Georgios K. D. Saharidis

Strategies for protecting supply chain networks against facility and transportation disruptions: an improved Benders decomposition approach

Disruptions rarely occur in supply chains, but their negative financial and technical impacts make the recovery process very slow. In this paper, we propose a capacitated supply chain network design (SCND) model under random disruptions both in facility and transportation, which seeks to determine the optimal location and types of distribution centers (DC) and also the best plan to assign customers to each opened DC. Unlike other studies in the extent literature, we use new concepts of reliability to model the strategic behavior of DCs and customers at the network: (1) Failure of DCs might be partial, i.e. a disrupted DC might still be able to serve with a portion of its initial capacity (2) The lost capacity of a disrupted DC shall be provided from a non-disrupted one and (3) The lost capacity fraction of a disrupted DC depends on its initial investment amount in the design phase.In order to solve the proposed model optimally, a modified version of Benders’ Decomposition (BD) is applied. This modification tackles the difficulties of the BD’s master problem (MP), which ultimately improves the solution time of BD significantly. The classical BD approach results in low density cuts in some cases, Covering Cut Bundle (CCB) generation addresses this issue by generating a bundle of cuts instead of a single cut, which could cover more decision variables of the MP. Our inspiration to improve the CCB generation led to a new method, namely Maximum Density Cut (MDC) generation. MDC is based on the observation that in some cases CCB generation is cumbersome to solve in order to cover all decision variables of the MP rather than to cover part of them. Thus the MDC method generates a cut to cover the remaining decision variables which are not covered by CCB. Numerical experiments demonstrate the practicability of the proposed model to be promising in the SCND area, also the modified BD approach decreases the number of BD iterations and improves the CPU times, significantly.

An improved Benders decomposition algorithm for the logistics facility location problem with capacity expansions

We investigate a logistics facility location problem to determine whether the existing facilities remain open or not, what the expansion size of the open facilities should be and which potential facilities should be selected. The problem is formulated as a mixed integer linear programming model (MILP) with the objective to minimize the sum of the savings from closing the existing facilities, the expansion costs, the fixed setup costs, the facility operating costs and the transportation costs. The structure of the model motivates us to solve the problem using Benders decomposition algorithm. Three groups of valid inequalities are derived to improve the lower bounds obtained by the Benders master problem. By separating the primal Benders subproblem, different types of disaggregated cuts of the primal Benders cut are constructed in each iteration. A high density Pareto cut generation method is proposed to accelerate the convergence by lifting Pareto-optimal cuts. Computational experiments show that the combination of all the valid inequalities can improve the lower bounds significantly. By alternately applying the high density Pareto cut generation method based on the best disaggregated cuts, the improved Benders decomposition algorithm is advantageous in decreasing the total number of iterations and CPU time when compared to the standard Benders algorithm and optimization solver CPLEX, especially for large-scale instances.

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.

Minimizing Waiting Times at Transitional Nodes for Public Bus Transportation in Greece

Scheduling of transit networks is one of the most addressed problems in the mathematical optimization science, due to the increase of public transportation in the last decade. Researchers have introduced various formulations to address the problem of timetabling, using different objectives like bus synchronization and passenger demand. In this paper, we present a mixed-integer linear programming formulation with the objective of minimizing passenger waiting times at transitional transfer nodes, taking also into consideration high passenger demand that occurs at certain times.

Advances in Truck Scheduling at a Cross Dock Facility

In this paper the authors deal with the scheduling of inbound and outbound trucks to the available inbound and outbound doors at a cross dock facility. They assume that all trucks served at the facility need to meet several deadlines for deliveries and pick-ups and thus request a departure time window from the facility, penalizing the facility operator, on a unit of time basis, if that deadline is not met. To solve the resulting problem with reasonable computational effort, a memetic algorithm is developed and a number of computational examples show the efficiency of the proposed solution algorithm and the advantages of scheduling inbound and outbound trucks simultaneously, as opposed to sequentially.

