A bicriteria solid transportation problem with fixed charge under stochastic environment

In this paper, a bicriteria solid transportation problem with stochastic parameters is investigated. Three mathematical models are constructed for the problem, including expected value goal programming model, chance-constrained goal programming model and dependent-chance goal programming model. A hybrid algorithm is also designed based on the random simulation algorithm and tabu search algorithm to solve the models. At last, some numerical experiments are presented to show the performance of models and algorithm.     

A successive linear programming algorithm with non-linear time series for the reservoir management problem

Computational Management Science - This paper proposes a multi-stage stochastic programming formulation based on affine decision rules for the reservoir management problem. Our approach seeks to...     

A chance-constrained approach to stochastic line balancing problem

In this paper, chance-constrained 0–1 integer programming models for the stochastic traditional and U-type line balancing (ULB) problem are developed. These models are solved for several test problems that are well known in the literature and the computational results are given. In addition, a goal programming approach is presented in order to increase the system reliability, which is arising from the stochastic case.     

A Stochastic Linear Programming Model for Corn Residue Production

This paper presents the results of a stochastic linear program for estimating the supply of corn residue for use as raw material in an ethanol plant. The model is based on the production capacity of an average Illinois farm, and considers the feasibility of three mutually exclusive residue harvesting alternatives-own baling, custom baling, and cob collection. Since the potential for residue use in animal feed may be even more promising, these results are directly useful for the feed industry. They also indicate the profitability of investing in residue harvesting equipment. From a methodological point of view, the paper contrasts the results of three OR approaches, a deterministic LP approach, a stochastic LP approach, and a chance-constrained approach. Because of the stochastic nature of the problem both Monte Carlo simulation and chance-constrained programming are found to be computationally viable, even though they differ in the way they incorporate risk information.     

A Chance-Constrained Goal Programming Model for Capital Budgeting

A chance-constrained formulation is presented for a zero-one goal programming problem whose coefficients in the technological matrix are stochastic. The model is presented with a numerical example. A capital budgeting problem is taken for illustration.     

Evolving System Architectures for Multimedia Network Design

This paper discusses implementation issues concerning a telecommunications planning system for networks with hypothetical multimedia stochastic traffic. Stochasticity of the traffic and probabilistic statements about service commitment are captured by a chance-constrained stochastic programming formulation of the complex network dimensioning and traffic management problem treated in our previous work. Our approach involves a hierarchy of design objectives associated with the respective network layers. These are met by constituting a set of models – the Integrated Network Design System (INDS) – with common data, solvers and a graphical user interface (GUI) operating under the interactive control of the network planner.     

Selecting tolerances in chance-constrained programming: A multiple objective linear programming approach

An importance issue concerning the practical application of chance-constrained programming is the lack of a rational method for choosing risk levels or tolerances on the chance constraints. While there has also been much recent debate on the relationship, equivalence, usefulness, and other characteristics of chance-constrained programming relative to stochastic programming with recourse, this paper focuses on the problem of improving the selection of tolerances within the chance-constrained framework. An approach is presented, based on multiple objective linear programming, which allows the decision maker to be more involved in the tolerance selection process, but does not demand a priori decisions on appropriate tolerances. An example is presented which illustrates the approach.     

Stochastic optimization for blending problem in brass casting industry

A critical process in brass casting is blending of the raw materials in a furnace so that the specified metal ratios are satisfied. The uncertainties in raw material compositions may cause violations of the specification limits and extra cost. In this study, we proposed a chance-constrained stochastic programming approach for blending problem in brass casting industry to handle the statistical variations in raw material compositions. The proposed approach is a non-linear mathematical model that is solved global optimally by using GAMS/BARON solver. An application has been performed in MKEK brass factory in Kırıkkale, Turkey and the solution of the application has been compared with alternative solution approaches based on cost and specification violation risk conditions. This comparison demonstrates that the proposed model is the most effective solution approach for managing stochastic uncertainties in blending problems and successfully can be used other industries such as alloy steel or secondary aluminum production.     

Approximations for chance-constrained programming problems

This paper proposes an approximation approach to the solution of chance-constrained stochastic programming problems. The results rely in a fundamental way on the theory of convergence of sequences of measurable multifunctions. Particular results are presented for stochastic linear programming problems.     

