This paper introduces a hybrid optimization approach, an inexact two-stage mixed integer linear programming (ITMILP) model, for the planning of regional solid waste management systems under uncertainty. The model impr...
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This paper introduces a hybrid optimization approach, an inexact two-stage mixed integer linear programming (ITMILP) model, for the planning of regional solid waste management systems under uncertainty. The model improves upon the existing mixed integer, two-stage stochastic and interval-parameter programming approaches by allowing uncertainties presented as random distributions and discrete intervals, as well as policies expressed as allowable waste-loading targets to be effectively incorporated within a general optimization framework. In the modeling formulation, penalties are imposed when the policies are violated. In its solutions algorithm, the ITMILP model is transformed into two deterministic submodels, which were solved sequentially. Application of the developed methodology to the planning of a waste management system indicates that reasonable solutions for the binary and continuous decision variables can be generated through this approach. Considerable information was generated regarding decisions of facility expansion within a multi-period, multi-scale and multi-waste-level context;and optimal waste flow allocation patterns were achieved within the waste management system. The ITMILP model was then employed to generate a number of decision alternatives under various policy conditions, allowing for more in-depth analyses of tradeoffs between environmental and economic objectives.
Two major approaches to deal with randomness or ambiguity involved in mathematical programming problems have been developed. They are stochastic programming approaches and fuzzy programming approaches. In this paper, ...
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Two major approaches to deal with randomness or ambiguity involved in mathematical programming problems have been developed. They are stochastic programming approaches and fuzzy programming approaches. In this paper, we focus on multiobjective linear programming problems with random variable coefficients in objective functions and/or constraints. Using the probability maximization model to maximize the probability that each objective function becomes a certain value under chance constrained conditions, the stochastic programming problems are transformed into deterministic ones. As a fusion of stochastic approaches and fuzzy ones, after determining the fuzzy, goals of the decision maker, an interactive fuzzy satisficing method to derive a satisficing solution for the decision maker by updating the reference membership levels is presented. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method. (C) 2004 Elsevier B.V. All rights reserved.
In this paper we study the 0-1 maximum probability model that consists in maximizing the probability that a certain quantity c(T)x is greater than a prescribed constant t, where c and x are n vectors. c(1),..., c(n), ...
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In this paper we study the 0-1 maximum probability model that consists in maximizing the probability that a certain quantity c(T)x is greater than a prescribed constant t, where c and x are n vectors. c(1),..., c(n), are mutually independent and normally distributed random variables and x is a vector of n binary variables such that Ax less than or equal to b, where b is an m vector and A is an m x n matrix. It is known that this problem can be formulated as a nonlinear fractional program. We show how to solve it exactly using mixed integer programming. The advantage of the approach is that it requires only standard, commercially available software. The computational results which we present show that this technique makes it possible to treat instances with up to 100 random variables in a few seconds of CPU time. (C) 2003 Elsevier B.V. All rights reserved.
This paper presents a modified version of the L-shaped method (Refs. 1 - 5), used to solve two-stage stochastic linear programs with fixed recourse, by employing the implicit LX method and the implicit LP method ( Ref...
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This paper presents a modified version of the L-shaped method (Refs. 1 - 5), used to solve two-stage stochastic linear programs with fixed recourse, by employing the implicit LX method and the implicit LP method ( Refs. 6 - 9) of the ABS class of methods. By exploiting the properties and special structure of the ABS class and applying these to the simplex method, the number of arithmetic operations is greatly decreased.
One approach to process design with uncertain parameters is to formulate a stochastic MINLP. When there are many uncertain parameters, the number of samples becomes unmanageably large and computing the solution to the...
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One approach to process design with uncertain parameters is to formulate a stochastic MINLP. When there are many uncertain parameters, the number of samples becomes unmanageably large and computing the solution to the MINLP can be difficult and very time consuming. In this paper, two new algorithms (the optimality gap method (OGM) and the confidence level method (CLM)) are presented for solving convex stochastic MINLPs. At each iteration, the sample average approximation method is applied to the NLP sub-problem and MILP master problem. A smaller sample size problem is solved multiple times with different batches of i.i.d. samples to make decisions and a larger sample size problem (with continuous/discrete decision variables fixed) is solved to re-evaluate the objective values. In the first algorithm, the sample sizes are iteratively increased until the optimality gap intervals of the upper and lower bound are within a pre-specified tolerance. Instead of requiring a small optimality gap, the second algorithm uses tight bounds for comparing the objective values of NLP sub-problems and weak bounds for cutting off solutions in the MILP master problems, hence the confidence of finding the optimal discrete solution can be adjusted by the parameter used to tighten and weaken the bounds. The case studies show that the algorithms can significantly reduce the computational time required to find a solution with a given degree of confidence. (C) 2003 Elsevier Ltd. All rights reserved.
