Speed-up Benders decomposition using maximum density cut (MDC) generation

The classical implementation of Benders decomposition in some cases results in low density Benders cuts. Covering Cut Bundle (CCB) generation addresses this issue with a novel way generating a bundle of cuts which could cover more decision variables of the Benders master problem than the classical Benders cut. Our motivation to improve further CCB generation led to a new cut generation strategy. This strategy is referred to as the Maximum Density Cut (MDC) generation strategy. MDC is based on the observation that in some cases CCB generation is computational expensive to cover all decision variables of the master problem than to cover part of them. Thus MDC strategy addresses this issue by generating the cut that involves the rest of the decision variables of the master problem which are not covered in the Benders cut and/or in the CCB. MDC strategy can be applied as a complimentary step to the CCB generation as well as a standalone strategy. In this work the approach is applied to two case studies: the scheduling of crude oil and the scheduling of multi-product, multi-purpose batch plants. In both cases, MDC strategy significant decreases the number of iterations of the Benders decomposition algorithm, leading to improved CPU solution times

Modeling and solution approach for the environmental traveling salesman problem

We consider the environmental traveling salesman problem in a connected graph driven by a cost function describing the impact of environmental externalities over the routes. The resulting problem is the asymmetric non-Euclidean TSP that we solve using a blend of cutting planes and 2-OPT algorithm. We test our solution approach on the well-known instances of the TSP-LIB and we present the results and the future research directions

Exact solution methodologies for linear and (mixed) integer bilevel programming

Bilevel programming is a special branch of mathematical programming that deals with optimization problemswhich involve two decisionmakers who make their decisions hierarchically. The problem's decision variables are partitioned into two sets, with the first decision maker (referred to as the leader) controlling the first of these sets and attempting to solve an optimization problem which includes in its constraint set a second optimization problem solved by the second decision maker (referred to as the follower), who controls the second set of decision variables. The leader goes first and selects the values of the decision variables that he controls.With the leader's decisions known, the follower solves a typical optimization problem in his self-controlled decision variables. The overall problem exhibits a highly combinatorial nature, due to the fact that the leader, anticipating the follower's reaction, must choose the values of his decision variables in such a way that after the problem controlled by the follower is solved, his own objective function will be optimized. Bilevel optimization models exhibit wide applicability in various interdisciplinary research areas, such as biology, economics, engineering, physics, etc. In this work, we review the exact solution algorithms that have been developed both for the case of linear bilevel programming (both the leader's and the follower's problems are linear and continuous), as well as for the case of mixed integer bilevel programming (discrete decision variables are included in at least one of these two problems). We also document numerous applications of bilevel programming models from various different contexts. Although several reviews dealing with bilevel programming ©Springer-Verlag Berlin Heidelberg 2013

A multi-periodic optimization modeling approach for the establishment of a bike sharing network: A case study of the City of Athens

This study introduces a novel mathematical formulation that addresses the strategic design of a bicycle sharing network. The developed pure integer linear program takes into consideration data such as the potential future demand patterns during the day, the bike's popularity in a city, the desired proximity of the stations and the available budget for such a network. With these input data, it optimizes the location of bike stations, the number of their parking slots and the distribution of the bicycle fleet over them in order to meet as much demand as possible and to offer the best service to the users. The estimated demand for the network is split into "Demand for Pick-Ups" and "Demand for Drop-offs" during the 24 hours of the day, which are discretized into time intervals. The proposed approach is implemented on the very center of the city of Athens, Greece

A new model to mitigating random disruption risks of facility and transportation in supply chain network design

In this article, we study the design problem of a reliable stochastic supply chain network in the presence of random disruptions in the location of distribution centers (DCs) and the transportation modes. It is assumed that a disrupted DC does not necessarily fail the whole of its capacity, and may lose a fraction of that, and rest of demand can be served by other DCs. We introduce a new strategy called soft-hardening strategy where the fraction of the lost capacity depends on the amount of investment for opening and operating. Additionally, the conditional value-at-risk (CVaR) approach is applied to control the risk of model. Finally, to solve the model, first we present an exact solution method by reformulating the problem as a second-order cone programming model, and second a hybrid algorithm combining tabu search and simulated annealing algorithms is developed