This article considers the empty vehicle redistribution problem in a hub-and-spoke transportation system, with random demands and stochastic transportation times. An event-driven model is formulated, which yields the ...
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This article considers the empty vehicle redistribution problem in a hub-and-spoke transportation system, with random demands and stochastic transportation times. An event-driven model is formulated, which yields the implicit optimal control policy. Based on the analytical results for two-depot systems, a dynamic decomposition procedure is presented which produces a near-optimal policy with linear computational complexity in terms of the number of spokes. The resulting policy has the same asymptotic behavior as that of the optimal policy. It is found that the threshold-type control policy is not usually optimal in such systems. The results are illustrated through small-scale numerical examples. Through simulation the robustness of the dynamic decomposition policy is tested using a variety of scenarios: more spokes, more vehicles, different combinations of distribution types for the empty vehicle travel times and loaded vehicle arrivals. This shows that the dynamic decomposition policy is significantly better than a heuristics policy in all scenarios and appears to be robust to the assumptions of the distribution types. (C) 2008 Wiley Periodicals, Inc.
In this paper, we propose learning-based adaptive control based on reinforcement learning for the booking policy in sea cargo revenue management. The problem setting is that the demand distribution is unknown while th...
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In this paper, we propose learning-based adaptive control based on reinforcement learning for the booking policy in sea cargo revenue management. The problem setting is that the demand distribution is unknown while the historical data is available, and the problem is formulated as a stochastic dynamic programming model. We demonstrate the existence of an optimal control limit policy and investigate the important properties and optimal policy structures of the model. We then propose a reinforcement learning approach for the data-driven approximation of the optimal booking policy to maximize shipping line revenue. The performance of the proposed approach is very close to that of the optimal policy and superior to that of the EMSR-b algorithm. (c) 2021 Elsevier Inc. All rights reserved.
We present a novel method for deriving tight Monte Carlo confidence intervals for solutions of stochastic dynamic programming equations. Taking some approximate solution to the equation as an input, we construct pathw...
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We present a novel method for deriving tight Monte Carlo confidence intervals for solutions of stochastic dynamic programming equations. Taking some approximate solution to the equation as an input, we construct pathwise recursions with a known bias. Suitably coupling the recursions for lower and upper bounds ensures that the method is applicable even when the dynamic program does not satisfy a comparison principle. We apply our method to three nonlinear option pricing problems, pricing under bilateral counterparty risk, under uncertain volatility, and under negotiated collateralization.
We consider a production-inventory system with product returns that are announced in advance by the customers. Demands and announcements of returns occur according to independent Poisson processes. An announced return...
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We consider a production-inventory system with product returns that are announced in advance by the customers. Demands and announcements of returns occur according to independent Poisson processes. An announced return is either actually returned or cancelled after a random return lead time. We consider both lost sale and backorder situations. Using a Markov decision formulation, the optimal production policy, with respect to the discounted cost over an infinite horizon, is characterized for situations with and without advance return information. We give insights in the potential value of this information. Also some attention is paid to combining advance return and advance demand information. Further applications of the model as well as topics for further research are indicated. (C) 2011 Elsevier B.V. All rights reserved.
Managing highly skilled employees is extremely complex because of the need to balance the costs and time lags associated with their training against the need to meet demand as quickly as possible. Unlike previous appr...
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Managing highly skilled employees is extremely complex because of the need to balance the costs and time lags associated with their training against the need to meet demand as quickly as possible. Unlike previous approaches to this problem in the staffing literature, this paper develops an optimal staffing policy at the strategic level to cope with nonstationary stochastic demand for a staff characterized by unproductive apprentice employees and fully productive experienced employees. The paper then explores the implications of this policy in different industries, using empirical data. Aside from the optimal policy, this paper's primary results include: (1) demand volatility reduces average productivity, most especially under conditions of low (or slightly negative) growth and - nonintuitively - low employee turnover or knowledge obsolescence rates;(2) there is a trade-off between meeting demand and high productivity;(3) firms with longer business cycles should smooth their hiring and firing policies;and (4) firms in industries with longer training times should smooth their hiring and firing policies. The paper also explores the possible rewards from reducing training times and turnover rates. Finally, it discusses managerial implications and possible future directions in research.
This paper studies the inventory management problem of dual channels operated by one vendor. Demands of dual channels are inventory-level-dependent. We propose a multi-period stochastic dynamic programming model which...
