The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension this where surgery durations are considered be uncertain. In order obtain solutions for the challenging model, we use sample average approximation develop two enhanced decomposition frameworks ...

Large scale dispatching problems are technically characterized as classical NP-hard problems which means that they cannot be solved optimally with existing methods in a polynomial time. Benders decomposition is recommended for solving large scale Mixed Integer Programming (MIP). In this paper we use the Bender Decomposition technique for reformulating the Ready Mixed Concrete Dispatching Proble...

In the context of convex mixed integer nonlinear programming (MINLP), we investigate how the outer approximation method and the generalized Benders decomposition method are affected when the respective nonlinear programming (NLP) subproblems are solved inexactly. We show that the cuts in the corresponding master problems can be changed to incorporate the inexact residuals, still rendering equiv...

In this paper, we introduce and study a two-stage distributionally robust mixed binary problem (TSDR-MBP) where the random parameters follow the worst-case distribution belonging to an uncertainty set of probability distributions. We present a decomposition algorithm, which utilizes distribution separation procedure and parametric cuts within Benders’ algorithm or Lshaped method, to solve TSDR-...

In this paper, two Benders decomposition algorithms and a novel two-stage integer programming-based heuristic are presented to optimize the beam angle and fluence map in Intensity Modulated Radiation Therapy (IMRT) planning. Benders decomposition is first implemented in the traditional manner by iteratively solving the restricted master problem and then identifying and adding the violated Bende...

This paper proposes a method of generating valid integer Benders cuts for a general class of integer programming problems. A generic valid Benders cut in disjunctive form is presented rst, as a basis for the subsequent derivations of simple valid cuts. Under a qualiication condition, a simple valid Benders cut in linear form can be identiied. A cut generation problem is formulated to elicit it....

This paper proposes a stochastic programming model and solution algorithm for solving supply chain network design problems of a realistic scale. Existing approaches for these problems are either restricted to deterministic environments or can only address a modest number of scenarios for the uncertain problem parameters. Our solution methodology integrates a recently proposed sampling strategy,...

We apply logic-based Benders decomposition (LBBD) to two-stage stochastic planning and scheduling problems in which the second stage is a task. solve master problem with mixed integer/linear programming subproblem constraint programming. As cuts, we use simple no-good cuts as well analytic develop for this application. find that LBBD computationally superior integer L-shaped method. In particul...

Novel Optimality Cuts for Two-Stage Stochastic Mixed-Integer Programs The applicability and use of two-stage stochastic mixed-integer programs is well-established, thus calling efficient decomposition algorithms to solve them. Such typically rely on optimality cuts approximate the expected second stage cost function from below. In “A Converging Benders’ Decomposition Algorithm Recourse Models,”...