Quantile Inverse Optimization: Improving Stability in Inverse Linear Programming

Although inverse linear programming (LP) has received increasing attention as a technique to identify an LP that can reproduce observed decisions that are originally from a complex system, the performance of the linear objective function inferred by existing inverse LP methods is often highly sensitive to noise, errors, and uncertainty in the underlying decision data. Inspired by robust regression techniques that mitigate the impact of noisy data on the model fitting, in “Quantile Inverse Optimization: Improving Stability in Inverse Linear Programming,” Shahmoradi and Lee propose a notion of stability in inverse LP and develop an inverse optimization model that identities objective functions that are stable against data imperfection. Although such a stability consideration renders the inverse model a large-scale mixed-integer program, the authors analyze the connection between the model and well-known biclique problems and propose an efficient exact algorithm as well as heuristics.

Probabilistic Set Covering Location Problem in Congested Networks

This paper focuses on designing a facility network, taking into account that the system may be congested. The objective is to minimize the overall fixed and service capacity costs, subject to the constraints that for any demand the disutility from travel and waiting times (measured as the weighted sum of the travel time from a demand to the facility serving that demand and the average waiting time at the facility) cannot exceed a predefined maximum allowed level (measured in units of time). We develop an analytical framework for the problem that determines the optimal set of facilities and assigns each facility a service rate (service capacity). In our setting, the consumers would like to maximize their utility (minimize their disutility) when choosing which facility to patronize. Therefore, the eventual choice of facilities is a user-equilibrium problem, where at equilibrium, consumers do not have any incentive to change their choices. The problem is formulated as a nonlinear mixed-integer program. We show how to linearize the nonlinear constraints and solve instead a mixed-integer linear problem, which can be solved efficiently.

A GRASP Approach for Solving Large-Scale Electric Bus Scheduling Problems

Electrifying public bus transportation is a critical step in reaching net-zero goals. In this paper, the focus is on the problem of optimal scheduling of an electric bus (EB) fleet to cover a public transport timetable. The problem is modelled using a mixed integer program (MIP) in which the charging time of an EB is pertinent to the battery’s state-of-charge level. To be able to solve large problem instances corresponding to real-world applications of the model, a metaheuristic approach is investigated. To be more precise, a greedy randomized adaptive search procedure (GRASP) algorithm is developed and its performance is evaluated against optimal solutions acquired using the MIP. The GRASP algorithm is used for case studies on several public transport systems having various properties and sizes. The analysis focuses on the relation between EB ranges (battery capacity) and required charging rates (in kW) on the size of the fleet needed to cover a public transport timetable. The results of the conducted computational experiments indicate that an increase in infrastructure investment through high speed chargers can significantly decrease the size of the necessary fleets. The results also show that high speed chargers have a more significant impact than an increase in battery sizes of the EBs.

Multigraph Modeling for Urban Distribution of Emergency Commodities with Semisoft Time Windows under Uncertainty

In this paper, we studied a stochastic bi-objective mathematical model for effective and reliable rescue operations in multigraph network. The problem is addressed by a two-stage stochastic nonlinear mixed-integer program where the reliability of routes is explicitly traded-off with total weighted completion time. The underlying transportation network is able to keep a group of multiattribute parallel arcs between every pair of nodes. By this, the proposed model should consider the routing decision in logistic planning along with the path selection in an uncertain condition. The first stage of the model concerns with the vehicle routing decisions which is not involved with random parameters; besides, the second stage of the model involves with the departure time at each demand node and path finding decisions after observation of random vectors in the first stage considering a finite number of scenarios. To efficiently solve the presented model, an enhanced nondominated sorting genetic algorithm II (NSGA-II) is proposed. The effectiveness of the introduced method is then evaluated by conducting several numerical examples. The results implied the high performance of our method in comparison to the standard NSGA-II. In further analyses, we investigated the beneficiary of using multigraph setting and showed the applicability of the proposed model using a real transportation case.

Integrated Vehicle Routing and Service Scheduling Under Time and Cancellation Uncertainties with Application in Nonemergency Medical Transportation

In this paper, we consider an integrated vehicle routing and service scheduling problem for serving customers in distributed locations who need pick-up, drop-off, or delivery services. We take into account the random trip time, nonnegligible service time, and possible customer cancellations, under which an ill-designed schedule may lead to undesirable vehicle idleness and customer waiting. We build a stochastic mixed-integer program to minimize the operational cost plus expected penalty cost of customers’ waiting time, vehicles’ idleness, and overtime. Furthermore, to handle real-time arrived service requests, we develop K-means clustering-based algorithms to dynamically update planned routes and schedules. The algorithms assign customers to vehicles based on similarities and then plan schedules on each vehicle separately. We conduct numerical experiments based on diverse instances generated from census data and data from the Ford Motor Company’s GoRide service, to evaluate result sensitivity and to compare the in-sample and out-of-sample performance of different approaches. Managerial insights are provided using numerical results based on different parameter choices and uncertainty settings.