Strong guidance on mitigating the effects of uncertainties in the brass casting blending problem: a hybrid optimization approach

The scrap charge optimization problem in the brass casting process is a critical management concern that aims to reduce the charge while preventing specification violations. Uncertainties in scrap material compositions often cause violations in product standards. In this study, we have discussed the aleatory and epistemic uncertainties and modelled them by using probability and possibility distributions, respectively. Mathematical models including probabilistic and possibilistic parameters are generally solved by transforming one type of parameter into the other. However, the transformation processes have some handicaps such as knowledge losses or virtual information production. In this paper, we have proposed a new solution approach that needs no transformation process and so eliminates these handicaps. The proposed approach combines both chance-constrained stochastic programming and possibilistic programming. The solution of the numerical example has shown that the blending problem including probabilistic and possibilistic uncertainties can be successfully handled and solved by the proposed approach.     

Scenario optimization

Uncertainty in the parameters of a mathematical program may present a modeller with considerable difficulties. Most approaches in the stochastic programming literature place an apparent heavy data and computational burden on the user and as such are often intractable. Moreover, the models themselves are difficult to understand. This probably explains why one seldom sees a fundamentally stochastic model being solved using stochastic programming techniques. Instead, it is common practice to solve a deterministic model with different assumed scenarios for the random coefficients. In this paper we present a simple approach to solving a stochastic model, based on a particular method for combining such scenario solutions into a single, feasible policy. The approach is computationally simple and easy to understand. Because of its generality, it can handle multiple competing objectives, complex stochastic constraints and may be applied in contexts other than optimization. To illustrate our model, we consider two distinct, important applications: the optimal management of a hydro-thermal generating system and an application taken from portfolio optimization.     

随机环境下资金预算问题的机会约束整数规划模型

本文基于最新的机会约束规划理论,提出了两类随机环境下资金预算问题的整数规划模型,并且设计了一种基于随机模拟的遗传算法来计算给出的模型．为了例证算法的有效性,本文给出了两类模型的数值例子,并且对其中一个例子给出了不同的参数,测试遗传算法的有效性,数值例子及测试结果均显示,本文所设计的基于随机模拟的遗传算法对于解决本文提出的两类模型是有效的．     

Capital rationing problems under uncertainty and risk

Capital rationing is a major problem in managerial decision making. The classical mathematical formulation of the problem relies on a multi-dimensional knapsack model with known input parameters. Since capital rationing is carried out in conditions where uncertainty is the rule rather than the exception, the hypothesis of deterministic data limits the applicability of deterministic formulations in real settings. This paper proposes a stochastic version of the capital rationing problem which explicitly accounts for uncertainty. In particular, a mathematical formulation is provided in the framework of stochastic programming with joint probabilistic constraints and a novel solution approach is proposed. The basic model is also extended to include specific risk measures. Preliminary computational results are presented and discussed.     

Decision-dependent probabilities in stochastic programs with recourse

Stochastic programming with recourse usually assumes uncertainty to be exogenous. Our work presents modelling and application of decision-dependent uncertainty in mathematical programming including a taxonomy of stochastic programming recourse models with decision-dependent uncertainty. The work includes several ways of incorporating direct or indirect manipulation of underlying probability distributions through decision variables in two-stage stochastic programming problems. Two-stage models are formulated where prior probabilities are distorted through an affine transformation or combined using a convex combination of several probability distributions. Additionally, we present models where the parameters of the probability distribution are first-stage decision variables. The probability distributions are either incorporated in the model using the exact expression or by using a rational approximation. Test instances for each formulation are solved with a commercial solver, BARON, using selective branching.     

Conditional Value-at-Risk in Stochastic Programs with Mixed-Integer Recourse

In classical two-stage stochastic programming the expected value of the total costs is minimized. Recently, mean-risk models - studied in mathematical finance for several decades - have attracted attention in stochastic programming. We consider Conditional Value-at-Risk as risk measure in the framework of two-stage stochastic integer programming. The paper addresses structure, stability, and algorithms for this class of models. In particular, we study continuity properties of the objective function, both with respect to the first-stage decisions and the integrating probability measure. Further, we present an explicit mixed-integer linear programming formulation of the problem when the probability distribution is discrete and finite. Finally, a solution algorithm based on Lagrangean relaxation of nonanticipativity is proposed. Received: April, 2004     

A dual-uncertainty-based chance-constrained model for municipal solid waste management

