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1.
We consider two-stage stochastic programming problems with integer recourse. The L-shaped method of stochastic linear programming is generalized to these problems by using generalized Benders decomposition. Nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques. Finite convergence of the method is established when Gomory’s fractional cutting plane algorithm or a branch-and-bound algorithm is applied.  相似文献   

2.
Stochastic programming problems have very large dimension and characteristic structures which are tractable by decomposition. We review basic ideas of cutting plane methods, augmented Lagrangian and splitting methods, and stochastic decomposition methods for convex polyhedral multi-stage stochastic programming problems.  相似文献   

3.
Decomposition has proved to be one of the more effective tools for the solution of large-scale problems, especially those arising in stochastic programming. A decomposition method with wide applicability is Benders' decomposition, which has been applied to both stochastic programming as well as integer programming problems. However, this method of decomposition relies on convexity of the value function of linear programming subproblems. This paper is devoted to a class of problems in which the second-stage subproblem(s) may impose integer restrictions on some variables. The value function of such integer subproblem(s) is not convex, and new approaches must be designed. In this paper, we discuss alternative decomposition methods in which the second-stage integer subproblems are solved using branch-and-cut methods. One of the main advantages of our decomposition scheme is that Stochastic Mixed-Integer Programming (SMIP) problems can be solved by dividing a large problem into smaller MIP subproblems that can be solved in parallel. This paper lays the foundation for such decomposition methods for two-stage stochastic mixed-integer programs.  相似文献   

4.
We present a new exact approach for solving bi-objective integer linear programs. The new approach employs two of the existing exact algorithms in the literature, including the balanced box and the ?-constraint methods, in two stages. A computationally study shows that the new approach has three desirable characteristics. (1) It solves less single-objective integer linear programs. (2) Its solution time is significantly smaller. (3) It is competitive with the two-stage algorithm proposed by Leitner et al. (2016).  相似文献   

5.
Based on the polyhedral representation of Künzi-Bay and Mayer [Künzi-Bay, A., Mayer, J., 2006. Computational aspects of minimizing conditional value-at-risk. Computational Management Science 3, 3–27] , we propose decomposition frameworks for handling CVaR objectives and constraints in two-stage stochastic models.  相似文献   

6.
An efficient procedure that concurrently generates Outer-Approximation and Benders cuts is devised to tackle the single allocation hub location problem under congestion, an MINLP. The proposed method is able to optimally solve large instances (up to 200 nodes) in reasonable time. The combination of both cuts is an algorithmic novelty.  相似文献   

7.
We consider a class of two-stage stochastic integer programs and their equivalent reformulation that uses the integer programming value functions in both stages. One class of solution methods in the literature is based on the idea of pre-computing and storing exact value functions, and then exploiting this information within a global branch-and-bound framework. Such methods are known to be very sensitive to the magnitude of feasible right-hand side values. In this note we propose a simple constraint-aggregation based approach that potentially alleviates this limitation.  相似文献   

8.
We present an algorithmic framework, so-called BFC-TSMIP, for solving two-stage stochastic mixed 0–1 problems. The constraints in the Deterministic Equivalent Model have 0–1 variables and continuous variables at any stage. The approach uses the Twin Node Family (TNF) concept within an adaptation of the algorithmic framework so-called Branch-and-Fix Coordination for satisfying the nonanticipativity constraints for the first stage 0–1 variables. Jointly we solve the mixed 0–1 submodels defined at each TNF integer set for satisfying the nonanticipativity constraints for the first stage continuous variables. In these submodels the only integer variables are the second stage 0–1 variables. A numerical example and some theoretical and computational results are presented to show the performance of the proposed approach.  相似文献   

9.
An algorithm incorporating the logarithmic barrier into the Benders decomposition technique is proposed for solving two-stage stochastic programs. Basic properties concerning the existence and uniqueness of the solution and the underlying path are studied. When applied to problems with a finite number of scenarios, the algorithm is shown to converge globally and to run in polynomial-time. Received: August 1998 / Accepted: August 2000?Published online April 12, 2001  相似文献   