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This paper studies the inventory management problem of dual channels operated by one vendor. Demands of dual channels are inventory-level-dependent. We propose a multi-period stochastic dynamic programming model which shows that under mild conditions, the myopic inventory policy is optimal for the infinite horizon problem. To investigate the importance of capturing demand dependency on inventory levels, we consider a heuristic where the vendor ignores demand dependency on inventory levels, and compare the optimal inventory levels with those recommended by the heuristic. Through numerical examples, we show that the vendor may order less for dual channels than those recommended by the heuristic, and the difference between the inventory levels in the two cases can be so large that the demand dependency on inventory levels cannot be neglected. In the end, we numerically examine the impact of different ways to treat unmet demand and obtain some managerial insights.
This paper studies two closely related online-list scheduling problems of a set of n jobs with unit processing times on a set of m multipurpose machines. It is assumed that there are k different job types, where each ...
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This paper studies two closely related online-list scheduling problems of a set of n jobs with unit processing times on a set of m multipurpose machines. It is assumed that there are k different job types, where each job type can be processed on a unique subset of machines. In the classical definition of online-list scheduling, the scheduler has all the information about the next job to be scheduled in the list while there is uncertainty about all the other jobs in the list not yet scheduled. We extend this classical definition to include lookahead abilities, i.e., at each decision point, in addition to the information about the next job in the list, the scheduler has all the information about the next h jobs beyond the current one in the list. We show that for the problem of minimizing the makespan there exists an optimal (1-competitive) algorithm for the online problem when there are two job types. That is, the online algorithm gives the same minimal makespan as the optimal offline algorithm for any instance of the problem. Furthermore, we show that for more than two job types no such online algorithm exists. We also develop several dynamicprogramming algorithms to solve a stochastic version of the problem, where the probability distribution of the job types is known and the objective is to minimize the expected makespan.
We consider a sequencing problem in which there are n jobs to be processed nonpreemptively on m nonidentical processors. The processing time of the j- th processor is exponentially distributed with rate μ j , where ...
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We consider a sequencing problem in which there are n jobs to be processed nonpreemptively on m nonidentical processors. The processing time of the j- th processor is exponentially distributed with rate μ j , where μ 1 ⩾μ 2 ⩾⋯⩾μ m . Job i incurs a holding cost at rate c i per unit time while still in the system, where c 1 ⩾c 2 ⩾⋯⩾c n . We show that to minimize total expected holding costs (weighted flowtime), it is optimal to take the fastest (lowest indexed) available processor, say processor j , and assign job k to it if k>(Σ i j − 1 μ i )/μ j −j ⩾ k−1 . After each assignment the jobs are renumbered (so that job k+1 becomes job k , etc.), and the procedure is repeated with the next fastest available processor, etc. Note that the policy does not depend on the values of the holding costs c i . This result is a generalization of the result of Agrawala et al. (1984) for minimizing expected flowtime, i.e., minimizing total holding cost when the holding costs of all the jobs are the same. We give a simpler proof of the more general result.
Decline of cavity-using wildlife species is a major forest management issue. One of the causes of this problem is the loss in cavity tree abundance, resulting from short rotation silviculture, stand-replacing disturba...
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Decline of cavity-using wildlife species is a major forest management issue. One of the causes of this problem is the loss in cavity tree abundance, resulting from short rotation silviculture, stand-replacing disturbance events and timber harvesting in disturbed stands. Cavity tree availability cannot be guaranteed due to the stochastic nature of disturbance events. We developed a Markov model to predict future cavity tree availability under alternative tree felling and fire protection strategies using information on cavity tree dynamics and fire history. stochastic dynamic programming was used to find a strategy that maximizes timber revenues less forest management costs, including the cost of an artificial nest-box program that must be implemented whenever cavity trees become critically scarce. The requirement to implement a nest-box program in such circumstances strongly influenced the optimal tree felling strategy and resulted in a higher probability of having cavity trees in the future. This reflected an increase in the retention of old growth forest and stands with fire-killed cavity trees as well as stands of younger trees to provide a future source of cavities. These results demonstrate the need to consider the costs of artificial habitat enhancement and the risk Of future cavity tree scarcity in multiple-use forest management planning. (C) 2008 Elsevier B.V. All rights reserved.
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