We investigate the preventive maintenance and inventory control problem of a one-machine, one-product manufacturing system subject to random breakdowns. Both preventive and corrective interventions have random and non...
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We investigate the preventive maintenance and inventory control problem of a one-machine, one-product manufacturing system subject to random breakdowns. Both preventive and corrective interventions have random and non-negligible durations during which an excess of final products inventory is necessary to fulfill demand. The objective of this study is to find the production rate and the preventive maintenance schedule that minimize the total cost of maintenance and inventory/backlog in the case of periodic preventive maintenance. A near-optimal policy characterization with a simple structure is carried out using a numerical approach. Such a policy is a combination of a hedging point policy and a modified periodic preventive maintenance strategy, under which preventive maintenance actions are performed only if the inventory level exceeds a sufficient level. A simulation-based experimental approach is adopted to achieve a close approximation of the optimal control parameters. It is concluded from a sensitivity analysis and a comparative analysis that the near-optimal control policy leads to a significant cost reduction as compared to the combination of a hedging point policy and a classical periodic preventive maintenance policy. (C) 2010 Elsevier B.V. All rights reserved.
This paper examines the problem of finding an optimal operating policy for Hydro-Quebec's Manicouagan River and Outardes River hydroelectric installations. The solution method is based on the sampling dynamic prog...
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This paper examines the problem of finding an optimal operating policy for Hydro-Quebec's Manicouagan River and Outardes River hydroelectric installations. The solution method is based on the sampling dynamicprogramming (SSDP) algorithm. We use a new hydrologic state variable to capture the inflows regime, and this variable is given by a linear combination of the snow water equivalent and soil moisture. In real-time operation, this variable is calculated by a hydrologic model and incorporated in the operating policy to calculate the water released at each power plant. The algorithm is compared to the lag-1 stochastic dynamic programming (SDP) already implemented at Hydro-Quebec, through a statistical analysis with a set of 40 synthetic historical inflow scenarios obtained by hydrologic modeling, using synthetic temperature and precipitation produced by a stochastic weather generator. The results of the analysis show that the SSDP operating policy is statistically superior to the operating policy of the lag-1 SDP model. The SSDP operating policy does not underestimate the volume of runoff occurring during the spring season contrary to SDP. Consequently, there is a reduction in the hm(3) of water spilled, while the average annual generation is increased.
Sustainable product lifecycle systems are attracting increasing attention because of cost competition, resource constraints and environmental issues. Short lifecycle products, such as consumer and defense electronics,...
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Sustainable product lifecycle systems are attracting increasing attention because of cost competition, resource constraints and environmental issues. Short lifecycle products, such as consumer and defense electronics, are of particular concern. We formulate a product lifecycle evolution system based on stochastic dynamic programming. By applying the concept of a sustainable product lifecycle system on a product line, conclusions and guidelines for rational decision making can be developed through each phase of the product life cycle. Published by Elsevier B.V.
This contribution focuses on the cost-effective management of the combined use of two procurement options: the short-term option is given by a spot market with random price, whereas the long-term alternative is charac...
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This contribution focuses on the cost-effective management of the combined use of two procurement options: the short-term option is given by a spot market with random price, whereas the long-term alternative is characterized by a multi period capacity reservation contract with fixed purchase price and reservation level. A reservation cost, proportional with the reservation level, has to be paid for the option of receiving any amount per period up to the reservation level. A long-term decision has to be made regarding the reserved capacity level, and then it has to be decided - period by period - which quantities to procure from the two sources. Considering the multi-period problem with stochastic demand and spot price, the structure of the optimal combined purchasing policy is derived using stochastic dynamic programming. Exploiting these structural properties, an advanced heuristic is developed to determine the respective policy parameters. This heuristic is compared with two rolling-horizon approaches which use the one-period and two-period optimal solution. A comprehensive numerical study reveals that the approaches based on one-period and two-period solutions have considerable drawbacks, while the advanced heuristic performs very well compared to the optimal solution. Finally, by exploiting our numerical results we give some insights into the system's behavior under problem parameter variations. (C) 2012 Elsevier B.V. All rights reserved.
The zero-emission zone (ZEZ) is a recent environmental regulation that restricts the entry of internal combustion engine vehicles. In a ZEZ, hybrid electric vehicles (HEVs) are allowed but must operate in full-electri...
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The zero-emission zone (ZEZ) is a recent environmental regulation that restricts the entry of internal combustion engine vehicles. In a ZEZ, hybrid electric vehicles (HEVs) are allowed but must operate in full-electric mode. Therefore, it is important for HEVs entering a ZEZ to have a sufficiently charged battery. This study presents a stochastic dynamic programming-based power management strategy for optimizing HEV charging in preparation for ZEZ drives. stochastic dynamic programming models the driver's intentions as a Markov chain and designs optimal controllers by incorporating future probabilistic information up to an infinite time horizon. Furthermore, the proposed controller takes into account the remaining distance to the zero-emission zone, enabling efficient charging. Compared to stochastic dynamic programming strategies that do not consider the remaining distance, the proposed power management strategy improves the equivalent fuel efficiency by up to about 21%.
This paper considers the vehicle routing problem with stochastic demands under optimal restocking. We develop an exact algorithm that is effective for solving instances with many vehicles and few customers per route. ...
