end, we apply the adjustable RO (AARC) to a single new product multi-period production planning problem under an uncertain and bounded demand so as to maximize the total profit. The demand for the product is assumed to follow a typical life-cycle pattern, whose length is typically hard to anticipate. We suggest a novel approach to predict the production plan’s profitable cycle length, already at the outset of the planning horizon. The AARC is an offline method that is employed online and adjusted to past realizations of the demand by a linear decision rule (LDR). We compare it to an alternative offline method, aiming at maximum expected profit, applying the same LDR. Although the AARC maximizes the profit against a worst-case demand scenario, our empirical results show that the average performance of both methods is very similar. Further, AARC consistently guarantees a worst profit over the entire uncertainty set, and its model’s size is considerably smaller and thus exhibit superior performance. 相似文献
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Decision makers usually have to face a budget and other type of constraints when they have to decide which projects are going to be undertaken (to satisfy their requirements and guarantee profitable growth). Our purpose is to assist them in the task of selecting project portfolios. We have approached this problem by proposing a general nonlinear binary multi-objective mathematical model, which takes into account all the most important factors mentioned in the literature related with Project Portfolio Selection and Scheduling. Due to the existence of uncertainty in different aspects involved in the aforementioned decision task, we have also incorporated into the model some fuzzy parameters, which allow us to represent information not fully known by the decision maker/s. The resulting problem is both fuzzy and multiobjective. The results are complemented with graphical tools, which show the usefulness of the proposed model to assist the decision maker/s. 相似文献
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Boaz Golany Edward H. Kaplan Abraham Marmur Uriel G. Rothblum 《European Journal of Operational Research》2009
Probabilistic uncertainty is caused by “chance”, whereas strategic uncertainty is caused by an adverse interested party. Using linear impact functions, the problems of allocating a limited resource to defend sites that face either probabilistic risk or strategic risk are formulated as optimization problems that are solved explicitly. The resulting optimal policies differ – under probabilistic risk, the optimal policy is to focus the investment of resources on priority sites where they yield the highest impact, while under strategic risk, the best policy is to spread the resources so as to decrease the potential damage level of the most vulnerable site(s). Neither solution coincides with the commonly practiced proportionality allocation scheme. 相似文献
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This paper addresses the problem of scheduling activities in projects with stochastic activity durations. The aim is to determine
for each activity a gate—a time before it the activity cannot begin. Setting these gates is analogous to setting inventory
levels in the news vendor problem. The resources required for each activity are scheduled to arrive according to its gate.
Since activities’ durations are stochastic, the start and finish time of each activity is uncertain. This fact may lead to
one of two outcomes: (1) an activity is ready to start its processing as all its predecessors have finished, but it cannot
start because the resources required for it were scheduled to arrive at a later time. (2) The resources required for the activity
have arrived and are ready to be used but the activity is not ready to start because of precedence constraints. In the first
case we will incur a “holding” cost while in the second case, we will incur a “shortage” cost. Our objective is to set gates
so as to minimize the sum of the expected holding and shortage costs. We employ the Cross-Entropy method to solve the problem.
The paper describes the implementation of the method, compares its results to various heuristic methods and provides some
insights towards actual applications. 相似文献
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We show the optimality of sphere-separable partitions for problems where n vectors in d-dimensional space are to be partitioned into p categories to minimize a cost function which is dependent in the sum of the vectors in each category; the sum of the squares of their Euclidean norms; and the number of elements in each category. We further show that the number of these partitions is polynomial in n. These results broaden the class of partition problems for which an optimal solution is guaranteed within a prescribed set whose size is polynomially bounded in n. Applications of the results are demonstrated through examples. 相似文献
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Robust multi-echelon multi-period inventory control 总被引:2,自引:0,他引:2
Ben-Tal Aharon Golany Boaz Shtern Shimrit 《European Journal of Operational Research》2009,199(3):922-935
We consider the problem of minimizing the overall cost of a supply chain, over a possible long horizon, under demand uncertainly which is known only crudely. Under such circumstances, the method of choice is Robust Optimization, in particular the Affinely Adjustable Robust Counterpart (AARC) method which leads to tractable deterministic optimization problems. The latter is due to a recent re-parametrization technique for discrete time linear control systems. In this paper we model, analyze and test an extension of the AARC method known as the Globalized Robust Counterpart (GRC) in order to control inventories in serial supply chains. A simulation study demonstrates the merit of the methods employed here, in particular, it shows that a good control law that minimizes cost achieves simultaneously good control of the bullwhip effect. 相似文献
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