A double-sided dual-uncertainty-based chance-constrained programming (DDCCP) model was developed for supporting municipal solid waste management under uncertainty. The model was capable of tackling left-hand- and right-hand-side variables in constraints where those variables were affected by dual uncertainties (i.e. e.g. both fuzziness and randomness); and they were expressed as fuzzy random variables (FRVs). In this study, DDCCP model were formulated and solved based on stochastic and fuzzy chance-constrained programming techniques, leading to optimal solutions under different levels of constraints violation and satisfaction reliabilities. A long-term solid waste management problem was used to demonstrate the feasibility and applicability of DDCCP model. The obtained results indicated that DDCCP was effective in handling constraints with FRVs through satisfying them at a series of allowable levels, generating various solutions that facilitated evaluation of trade-offs between system economy and reliability. The proposed model could help decision makers establish cost-effective waste-flow allocation patterns under complex uncertainties, and gain in-depth insights into the municipal solid waste management system.     

Two storage inventory model in a mixed environment

Multi-item inventory models with two storage facility and bulk release pattern are developed with linearly time dependent demand in a finite time horizon under crisp, stochastic and fuzzy-stochastic environments. Here different inventory parameters—holding costs, ordering costs, purchase costs, etc.—are assumed as probabilistic or fuzzy in nature. In particular cases stochastic and crisp models are derived. Models are formulated as profit maximization principle and three different approaches are proposed for solution. In the first approach, fuzzy extension principle is used to find membership function of the objective function and then it’s Graded Mean Integration Value (GMIV) for different optimistic levels are taken as equivalent stochastic objectives. Then the stochastic model is transformed to a constraint multi-objective programming problem using Stochastic Non-linear Programming (SNLP) technique. The multi-objective problems are transferred to single objective problems using Interactive Fuzzy Satisfising (IFS) technique. Finally, a Region Reducing Genetic Algorithm (RRGA) based on entropy has been developed and implemented to solve the single objective problems. In the second approach, the above GMIV (which is stochastic in nature) is optimized with some degree of probability and using SNLP technique model is transferred to an equivalent single objective crisp problem and solved using RRGA. In the third approach, objective function is optimized with some degree of possibility/necessity and following this approach model is transformed to an equivalent constrained stochastic programming problem. Then it is transformed to an equivalent single objective crisp problem using SNLP technique and solved via RRGA. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.     

Toward Fuzzy Optimization without Mathematical Ambiguity

Fuzzy programming has been discussed widely in literature and applied in such various disciplines as operations research, economic management, business administration, and engineering. The main purpose of this paper is to present a brief review on fuzzy programming models, and classify them into three broad classes: expected value model, chance-constrained programming and dependent-chance programming. In order to solve general fuzzy programming models, a hybrid intelligent algorithm is also documented. Finally, some related topics are discussed.     

Optimization models and a GA-based algorithm for stochastic time-cost trade-off problem

In real-life projects, both the trade-off between the project cost and the project completion time, and the uncertainty of the environment are considerable aspects for decision-makers. However, the research on the time-cost trade-off problem seldom concerns stochastic environments. Besides, optimizing the expected value of the objective is the exclusive decision-making criterion in the existing models for the stochastic time-cost trade-off problem. In this paper, two newly developed alternative stochastic time-cost trade-off models are proposed, in which the philosophies of chance-constrained programming and dependent-chance programming are adopted for decision-making. In addition, a hybrid intelligent algorithm integrating stochastic simulations and genetic algorithm is designed to search the quasi-optimal schedules under different decision-making criteria. The goal of the paper is to reveal how to obtain the optimal balance of the project completion time and the project cost in stochastic environments.     

Re-solving stochastic programming models for airline revenue management

We study some mathematical programming formulations for the origin-destination model in airline revenue management. In particular, we focus on the traditional probabilistic model proposed in the literature. The approach we study consists of solving a sequence of two-stage stochastic programs with simple recourse, which can be viewed as an approximation to a multi-stage stochastic programming formulation to the seat allocation problem. Our theoretical results show that the proposed approximation is robust, in the sense that solving more successive two-stage programs can never worsen the expected revenue obtained with the corresponding allocation policy. Although intuitive, such a property is known not to hold for the traditional deterministic linear programming model found in the literature. We also show that this property does not hold for some bid-price policies. In addition, we propose a heuristic method to choose the re-solving points, rather than re-solving at equally-spaced times as customary. Numerical results are presented to illustrate the effectiveness of the proposed approach.