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.
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.
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.
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.
In this paper, we consider optimal market timing, strategies under transaction costs. We assume that the asset's return follows an auto-regressive model and use long-term investment growth as the objective of a ma...
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In this paper, we consider optimal market timing, strategies under transaction costs. We assume that the asset's return follows an auto-regressive model and use long-term investment growth as the objective of a market timing strategy which entails the shifting of funds between a risky asset and a riskless asset. We give the optimal trading strategy for a finite investment horizon, and analyze its limiting behavior. For a finite horizon, the optimal decision in each step depends on two threshold values. If the return today is between the two values, nothing needs to be done, otherwise funds will be shifted from one asset to another, depending on which threshold value is being exceeded. When investment horizon tends to infinity, the optimal strategy converges to a stationary policy, which is shown to be closely related to a well-known technical trading rule, called Momentum Index trading rule. An integral equation of them two threshold values is given. Numerical results for the limiting stationary strategy are presented. The results confirm the obvious guess that the no-transaction region increases as the transaction cost increase. Finally, the limiting stationary strategy is applied to data in the Hang Seng Index Futures market in Hong Kong. The out-of-sample performance of the limiting stationary strategy is found to be better than the simple strategy sed in literature, which is based on an 1-step ahead forecast of return. (C) 2002 Elsevier Science Ltd. All rights reserved.
Water blending is modelled as a combination of a linear program and a stochasticdynamic program. Optimal policies are found for linear and integer-linear formulations using both an expected monetary value and conditi...
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Water blending is modelled as a combination of a linear program and a stochasticdynamic program. Optimal policies are found for linear and integer-linear formulations using both an expected monetary value and conditional value-at-risk criterion. The sensitivity of these solutions to the discretisation over volume and over time is investigated.
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.
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.
A discrete search strategy is presented for potential real-time generations of four-dimensional trajectories for a single autonomous aerospace vehicle amid known obstacles and conflicts. A model of autonomous operatio...
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A discrete search strategy is presented for potential real-time generations of four-dimensional trajectories for a single autonomous aerospace vehicle amid known obstacles and conflicts. A model of autonomous operation is first developed. The problem of and requirements on real-time trajectory generations for autonomous aerospace vehicles are discussed. After an overview of various potential solution frameworks, a discrete search strategy is developed. In this strategy, a four-dimensional search space is defined and discretized. Potential obstacles and conflicts are represented by several basic geometric shapes and their combinations. Mathematical conditions are developed for a trajectory segment to be outside of an obstacle or conflict. Then, the A* search technique is used to obtain trajectory solutions, in which successor points are selected that avoid obstacles and conflicts and that satisfy dynamic motion constraints of the vehicle. A linear combination of flight distance and flight time is optimized in the trajectory generation process. A heuristic function that approximates this performance index is developed for the A* search procedure. Examples are provided that illustrate the application of the proposed method.
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