Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion

Mixed-Integer Second-Order Cone Programs (MISOCPs) form a nice class of mixed-inter convex programs, which can be solved very efficiently due to the recent advances in optimization solvers. Our paper bridges the gap between modeling a class of optimization problems and using MISOCP solvers. It is shown how various performance metrics of M/G/1 queues can be molded by different MISOCPs. To motivate our method practically, it is first applied to a challenging stochastic location problem with congestion, which is broadly used to design socially optimal service networks. Four different MISOCPs are developed and compared on sets of benchmark test problems. The new formulations efficiently solve large-size test problems, which cannot be solved by the best existing method. Then, the general applicability of our method is shown for similar optimization problems that use queue-theoretic performance measures to address customer satisfaction and service quality

Practicable robust stochastic optimization under divergence measures with an application to equitable humanitarian response planning

We seek to provide practicable approximations of the two-stage robust stochastic optimization (RSO) model when its ambiguity set is constructed with an f-divergence radius. These models are known to be numerically challenging to various degrees, depending on the choice of the f-divergence function. The numerical challenges are even more pronounced under mixed-integer first-stage decisions. In this paper, we propose novel divergence functions that produce practicable robust counterparts, while maintaining versatility in modeling diverse ambiguity aversions. Our functions yield robust counterparts that have comparable numerical difficulties to their nominal problems. We also propose ways to use our divergences to mimic existing f-divergences without affecting the practicability. We implement our models in a realistic location-allocation model for humanitarian operations in Brazil. Our humanitarian model optimizes an effectiveness-equity trade-off, defined with a new utility function and a Gini mean difference coefficient. With the case study, we showcase 1) the significant improvement in practicability of the RSO counterparts with our proposed divergence functions compared to existing f-divergences, 2) the greater equity of humanitarian response that our new objective function enforces and 3) the greater robustness to variations in probability estimations of the resulting plans when ambiguity is considered

Service Center Location with Decision Dependent Utilities

We study a service center location problem with ambiguous utility gains upon receiving service. The model is motivated by the problem of deciding medical clinic/service centers, possibly in rural communities, where residents need to visit the clinics to receive health services. A resident gains his utility based on travel distance, waiting time, and service features of the facility that depend on the clinic location. The elicited location-dependent utilities are assumed to be ambiguously described by an expected value and variance constraint. We show that despite a non-convex nonlinearity, given by a constraint specified by a maximum of two second-order conic functions, the model admits a mixed 0-1 second-order cone (MISOCP) formulation. We study the non-convex substructure of the problem, and present methods for developing its strengthened formulations by using valid tangent inequalities. Computational study shows the effectiveness of solving the strengthened formulations. Examples are used to illustrate the importance of including decision dependent ambiguity.Comment: 29 page

Mathematical Optimization for Routing and Logistic Problems

In this thesis, we focus on mathematical optimization models and algorithms for solving routing and logistic problems. The first contribution regards a path and mission planning problem, called Carrier-Vehicle Traveling Salesman Problem (CVTSP), for a system of heterogeneous vehicles. A Mixed-Integer Second Order Conic Programming (MISOCP) model and a Benders-like enumeration algorithm are presented for solving CVTSP. The second work concerns a class of routing problems, referred to as Interceptor Vehicle Routing Problems (IVRPs). They generalize VRPs in the sense that target points are allowed to move from their initial location according to a known motion. We present a novel MISOCP formulation and a Branch-and-Price algorithm based on a Lagrangian Relaxation of the vehicle-assignment constraints. Other two contributions focus on waste flow management problems: the former considers a deterministic setting in which a Mixed-Integer Linear Programming (MILP) formulation is used as a Decision Support System for a real-world waste operator, whereas the latter deals with the uncertainty of the waste generation amounts by means of Two-Stage Multiperiod Stochastic Mixed-Integer Programming formulations. Finally, we give an overview on the optimization challenges arising in electric car-sharing systems, both at strategic and tactical planning level

