In this paper, we develop and test scenario generation methods for asset liability management models. We propose a multi-stage stochastic programming model for a Dutch pension fund. Both randomly sampled event trees a...
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In this paper, we develop and test scenario generation methods for asset liability management models. We propose a multi-stage stochastic programming model for a Dutch pension fund. Both randomly sampled event trees and event trees fitting the mean and the covariance of the return distribution are used for generating the coefficients of the stochastic program. In order to investigate the performance of the model and the scenario generation procedures we conduct rolling horizon simulations. The average cost and the risk of the stochastic programming policy are compared to the results of a simple fixed mix model. We compare the average switching behavior of the optimal investment policies, Our results show that the performance of the multi-stage stochastic program could be improved drastically by choosing an appropriate scenario generation method. (C) 2001 Elsevier Science B.V. All rights reserved.
This study addresses the production planning problem for perishable products, in which the cost and shortage of products are minimised subject to a set of constraints such as warehouse space, labour working time and m...
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This study addresses the production planning problem for perishable products, in which the cost and shortage of products are minimised subject to a set of constraints such as warehouse space, labour working time and machine time. Using the concept of postponement, the production process for perishable products is differentiated into two phases to better utilise the resources. A two-stage stochastic programming with recourse model is developed to determine the production loading plan with uncertain demand and parameters. A set of data from a toy company shows the benefits of the postponement strategy: these include lower total cost and higher utilisation of resources. The impact of unit shortage cost under different probability distribution of economic scenarios on the total cost is analyzed. Comparative analysis of solutions with and without postponement strategies is also performed.
Bayesian forecasting models provide distributional estimates for random parameters, and relative to classical schemes, have the advantage that they can rapidly capture changes in nonstationary systems using limited hi...
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Bayesian forecasting models provide distributional estimates for random parameters, and relative to classical schemes, have the advantage that they can rapidly capture changes in nonstationary systems using limited historical data. Unlike deterministic optimization, stochastic programs explicitly incorporate distributions for random parameters in the model formulation, and thus have the advantage that the resulting solutions more fully hedge against future contingencies. In this paper, we exploit the strengths of Bayesian prediction and stochastic programming in a rolling-horizon approach that can be applied to solve real-world problems. We illustrate the methodology on an employee production scheduling problem with uncertain up-times of manufacturing equipment and uncertain production rates. Computational results indicate the value of our approach.
The literature of portfolio optimization is extensive and covers several important aspects of the asset allocation problem. However, previous works consider simplified linear borrowing cost functions that leads to sub...
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The literature of portfolio optimization is extensive and covers several important aspects of the asset allocation problem. However, previous works consider simplified linear borrowing cost functions that leads to suboptimal allocations. This paper aims at efficiently solving the leveraged portfolio selection problem with a thorough borrowing cost representation comprising a number lenders with different rates and credit limits. We propose a two-stage stochastic programming model for asset and debt allocation considering a CVaR-based risk constraint and a convex piecewise-linear borrowing cost function. We compare our model to its counterpart with the fixed borrowing rate approximation used in literature. Numerical results show our model significantly improves performance in terms of risk-return trade-off.
The location of multiple cross-docking centers (CDCs) and vehicle routing scheduling are two crucial choices to be made in strategic/tactical and operational decision levels for logistics companies. The choices lead t...
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The location of multiple cross-docking centers (CDCs) and vehicle routing scheduling are two crucial choices to be made in strategic/tactical and operational decision levels for logistics companies. The choices lead to more realistic problem under uncertainty by covering the decision levels in cross-docking distribution networks. This paper introduces two novel deterministic mixed-integer linear programming (MILP) models that are integrated for the location of CDCs and the scheduling of vehicle routing problem with multiple CDCs. Moreover, this paper proposes a hybrid fuzzy possibilistic-stochastic programming solution approach in attempting to incorporate two kinds of uncertainties into mathematical programming models. The proposed solving approach can explicitly tackle uncertainties and complexities by transforming the mathematical model with uncertain information into a deterministic model. m' imprecise constraints are converted into 2Rm' precise inclusive constraints that agree with R alpha-cut levels, along with the concept of feasibility degree in the objective functions based on expected interval and expected value of fuzzy numbers. Finally, several test problems are generated to appraise the applicability and suitability of the proposed new two-phase MILP model that is solved by the developed hybrid solution approach involving a variety of uncertainties and complexities. (C) 2013 Elsevier Inc. All rights reserved.
We consider multistage stochastic programs, in which decisions can adapt over time, (i.e., at each stage), in response to observation of one or more random variables (uncertain parameters). The case that the time at w...