10.
The treasurer of a bank is responsible for the cash management of several banking activities. In this work, we focus on two of them: cash management in automatic teller machines (ATMs), and in the compensation of credit card transactions. In both cases a decision must be taken according to a future customers demand, which is uncertain. From historical data we can obtain a discrete probability distribution of this demand, which allows the application of stochastic programming techniques. We present stochastic programming models for each problem. Two short-term and one mid-term models are presented for ATMs. The short-term model with fixed costs results in an integer problem which is solved by a fast (i.e. linear running time) algorithm. The short-term model with fixed and staircase costs is solved through its MILP equivalent deterministic formulation. The mid-term model with fixed and staircase costs gives rise to a multi-stage stochastic problem, which is also solved by its MILP deterministic equivalent. The model for compensation of credit card transactions results in a closed form solution. The optimal solutions of those models are the best decisions to be taken by the bank, and provide the basis for a decision support system.  相似文献   

11.
The fleet assignment model assigns a fleet of aircraft types to the scheduled flight legs in an airline timetable published six to twelve weeks prior to the departure of the aircraft. The objective is to maximize profit. While costs associated with assigning a particular fleet type to a leg are easy to estimate, the revenues are based upon demand, which is realized close to departure. The uncertainty in demand makes it challenging to assign the right type of aircraft to each flight leg based on forecasts taken six to twelve weeks prior to departure. Therefore, in this paper, a two-stage stochastic programming framework has been developed to model the uncertainty in demand, along with the Boeing concept of demand driven dispatch to reallocate aircraft closer to the departure of the aircraft. Traditionally, two-stage stochastic programming problems are solved using the L-shaped method. Due to the slow convergence of the L-shaped method, a novel multivariate adaptive regression splines cutting plane method has been developed. The results obtained from our approach are compared to that of the L-shaped method, and the value of demand-driven dispatch is estimated.  相似文献   

12.
In this paper we consider stochastic programming problems where the objective function is given as an expected value function. We discuss Monte Carlo simulation based approaches to a numerical solution of such problems. In particular, we discuss in detail and present numerical results for two-stage stochastic programming with recourse where the random data have a continuous (multivariate normal) distribution. We think that the novelty of the numerical approach developed in this paper is twofold. First, various variance reduction techniques are applied in order to enhance the rate of convergence. Successful application of those techniques is what makes the whole approach numerically feasible. Second, a statistical inference is developed and applied to estimation of the error, validation of optimality of a calculated solution and statistically based stopping criteria for an iterative alogrithm. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Supported by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), Brasília, Brazil, through a Doctoral Fellowship under grant 200595/93-8.  相似文献   

13.
In this study, a two-stage fuzzy robust integer programming (TFRIP) method has been developed for planning environmental management systems under uncertainty. This approach integrates techniques of robust programming and two-stage stochastic programming within a mixed integer linear programming framework. It can facilitate dynamic analysis of capacity-expansion planning for waste management facilities within a multi-stage context. In the modeling formulation, uncertainties can be presented in terms of both possibilistic and probabilistic distributions, such that robustness of the optimization process could be enhanced. In its solution process, the fuzzy decision space is delimited into a more robust one by specifying the uncertainties through dimensional enlargement of the original fuzzy constraints. The TFRIP method is applied to a case study of long-term waste-management planning under uncertainty. The generated solutions for continuous and binary variables can provide desired waste-flow-allocation and capacity-expansion plans with a minimized system cost and a maximized system feasibility.  相似文献   

14.
Master Production Schedules (MPS) are widely used in industry, especially within Enterprise Resource Planning (ERP) software. The classical approach for generating MPS assumes infinite capacity, fixed processing times, and a single scenario for demand forecasts. In this paper, we question these assumptions and consider a problem with finite capacity, controllable processing times, and several demand scenarios instead of just one. We use a multi-stage stochastic programming approach in order to come up with the maximum expected profit given the demand scenarios. Controllable processing times enlarge the solution space so that the limited capacity of production resources are utilized more effectively. We propose an effective formulation that enables an extensive computational study. Our computational results clearly indicate that instead of relying on relatively simple heuristic methods, multi-stage stochastic programming can be used effectively to solve MPS problems, and that controllability increases the performance of multi-stage solutions.  相似文献   

