We report a computational study of two-stage SP models on a large set of benchmark problems and consider the following methods: (i) Solution of the deterministic equivalent problem by the simplex method and an interior point method, (ii) Benders decomposition (L-shaped method with aggregated cuts), (iii) Regularised decomposition of Ruszczyński (Math Program 35:309–333, 1986), (iv) Benders deco...

There are many situations in mathematical programming where cutting planes can be generated by solving a certain “cut generation linear program” whose feasible solutions define a family of valid inequalities for the problem at hand. Disjunctive cuts and Benders cuts are two familiar examples. In this paper we concentrate on classical Benders cuts, as they belong to the basic toolbox for mixed-i...

We consider a supply chain setting where multiple uncapacitated facilities serve a set of customers with a single product. The majority of literature on such problems requires assigning all of any given customer’s demand to a single facility. While this single-sourcing strategy is optimal under linear (or concave) cost structures, it will often be suboptimal under the nonlinear costs that arise...

2 Benders' method usually divides the collection of decision variables of a two-stage mathematical problem into two sets: a first set that comprises the collection of variables that represent first-stage decisions and a second set that includes the collection of variables that represent recourse actions or second-stage decisions. Usually, integer variables appear in the first set whereas the se...

This paper proposes an efficient solution approach based on Benders’ decomposition to solve a network-constrained ac unit commitment problem under uncertainty. The wind power production is the only source of uncertainty considered in this paper, which is modeled through a suitable set of scenarios. The proposed model is formulated as a two-stage stochastic programming problem, whose first-stage...

Traditional two-stage stochastic programming is risk-neutral; that is, it considers the expectation as the preference criterion while comparing the random variables (e.g., total cost) to identify the best decisions. However, in the presence of variability risk measures should be incorporated into decision making problems in order to model its effects. In this study, we consider a risk-averse tw...

this paper presents an application of benders decomposition to deal with the complexities in the simultaneous generation expansion planning (gep) and transmission expansion planning (tep). unlike the power system operation fields of study, the power system planning methods are not expected to be fast. however, it is always preferable to speed up computations to provide more analysis options for...

We present a cooperation technique using an accurate management of nogoods to solve a hard real-time problem which consists in assigning periodic tasks to processors in the context of fixed priorities preemptive scheduling. The problem is to be solved off-line and our solving strategy is related to the logic based Benders decomposition. A master problem is solved using constraint programming wh...

We investigate new methods for generating Lagrangian cuts to solve two-stage stochastic integer programs. can be added a Benders reformulation, and are derived from solving single scenario programming subproblems identical those used in the nonanticipative dual of program. While have potential significantly strengthen relaxation, computationally demanding. techniques with goal obtaining that pr...