Stochastic Multi-Objective Programming Problem: A Two-Phase Weighted Coefficient Approach

This paper deals with multi-objective stochastic linear programming problem. The problem is considered by introducing the coefficients of the decision variables and the right-hand-side parameters in the constraints as normal random variables. A method for converting the problem into its deterministic problem is proposed and hence two- phase approach with equal weights is proposed for finding an efficient solution. The advantages of the approach are: as weights which is positive, not necessarily equal and generate an efficient solution. A numerical example is given to illustrate the suggested methodology.

A novel approach for solving stochastic problems with multiple objective functions

In this paper we suggest an approach for solving a multiobjective stochastic linear programming problem with normal multivariate distributions. Our solution method is a combination between the multiobjective approach and a nonconvex technique. The problem is first transformed into a deterministic multiobjective problem introducing the expected value criterion and an utility function that represents the decision makers’ preferences. The obtained problem is reduced to a mono-objective quadratic problem using a weighting method. This last problem is solved by DC programming and DC algorithm. A numerical example is included for illustration.

About a regional development model that takes into account environmental problems with budgeting uncertainty

Raw-materials base (hereinafter RMB) is one of the largest industries for financial investments in Russia. There are various mathematical descriptions for the development of regions with resource-based economy. Earlier in [1] the researchers considered the model based on bilevel integer stochastic programming problems with Boolean variables. This paper proposes a new approach to public-private partnership modelling, including a bilevel linear stochastic programming problem. This model assumes that budget constraints of the state and the investor can vary in a random manner with a specific probability distribution. We put forward two methods to solve this problem: problem’s reduction to the deterministic bilevel one and formulation of deterministic problems sequence with help of Monte Carlo methods. In order to solve deterministic problems of integer programming, we suggest two approaches: direct enumeration and heuristic “Game” approach. The numerical experiments for proposed algorithms validation are conducted on the basis of actual data of Zabaykalsky Krai development. Multiple input parameters of the model vary in these experiments. Finally, we present a brief analysis of the obtained solutions to the stochastic linear programming problems with Boolean variables.

A Generalized Alternating Linearization Bundle Method for Structured Convex Optimization with Inexact First-Order Oracles

In this paper, we consider a class of structured optimization problems whose objective function is the summation of two convex functions: f and h, which are not necessarily differentiable. We focus particularly on the case where the function f is general and its exact first-order information (function value and subgradient) may be difficult to obtain, while the function h is relatively simple. We propose a generalized alternating linearization bundle method for solving this class of problems, which can handle inexact first-order information of on-demand accuracy. The inexact information can be very general, which covers various oracles, such as inexact, partially inexact and asymptotically exact oracles, and so forth. At each iteration, the algorithm solves two interrelated subproblems: one aims to find the proximal point of the polyhedron model of f plus the linearization of h; the other aims to find the proximal point of the linearization of f plus h. We establish global convergence of the algorithm under different types of inexactness. Finally, some preliminary numerical results on a set of two-stage stochastic linear programming problems show that our method is very encouraging.

Application of stochastic linear programming in managerial accounting

Purpose This paper aims to focus on applications of stochastic linear programming (SLP) to managerial accounting issues by providing a theoretical foundation and practical examples. SLP models may have more implications – and broader ones – in industry practice than deterministic linear programming (DLP) models do. Design/methodology/approach This paper introduces both DLP and SLP methods. In addition, continuous and discrete SLP models are explained. Applications are demonstrated using practical examples and simulations. Findings This research work extends the current knowledge of SLP, especially concerning managerial accounting issues. Through numerical examples, SLP demonstrates its great ability of hedging against all scenarios. Originality/value This study serves as an addition to building a cumulative tradition of research on SLP in managerial accounting. Only a few SLP studies in managerial accounting have focused on the development of such an instrument. Thus, the measurement scales in this research can be used as the starting point for further refining the instrument of optimization in managerial accounting.