We propose a heuristic adaptation of logic-based Benders decomposition to the home health care problem. The objective is design routes and schedules for health care workers who visit patient homes, so as to minimize cost while meeting all patient needs and work requirements. We solve the Benders master problem by a greedy heuristic that is enhanced by the propagation facilities of constraint pr...

Robust optimization extends stochastic programming models by incorporating measures of variability into the objective function. This paper explores robust optimization in the context of two-stage planning systems. First, we propose the use of a generalized Benders decomposition algorithm for solving robust models. Next, we argue that using an arbitrary measure for variability can lead to sub-op...

The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques....

Environmental, social and economic concerns motivate the operation of closed-loop supply chain networks (CLSCN) in many industries. We propose a novel profit maximization model for CLSCN design as a mixedinteger linear program inwhich there is flexibility in covering the proportions of demand satisfied and returns collected based on the firm’s policies. Our major contribution is to develop a no...

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...

This paper addresses a class of two-stage robust optimization models with integer adversarial variables. We discuss the importance of this class of problems in modeling two-stage robust resource planning problems where some tasks have uncertain arrival times and duration periods. We apply Dantzig-Wolfe decomposition to exploit the structure of these models and show that the original problem red...

We study stochastic uncapacitated hub location problems in which uncertainty is associated to demands and transportation costs. We show that the stochastic problems with uncertain demands or dependent transportation costs are equivalent to their associated deterministic expected value problem (EVP), in which random variables are replaced by their expectations. In the case of uncertain independe...

Recent work have exhibited specific structure among combinatorial problem instances that could be used to speed up search or to help users understand the dynamic and static intimate structure of the problem being solved. Several Operations Research approaches apply decomposition or relaxation strategies upon such a structure identified within a given problem. This paper presents how Benders dec...

We consider Benders decomposition for solving two-stage stochastic programs with complete recourse based on finite samples of the uncertain parameters. define cuts binding at final optimal solution or ones significantly improving bounds over iterations as valuable cuts. propose a learning-enhanced (LearnBD) algorithm, which adds cut classification step in each iteration to selectively generate ...

Benders decomposition uses a strategy of “learning from one’s mistakes.” The aim of this paper is to extend this strategy to a much larger class of problems. The key is to generalize the linear programming dual used in the classical method to an “inference dual.” Solution of the inference dual takes the form of a logical deduction that yields Benders cuts. The dual is therefore very different f...