作者：
Dai, LLChan, VWSMIT
LIDS Dept Elect Engn & Comp Sci Cambridge MA 02139 USA
Satellite network architecture plays an important role in the success of a satellite business. For future commercial broadband data satellite networks integrated with the terrestrial network, satellite network topolog...
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Satellite network architecture plays an important role in the success of a satellite business. For future commercial broadband data satellite networks integrated with the terrestrial network, satellite network topology, link capacity, and routing have major impacts on the cost of the network and the amount of revenue the network can generate. To rind the most cost-effective satellite network topology, we propose a unified mathematical framework using a two-stage stochastic programming formulation. The solution to the stochastic programming formulation gives optimal link capacities and an optimal routing strategy for different network topologies, taking into account uncertainties in long-term aggregate traffic statistic estimation. Using a simple satellite network example, we show the feasible topology regions for three different satellite topologies and show that, for some parameter values, the hybrid topology is more cost effective than nonhybrid topologies. In the limit of high traffic rejection cost, stochastic dimensioning reduces to static dimensioning. We study worst case static dimensioning for a general geosynchronous earth orbit satellite network and show the feasible topology regions, as well as effective cost comparisons for different topologies. We conclude with a discussion on network cost and architectural flexibility relating to satellite network design.
作者：
Akçay, YXu, SHKoc Univ
Coll Adm Sci & Econ TR-34450 Istanbul Turkey Penn State Univ
Smeal Coll Business Adm Dept Supply Chain & Informat Syst University Pk PA 16802 USA
This paper considers a multicomponent, multiproduct periodic-review assemble-to-order (ATO) system that uses an independent base-stock policy for inventory replenishment. Product demands in each period are integer-val...
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This paper considers a multicomponent, multiproduct periodic-review assemble-to-order (ATO) system that uses an independent base-stock policy for inventory replenishment. Product demands in each period are integer-valued correlated random variables, with each product being assembled from multiple units of a subset of components. The system quotes a prespecified response time window for each product and receives a reward if the demand for that product is filled within its response time window. We formulate a two-stage stochastic integer program with recourse to determine the optimal base-stock policy and the optimal component allocation policy for the ATO system. We show that the component allocation problem is a general multidimensional knapsack problem (MDKP) and is NP-hard. We propose a simple, order-based component allocation rule and show that it can be solved in either polynomial or pseudopolynomial time. We also use the sample average approximation method to determine the optimal base-stock levels and compare it with two variations of the equal fractile heuristic. Intensive testing indicates that our solution method for each stage of the stochastic program is robust, effective, and that it significantly outperforms existing methods. Finally, we discuss several managerial implications of our findings.
We propose the use of sequences of separable, piecewise linear approximations for solving nondifferentiable stochastic optimization problems. The approximations are constructed adaptively using a combination of stocha...
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We propose the use of sequences of separable, piecewise linear approximations for solving nondifferentiable stochastic optimization problems. The approximations are constructed adaptively using a combination of stochastic subgradient information and possibly sample information on the objective function itself. We prove the convergence of several versions of such methods when the objective function is separable and has integer break points, and we illustrate their behavior on numerical examples. We then demonstrate the performance on nonseparable problems that arise in the context of two-stage stochastic programming problems, and demonstrate that these techniques provide near-optimal solutions with a very fast rate of convergence compared with other solution techniques.
We consider multiperiod capacity expansion of a telecommunications connection with uncertain demand. We present a new preprocessing rule which drastically reduces computation time of an existing algorithm for a two-st...
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We consider multiperiod capacity expansion of a telecommunications connection with uncertain demand. We present a new preprocessing rule which drastically reduces computation time of an existing algorithm for a two-stage formulation of the problem. Also, an alternative multistage formulation of the problem is given and we elaborate a recursive solution procedure. Both algorithms have been implemented in C++, and we present the results of a series of computational experiments, demonstrating the effect of the new preprocessing rule and the practicability of the multistage procedure. (C) 2003 Elsevier Ltd. All rights reserved.
We explicitly characterize the robust counterpart of a linear programming problem with uncertainty set described by an arbitrary norm. Our approach encompasses several approaches from the literature and provides guara...
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We explicitly characterize the robust counterpart of a linear programming problem with uncertainty set described by an arbitrary norm. Our approach encompasses several approaches from the literature and provides guarantees for constraint violation under probabilistic models that allow arbitrary dependencies in the distribution of the uncertain coefficients. (C) 2004 Elsevier B.V. All rights reserved.
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