Exact Solution Methodologies for Linear and (Mixed) Integer Bilevel Programming

Bilevel programming is a special branch of mathematical programming that deals with optimization problems which involve two decision makers 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 have previously appeared in the related literature, the significant contribution of the present work lies in that a) it is meant to be complete and up to date, b) it puts together various related works that have been revised/corrected in follow-up works, and reports in sequence the works that have provided these corrections, c) it identifies the special conditions and requirements needed for the application of each solution algorithm, and d) it points out the limitations of each associated methodology. The present collection of exact solution methodologies for bilevel optimization models can be proven extremely useful, since generic solution methodologies that solve such problems to global or local optimality do not exist.

Review of Solution Approaches for the Symmetric Traveling Salesman Problem

In this paper, the main known exact and heuristic solution approaches and algorithms for the symmetric Traveling Salesman Problem TSP, published after 1992, are surveyed. The paper categorize the most important existing algorithm to 6 main groups: i Genetic algorithms, ii Ant colony methods, iii Neural Methods, iv Local search algorithms and Tabu search, v Lagrangian methods and vi Branch and bound and branch & cut algorithms.

Operational research in energy and environment

Operational Research has been successfully used in a variety of applications in the field of engineering, energy, environment, transportation, economics, medicine, biology, etc. Although there have been successful efforts in both theoretical and applied domains, there is still a number of outstanding questions regarding: (a) energy and environmental performance (b) energy planning, (c) environmental impact, and (d) sustainability. In this Special Volume on Operational Research in Energy and Environment, a number of relevant papers provide contributions to both theoretical development and applications in this field. Applications to supply chain, energy and environmental performance and planning, dynamic parking prices, power networks, emissions estimation, as well as theoretical developments on Data Envelopment Analysis, bi-level/multi-criteria optimization, and stochastic programming are addressed. Data Envelopment Analysis (DEA) widely used approach in operations research. In industrial production processes, decision makers seek certainty in taking optimal decisions. However, because of the uncertainty in a range of factors, the information they obtain always carries some degree of fuzziness. As a result, research in the field of uncertainty has become the leading edge of DEA modeling. Ma-Lin Song et al. based on a DEA approach present fuzzy slacks-based measure (F-SBM) model incorporating a confidence coefficient on the postulation. The model provides a basis for decision making in a wider range of situations to reduce undesirable outputs, control the quantities of pollutants discharged, and improve the environment. In order to quantify the benefits to the environment, an analysis of the

Modeling and Solution Approaches for Crude Oil Scheduling in a Refinery

One of the most critical activities in a refinery is the scheduling of loading and unloading of crude oil. Better analysis of this activity gives rise to better use of a system’s resources, decrease losses, increase security as well as control of the entire supply chain. It is important that the crude oil is loaded and unloaded contiguously in storage tanks, primarily for security reasons (e.g. possibility of system failures) but also to reduce the setup costs incurred when flow between a dock/ports and a tank and/or between a tank and a crude distillation unit is reinitialized. The aim of this book chapter is to present a review on modeling and solution approaches in refinery industry. Mathematical programming modeling approaches are presented as well as exact, heuristic and hybrid solution approaches, widely applicable to most refineries where several modes of blending and several recipe preparation alternatives are used.

Accelerating techniques on nested decomposition

In this paper, we consider the nested decomposition method in the context of multistage stochastic problems with scenario trees where we contribute with improvements in accelerating convergence to optimum. We first propose a hybrid protocol for transmitting cuts across nodes aiming at a trade-off between the inherent benefits and drawbacks of the single (aggregated) versus multi-cut (desegregated) versions. The idea we aim to explore is to reduce the size of the problem solved at each iteration by applying the aggregated version of the cuts on the furthest nodes of the tree. We then turn our attention towards the selection of first-stage solutions by employing sampling and simulation aiming to carefully choose those first-stage solution that are potentially capable to drastically decrease the gap between the upper and lower bound at each iteration. The problems on which the latter technique is applied present a special structure, according to which the first-stage variables are linked to all further stages. We test both accelerating techniques on a generic problem which displays a blend of two-stage and multistage structure and we report significant savings in terms of CPU time and number of iterations to convergence.