Robust supplier selection problem, in a scenario-based approach has been proposed, when the demand and exchange rates are subject to uncertainties. First, a deterministic multi-objective mixed integer linear programming is developed; then, the robust counterpart of the proposed mixed integer linear programming is presented using the recent extension in robust optimization theory. We discuss dec...

We propose the concept of partial Benders decomposition, based on the idea of retaining a subset of scenario subproblems in the master formulation and develop a theory to support it that illustrates how it may be applied to any stochastic integer program with continuous recourse. Such programs are used to model many practical applications such as the one considered in this paper, network design...

• A location-allocation problem under uncertainty is investigated. two-stage stochastic programming model proposed. The mode solved by sample average approximation. Emergencies, especially those considered routine (i.e., occurring on a daily basis), pose great threats to health, life, and property. Immediate response treatment can greatly mitigate these threats. This research conducted optimize...

This paper presents a two-layer energy management model (EMM) in the smart distribution network (SDN) considering flexi-renewable virtual power plants (FRVPPs) that participate day-ahead and reserve markets. The first layer of EMM is applied to FRVPPs maximize their profit proposed markets subjected constraints renewable flexible sources with coordination between these VPP operator (VPPO). Also...

Abstract The high penetration of intermittent renewable generation has prompted the development Stochastic Hydrothermal Unit Commitment (SHUC) models, which are more difficult to be solved than their thermal-based counterparts due hydro constraints and inflow uncertainties. This work presents a SHUC model applied in centralized cost-based dispatch. is represented by two-stage stochastic model, ...

A number of methods for solving multistage stochastic linear programs with recourse decompose the deterministic equivalent [4] to form subproblems based on scenarios (e.g., Rockafellar and Wets [6] and Mulvey and Ruszczyński [5]). Other methods use forms of Benders decomposition to form subproblems based on nodes of the scenario tree (e.g., Birge [1] and Gassmann [2]). Both types of algorithms ...

This paper focuses on solving two-stage stochastic mixed integer programs (SMIPs) with general mixed integer decision variables in both stages. We develop a decomposition algorithm in which the first stage approximation is solved using a branch-and-bound tree with nodes inheriting Benders’ cuts that are valid for their ancestor nodes. In addition, we develop two closely related convexification ...

abstract one of the basic assumptions in hub covering problems is considering the covering radius as an exogenous parameter which cannot be controlled by the decision maker. practically and in many real world cases with a negligible increase in costs, to increase the covering radii, it is possible to save the costs of establishing additional hub nodes. change in problem parameters during the pl...

We present a brief overview of four stages of nurse planning. For the last stage, which assigns nurses to patients, a stochastic integer programming model is developed. A Benders’ decomposition approach is proposed to solve this problem, and a greedy algorithm is employed to solve the recourse subproblem. Patient-to-nurse ratio constraints are introduced to balance the workload of nurses as wel...

We formulate a two-stage stochastic integer program to determine an optimal schedule for jobs requiring multiple classes of resources under uncertain processing times, due dates, resource consumption and availabilities. We allow temporary resource capacity expansion for a penalty. Potential applications of this model include team scheduling problems that arise in service industries such as engi...