Optimization of district heating production with thermal storage using mixed-integer nonlinear programming with a new initialization approach

Non-convex scheduling of energy production allows for more complex models that better describe the physical nature of the energy production system. Solutions to non-convex optimization problems can only be guaranteed to be local optima. For this reason, there is a need for methodologies that consistently provide low-cost solutions to the non-convex optimal scheduling problem. In this study, a novel Monte Carlo Tree Search initialization method for branch and bound solvers is proposed for the production planning of a combined heat and power unit with thermal heat storage in a district heating system. The optimization problem is formulated as a non-convex mixed-integer program, which is incorporated in a sliding time window framework. Here, the proposed initialization method offers lower-cost production planning compared to random initialization for larger time windows. For the test case, the proposed method lowers the yearly operational cost by more than 2,000,000 DKK per year. The method is one step in the direction of more reliable non-convex optimization that allows for more complex models of energy systems.

Formulation Matters: Reciprocating Integer Programming for Birchbox Product Assortment

Birchbox created a mixed-integer programming formulation to determine the products that it will send to its subscribers in individual boxes on a monthly basis. The goal of this formulation is to produce a set of different box configurations that are then assigned to customers to meet the diverse needs of its varied customer base. As Birchbox’s business grew, the mixed-integer program was taking days to solve, and experimenting with different business requirements to determine the best set of configurations became impossible. Therefore, Princeton Consultants created the Reciprocating Integer Programming technique to reduce these solution times, thus decreasing them to typically under 20 minutes. This has dramatically changed the way that Birchbox can run its subscription business.

Introduction: 2020 Daniel H. Wagner Prize for Excellence in the Practice of Advanced Analytics and Operations Research

The judges for the 2020 Daniel H. Wagner Prize for Excellence in the Practice of Advanced Analytics and Operations Research selected the five finalist papers featured in this special issue of the INFORMS Journal on Applied Analytics (IJAA). The prestigious Wagner Prize—awarded for achievement in implemented operations research, management science, and advanced analytics—emphasizes the quality and originality of mathematical models along with clarity of written and oral exposition. This year’s winning application is a system for optimally managing Dow Agrosciences’ (now Corteva) seed corn portfolio, which includes seeds for several hundred varieties of corn and is valued at more than $1 billion. The model employs Bayesian analytic methods to estimate crop yields from expert judgement. Stochastic optimization is then used to determine backup production in South America while dealing with yield uncertainty in North America. The remaining four papers include an efficient mixed-integer program used by Birchbox to determine individualized subscriber product sets; a scheduling system for Argentina’s premier soccer league; an incentive system for encouraging Lyft drivers to reposition to provide improved service; and a system for optimizing the electric bus network design in Rotterdam.

Dynamic Rebalancing Dockless Bike-Sharing System based on Station Community Discovery

Influenced by the era of the sharing economy and mobile payment, Dockless Bike-Sharing System (Dockless BSS) is expanding in many major cities. The mobility of users constantly leads to supply and demand imbalance, which seriously affects the total profit and customer satisfaction. In this paper, we propose the Spatio-Temporal Mixed Integer Program (STMIP) with Flow-graphed Community Discovery (FCD) approach to rebalancing the system. Different from existing studies that ignore the route of trucks and adopt a centralized rebalancing, our approach considers the spatio-temporal information of trucks and discovers station communities for truck-based rebalancing. First, we propose the FCD algorithm to detect station communities. Significantly, rebalancing communities decomposes the centralized system into a distributed multi-communities system. Then, by considering the routing and velocity of trucks, we design the STMIP model with the objective of maximizing total profit, to find a repositioning policy for each station community. We design a simulator built on real-world data from DiDi Chuxing to test the algorithm performance. The extensive experimental results demonstrate that our approach outperforms in terms of service level, profit, and complexity compared with the state-of-the-art approach.

Conflict Analysis for MINLP

The generalization of mixed integer program (MIP) techniques to deal with nonlinear, potentially nonconvex, constraints has been a fruitful direction of research for computational mixed integer nonlinear programs (MINLPs) in the last decade. In this paper, we follow that path in order to extend another essential subroutine of modern MIP solvers toward the case of nonlinear optimization: the analysis of infeasible subproblems for learning additional valid constraints. To this end, we derive two different strategies, geared toward two different solution approaches. These are using local dual proofs of infeasibility for LP-based branch-and-bound and the creation of nonlinear dual proofs for NLP-based branch-and-bound, respectively. We discuss implementation details of both approaches and present an extensive computational study, showing that both techniques can significantly enhance performance when solving MINLPs to global optimality. Summary of Contribution: This original article concerns the advancement of exact general-purpose algorithms for solving one of the largest and most prominent problem classes in optimization, mixed integer nonlinear programs (MINLPs). It demonstrates how methods for conflict analysis that learn from infeasible subproblems can be transferred to nonlinear optimization. Further, it develops theory for how nonlinear dual infeasibility proofs can be derived from a nonlinear relaxation. This paper features a thoroughly computational study regarding the impact of conflict analysis techniques on the overall performance of a state-of-the-art MINLP solver when solving MINLPs to global optimality.