Service Region Design for Urban Electric Vehicle Sharing Systems

Emerging collaborative consumption business models have shown promise in terms of both generating business opportunities and enhancing the efficient use of resources. In the transportation domain, car sharing models are being adopted on a mass scale in major metropolitan areas worldwide. This mode of servicized mobility bridges the resource efficiency of public transit and the flexibility of personal transportation. Beyond the significant potential to reduce car ownership, car sharing shows promise in supporting the adoption of fuel- efficient vehicles, such as electric vehicles (EVs), due to these vehicles special cost structure with high purchase but low operating costs. Recently, key players in the car sharing business, such as Autolib, Car2Go and DriveNow, have begun to employ EVs in an operations model that accommodates one-way trips. On the one hand (and particularly in free-floating car sharing), the one-way model results in significant improvements in coverage of travel needs and therefore in adoption potential compared with the conventional round-trip-only model (advocated by ZipCar, for example). On the other hand, this model poses tremendous planning and operational challenges. In this work, we study the planning problem faced by service providers in designing a geographical service region in which to operate the service. This decision entails trade-offs between maximizing customer catchment by covering travel needs and controlling fleet operations costs. We develop a mathematical programming model that incorporates details of both customer adoption behavior and fleet management (including EV repositioning and charging) under imbalanced travel patterns. To address inherent planning uncertainty with regard to adoption patterns, we employ a distributionally robust optimization framework that informs robust decisions to overcome possible ambiguity (or lacking) of data. Mathematically, the problem can be approximated by a mixed integer second-order cone program, which is computationally tractable with practical scale data. Applying this approach to the case of Car2Go’s service with real operations data, we address a number of planning questions and suggest that there is potential for the future development of this service

Location, inventory and testing decisions in closed-loop supply chains: a multimedia company

Our partnering firm is a Chinese manufacturer of multimedia products that needs guidance developing its imminent Closed-Loop Supply Chain (CLSC). To study this problem, we take into account location, inventory, and testing decisions in a CLSC setting with stochastic demands of new and time-sensitive returned products. Our analysis pays particular attention to the different roles assigned to the reverse Distribution Centers (DCs) and how each option affects the optimal CLSC design. The roles considered are collection and consolidation, additional testing tasks, and direct shipments with no reverse DCs. The problem concerning our partnering firm is formulated as a scenario-based chance-constrained mixed-integer program and it is reformulated to a conic quadratic mixed-integer program that can be solved efficiently via commercial optimization packages. The completeness of the model proposed allows us to develop a decision support tool for the firm and to offer several useful managerial insights. These insights are inferred from our computational experiments using data from the Chinese firm and a second data set based on the U.S. geography. Particularly interesting insights are related to how changes in the reverse flows can impact the forward supply chain and the inventory dynamics concerning the joint DCs.This research is partially supported by the National Natural Science Foundation of China under grants 71771135, 71371106 and 71332005

Balancing partner preferences for logistics costs and carbon footprint in a horizontal cooperation

Horizontal cooperation in logistics has gathered momentum in the last decade as a way to reach economic as well as environmental benefits. In the literature, these benefits are most often assessed through aggregation of demand and supply chain optimization of the partnership as a whole. However, such an approach ignores the individual preferences of the participating companies and forces them to agree on a unique coalition objective. Companies with different (potentially conflicting) preferences could improve their individual outcome by diverging from this joint solution. To account for companies preferences, we propose an optimization framework that integrates the individual partners’ interests directly in a cooperative model. The partners specify their preferences regarding the decrease of logistical costs versus reduced CO2 emissions. Doing so, all stakeholders are more likely to accept the solution, and the long-term viability of the collaboration is improved. First, we formulate a multi-objective, multi-partner location-inventory model. Second, we distinguish two approaches for solving it, each focusing primarily on one of these two dimensions. The result is a set of Pareto-optimal solutions that support the decision and negotiation process. Third, we propose and compare three different approaches to construct a unique solution which is fair and efficient for the coalition. Extensive numerical results not only confirm the potential of collaboration but, more importantly, also reveal valuable managerial insights on the effect of dissimilarities between partners with respect to size, geographical overlap and operational preferences