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We consider multistage stochastic programs, in which decisions can adapt over time, (i.e., at each stage), in response to observation of one or more random variables (uncertain parameters). The case that the time at which each observation occurs is decision-dependent, known as stochastic programming with endogeneous observation of uncertainty, presents particular challenges in handling non-anticipativity. Although such stochastic programs can be tackled by using binary variables to model the time at which each endogenous uncertain parameter is observed, the consequent conditional non-anticipativity constraints form a very large class, with cardinality in the order of the square of the number of scenarios. However, depending on the properties of the set of scenarios considered, only very few of these constraints may be required for validity of the model. Here we characterize minimal sufficient sets of non-anticipativity constraints, and prove that their matroid structure enables sets of minimum cardinality to be found efficiently, under general conditions on the structure of the scenario set.
In this paper, we present an aggregate mathematical model for air traffic flow management (ATFM), a problem of great concern both in Europe and in the United States. The model extends previous approaches by simultaneo...
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In this paper, we present an aggregate mathematical model for air traffic flow management (ATFM), a problem of great concern both in Europe and in the United States. The model extends previous approaches by simultaneously taking into account three important issues: (i) the model explicitly incorporates uncertainty in the airport capacities;(ii) it also considers the trade-off between airport arrivals and departures, which is a crucial issue in any hub airport;and (iii) it takes into account the interactions between different hubs. The level of aggregation proposed for the mathematical model allows us to solve realistic size instances with a commercial solver on a PC. Moreover it allows us to compute solutions which are perfectly consistent with the Collaborative Decision-Making (CDM) procedure in ATFM, widely adopted in the USA and which is currently receiving a lot of attention in Europe. In fact, the proposed model suggests the number of flights that should be delayed, a decision that belongs to the ATFM Authority, rather than assigning delays to individual aircraft. (C) 2011 Elsevier B.V. All rights reserved.
Supply contracts are known as the communication link among supply chain members. As sourcing of required goods is a challenging issue for supply chain members, different sourcing types for different market conditions ...
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Supply contracts are known as the communication link among supply chain members. As sourcing of required goods is a challenging issue for supply chain members, different sourcing types for different market conditions have been presented in the literature. However, the uncertain price condition has not been much focused in the previous studies, and in the limited works on this issue the correlation between the periods has been ignored. In this paper, sourcing policies are analyzed in a multi-period system in which price and demand follow a Geometric Brownian Motion with drift. Wholesale contract, option contract, and purchase from the spot market are considered as the sourcing alternatives for the buyer. This paper applies the stochastic programming approach to model these three types of sourcing based upon price and demand uncertainties. Afterwards, a hybrid supply model of these sourcing types is developed. By a numerical example, the simulation results of the developed models reveal that each individual sourcing alternative can be selected as the best one in each price and demand behavior. The results also suggest that the proposed hybrid model dominates each of the individual sourcing types. Finally, the paper reports the effects of cost parameter alterations on the solution of the hybrid model through sensitivity analysis. (C) 2015 Published by Elsevier Ltd on behalf of The Society of Manufacturing Engineers.
We consider a partial disassembly line balancing problem with hazardous tasks whose successful completions are uncertain. When any hazardous task fails, it causes damages of the tasks on the workstation that it is per...
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We consider a partial disassembly line balancing problem with hazardous tasks whose successful completions are uncertain. When any hazardous task fails, it causes damages of the tasks on the workstation that it is performed on and all remaining tasks to be performed in the succeeding workstations. We attribute probabilities for the successful completion and failure of the hazardous tasks and aim to maximise the total expected net revenue. We formulate the problem as a two-stage stochastic mixed-integer programme where the assignment of the tasks to the workstations is decided in the first-stage, before the resolution of the uncertainty. We give the formulation for one, two and three hazardous tasks, and then extend to the arbitrary number of hazardous tasks. Our numerical results reveal that proposed stochastic programming models return satisfactory performance and can solve instances with up to 73 tasks very quickly. We observe that the number of tasks, number of hazardous tasks and success probabilities are the most significant parameters that affect the performance. We quantify the value of capturing uncertainty using the expected objective values attained by the solution of the stochastic model and that of the expected value model, and obtain very satisfactory results.
Existing complexity results in stochastic linear programming using the Turing model depend only on problem dimensionality. We apply techniques from the information-based complexity literature to show that the smoothne...
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Existing complexity results in stochastic linear programming using the Turing model depend only on problem dimensionality. We apply techniques from the information-based complexity literature to show that the smoothness of the recourse function is just as important. We derive approximation error bounds for the recourse function of two-stage stochastic linear programs and show that their worst case is exponential and depends on the solution tolerance, the dimensionality of the uncertain parameters and the smoothness of the recourse function. (C) 2013 Elsevier B.V. All rights reserved.
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