15.
A stochastic programming approach for multi-period portfolio optimization   总被引:1,自引:0,他引:1  
This paper extends previous work on the use of stochastic linear programming to solve life-cycle investment problems. We combine the feature of asset return predictability with practically relevant constraints arising in a life-cycle investment context. The objective is to maximize the expected utility of consumption over the lifetime and of bequest at the time of death of the investor. Asset returns and state variables follow a first-order vector auto-regression and the associated uncertainty is described by discrete scenario trees. To deal with the long time intervals involved in life-cycle problems we consider a few short-term decisions (to exploit any short-term return predictability), and incorporate a closed-form solution for the long, subsequent steady-state period to account for end effects.  相似文献   

16.
This paper proposes a fuzzy-robust stochastic multiobjective programming (FRSMOP) approach, which integrates fuzzy-robust linear programming and stochastic linear programming into a general multiobjective programming framework. A chosen number of noninferior solutions can be generated for reflecting the decision-makers’ preferences and subjectivity. The FRSMOP method can effectively deal with the uncertainties in the parameters expressed as fuzzy membership functions and probability distribution. The robustness of the optimization processes and solutions can be significantly enhanced through dimensional enlargement of the fuzzy constraints. The developed FRSMOP was then applied to a case study of planning petroleum waste-flow-allocation options and managing the related activities in an integrated petroleum waste management system under uncertainty. Two objectives are considered: minimization of system cost and minimization of waste flows directly to landfill. Lower waste flows directly to landfill would lead to higher system costs due to high transportation and operational costs for recycling and incinerating facilities, while higher waste flows directly to landfill corresponding to lower system costs could not meet waste diversion objective environmentally. The results indicate that uncertainties and complexities can be effectively reflected, and useful information can be generated for providing decision support.  相似文献   

17.
We discuss the almost-sure convergence of a broad class of sampling algorithms for multistage stochastic linear programs. We provide a convergence proof based on the finiteness of the set of distinct cut coefficients. This differs from existing published proofs in that it does not require a restrictive assumption.  相似文献   

18.
We propose an Integer Linear Programming (ILP) approach for solving integer programs with bilinear objectives and linear constraints. Our approach is based on finding upper and lower bounds for the integer ensembles in the bilinear objective function, and using the bounds to obtain a tight ILP reformulation of the original problem, which can then be solved efficiently. Numerical experiments suggest that the proposed approach outperforms a latest iterative ILP approach, with notable reductions in the average solution time.  相似文献   

19.
Planning horizon is a key issue in production planning. Different from previous approaches based on Markov Decision Processes, we study the planning horizon of capacity planning problems within the framework of stochastic programming. We first consider an infinite horizon stochastic capacity planning model involving a single resource, linear cost structure, and discrete distributions for general stochastic cost and demand data (non-Markovian and non-stationary). We give sufficient conditions for the existence of an optimal solution. Furthermore, we study the monotonicity property of the finite horizon approximation of the original problem. We show that, the optimal objective value and solution of the finite horizon approximation problem will converge to the optimal objective value and solution of the infinite horizon problem, when the time horizon goes to infinity. These convergence results, together with the integrality of decision variables, imply the existence of a planning horizon. We also develop a useful formula to calculate an upper bound on the planning horizon. Then by decomposition, we show the existence of a planning horizon for a class of very general stochastic capacity planning problems, which have complicated decision structure.  相似文献   

20.
We develop a model for a strategic freight-forwarding network design problem in which the design decisions involve the locations and capacities of consolidation and deconsolidation centers, and capacities on linehaul linkages as well as the shipment routes from origins to destinations through centers. We devise a solution approach based on Benders decomposition and conduct a computational study that illustrates the efficiency and the effectiveness of the approach.  相似文献   

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