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This paper considers the vehicle routing problem with stochastic demands under optimal restocking. We develop an exact algorithm that is effective for solving instances with many vehicles and few customers per route. In our experiments, we show that in these instances, solving the stochastic problem is most relevant (i.e., the potential gains over the deterministic equivalent solution are highest). The proposed branch-price- and-cut algorithm relies on an efficient labeling procedure, exact and heuristic dominance rules, and completion bounds to price profitable columns. Instances with up to 76 nodes could be solved in less than five hours, and instances with up to 148 nodes could be solved in long runs of the algorithm. The experiments also allowed new findings on the problem. The solution to the stochastic problem is up to 10% less costly than the deterministic equivalent solution. Opening new routes reduces restocking costs and in many cases results in solutions with less transportation costs. When the number of routes is not fixed, the optimal solutions under detour-to-depot and optimal restocking are nearly equivalent. However, when the number of routes is limited and the expected demand along a route is allowed to exceed the vehicle capacity, optimal restocking may be significantly more cost-effective than the detour-to-depot policy.
The production and inventory management of blood products at blood banks and hospitals is it problem of general human interest. As a shortage may put lives at risk, shortages are to be kept to a minimum. As the supply...
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The production and inventory management of blood products at blood banks and hospitals is it problem of general human interest. As a shortage may put lives at risk, shortages are to be kept to a minimum. As the supply is voluntary and costly, any spill of unused blood (products) is also to be minimized. Blood platelets (thrombocytes), which are the most expensive and perishable blood product, have the complication of a limited "shelf life" of only 5-7 days. A general figure in the Western world (the USA and Western Europe) for the spill of blood platelets is in the order of 15-20%. A combined new approach is therefore presented which combines stochastic dynamic programming (SDP) and simulation to provide: (i) Practical simple order-up-to rules that are nearly optimal. (ii) Formal theoretical support. The approach has been applied to a Dutch regional Blood bank. Numerical results show it significant reduction of the figures from: 1%, to 1% for shortages;20% to 1% for spill. A practical question for blood bank managers that still remains is: "How to anticipate irregular production breaks like at Easter and Christmas?" The present paper therefore will extend the combined SDP-Simulation approach to include such breaks. The main findings are: Also for these breaks a simple order-up-to rule remains to be nearly optimal. Also for these breaks the outdating and shortages call be kept less than M. The (stationary) periods with production and the (non-stationary) breaks without can be integrated. The approach thus seems suitable for practical implementation. (C) 2007 Elsevier B.V. All rights reserved.
Relying only on the classical Bahadur-Rao approximation for large deviations (LDs) of univariate sample means, we derive strong LD approximations for probabilities involving two sets of sample means. The main result c...
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Relying only on the classical Bahadur-Rao approximation for large deviations (LDs) of univariate sample means, we derive strong LD approximations for probabilities involving two sets of sample means. The main result concerns the exact asymptotics (as n -> infinity) of P(max(i is an element of{1,...,dx}) (X) over bar (i,n) <= min i is an element of({1,...,dy}) (Y) over bar (i,n)), with the (X) over bar (i, n) s (Y(i, n)s, respectively) denoting d(x) (d(y)) independent copies of sample means associated with the random variable X ( Y). Assuming E X > E Y, this is a rare event probability that vanishes essentially exponentially, but with an additional polynomial term. We also point out how the probability of interest can be estimated using importance sampling in a logarithmically efficient way. To demonstrate the usefulness of the result, we show how it can be applied to compare the order statistics of the sample means of the two populations. This has various applications, for instance in queuing or packing problems.
We seek the minimum harvest age and threshold price for sustaining forest management by constructing a stochastic dynamic programming model using a geometric mean-reverting process for log price dynamics. Three decisi...
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We seek the minimum harvest age and threshold price for sustaining forest management by constructing a stochastic dynamic programming model using a geometric mean-reverting process for log price dynamics. Three decisions-"Wait for harvest", "Harvest & Plant", and "Harvest & Abandon"aEuro"are assumed. The applied growth simulator is deterministic. Using the monthly time series data of sugi (Cryptomeria japonica) log price from 1975 to 2006, our analyses show that when the reverted mean is lower than the cost, the minimum harvest age increases as the current price approaches the threshold price, then declines. In other cases with a higher reverted mean, the minimum harvest age increases as the current or initial log price decreases. When the initial log price approaches the threshold price, the minimum harvest age tends to increase. These phenomena can be used to evaluate the possibility of management abandonment under a stochastic situation of log price dynamics.
This paper studies the problem of pricing high-dimensional American options. We propose a method based on the state-space partitioning algorithm developed by Jin et al. (2007) and a dimension-reduction approach introd...
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This paper studies the problem of pricing high-dimensional American options. We propose a method based on the state-space partitioning algorithm developed by Jin et al. (2007) and a dimension-reduction approach introduced by Li and Wu (2006). By applying the approach in the present paper, the computational efficiency of pricing high-dimensional American options is significantly improved, compared to the extant approaches in the literature, without sacrificing the estimation precision. Various numerical examples are provided to illustrate the accuracy and efficiency of the proposed method. Pseudcode for an implementation of the proposed approach is also included. (C) 2013 Elsevier B.V. All rights reserved.
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