Modeling Correlation in Vehicle Routing Problems with Makespan Objectives and Stochastic Travel Times

The majority of stochastic vehicle routing models consider travel times to be independent. However, in reality, travel times are often stochastic and correlated, such as in urban areas. We examine a vehicle routing problem with a makespan objective incorporating both stochastic and correlated travel times. We develop an approach based on extreme-value theory to estimate the expected makespan (and standard deviation) and embed this within a routing heuristic. We present results that demonstrate the impact of different correlation patterns and levels of correlation on route planning

Reduced cost-based variable fixing in two-stage stochastic programming

The explicit consideration of uncertainty is essential in addressing most planning and operation issues encountered in the management of complex systems. Unfortunately, the resulting stochastic programming formulations, integer ones in particular, are generally hard to solve when applied to realistically-sized instances. A common approach is to consider the simpler deterministic version of the formulation, even if it is well known that the solution quality could be arbitrarily bad. In this paper, we aim to identify meaningful information, which can be extracted from the solution of the deterministic problem, in order to reduce the size of the stochastic one. Focusing on two-stage formulations, we show how and under which conditions the reduced costs associated to the variables in the deterministic formulation can be used as an indicator for excluding/retaining decision variables in the stochastic model. We introduce a new measure, the Loss of Reduced Costs-based Variable Fixing (LRCVF), computed as the difference between the optimal values of the stochastic problem and its reduced version obtained by fixing a certain number of variables. We relate the LRCVF with existing measures and show how to select the set of variables to fix. We then illustrate the interest of the proposed LRCVF and related heuristic procedure, in terms of computational time reduction and accuracy in finding the optimal solution, by applying them to a wide range of problems from the literature

The SNS logistics network design : location and vehicle routing.

Large-scale emergencies caused by earthquake, tornado, pandemic flu, terrorism attacks and so on can wreak havoc to communities. In order to mitigate the impact of the events, emergency stockpiles of food, water, medicine and other materials have been set up around the US to be delivered to the affected areas during relief operations. One type of stockpile is called the Strategic National Stockpile (SNS). The SNS logistics network is designed to have multiple stages of facilities, each of which is managed by different levels of governmental authorities - federal, state and local authorities. The design of a logistics network for delivery of the SNS materials within a state are explored in this dissertation. There are three major areas of focus in this dissertation: (1) the SNS facility location model, which is used to determine sites for locating Receiving, Staging and Storage (RSS) and Regional Distribution Nodes (RDNs) to form a logistics network to deliver relief material to Points of Demand (PODs), where the materials are directly delivered to the affected population; (2) the SNS Vehicle Routing Problem (VRP), which is used to assist the SNS staff in determining the numbers of various types of trucks, and the routing schedules of each truck to develop an operational plan for delivering the required relief materials to the assigned PODs within the required duration; (3) the location-routing analysis of emergency scenarios, in which the facility location model and the VRP solution are integrated through the use of a computer program to run on several assumed emergency scenarios. Using real data from the department of public health in the Commonwealth of Kentucky, a transshipment and location model is formulated to determine the facility locations and the transshipment quantities of materials; a multiple-vehicle routing model allowing split deliveries and multiple routes per vehicle that must be completed within a required duration is formulated to determine the routing and scheduling of trucks. The facility location model is implemented using Microsoft Solver Foundation and C#. An algorithm combining the Clark and Wright saving algorithm and Simulated Annealing is designed and implemented in C# to solve the VRP. The algorithm can determine whether there is shortage of transportation capacity, and if so, how many of various types of trucks should be added for optimal performance. All the solution algorithms are integrated into a web-based SNS planning tool. In the location-routing analysis of emergency scenarios, a binary location model and an algorithm for solving VRP solution are integrated as a computer program to forecast the feasibility of distribution plans and the numbers of required trucks of various types. The model also compares the costs and benefits of direct and indirect shipment. A large-scale emergency scenario in which a specific type of vaccine is required to be delivered to the entire state of Kentucky is considered. The experiments are designed based on the real data provided by the Kentucky state government. Thus the experimental results provide valuable suggestions for future SNS preparedness planning

Stochastic models for analysis and optimization of unmanned aerial vehicle delivery on last-mile logistics

Doctor of PhilosophyDepartment of Industrial & Manufacturing Systems EngineeringAshesh K SinhaLand transportation is generally considered one of the most expensive, polluting and least efficient parts of the logistics chain. Due to these issues, using unmanned aerial vehicles such as drones for package delivery in last-mile logistics becomes increasingly attractive. However, there are several significant obstacles in terms of technical aspects and performance capabilities of drones like limited flight coverage. In addition, supply chains are exposed to a broad range of uncertainties some of which may cause disruptions in the whole supply chain system. To hedge against these issues, a well-designed reliable network is a top priority. Most existing models for optimization within logistics chain are deterministic, lack reliability, or they are not computationally efficient for larger problems. This dissertation aims to improve the reliability and efficiency of the supply chain network through the development of stochastic optimization models and methods to help address important problems related to delivery of products using drones. To achieve this goal, this study has developed a generalized optimization model that captures the dynamic and stochastic nature of problems by using stochastic optimization and stochastic control. At first, this study addresses issues bordering on capacitated supply chain problems, specifically on how reliable supply chain networks can be designed in the face of random facility disruptions and uncertain demand. The proposed multi-period capacitated facility location and allocation problem is modeled as a two-stage stochastic mixed-integer formulation that minimizes the total establishing and transportation cost. To overcome the complexity of the model, the L-shaped method of stochastic linear programming is applied by integrating two types of optimality and feasibility cuts for solving the stochastic model. This research improves the proposed algorithm in two ways: replacing the single-cut approach with a multi-cut and showing relatively complete recourse in the stochastic model by reformulating the original model. According to computational results, the proposed solution algorithm solves large-scale problems while avoiding long run times as well. It is also demonstrated that substantial improvements in reliability of the system can often be possible with minimal increases in facility cost. Next, this research aims to construct a feasible delivery network consisting of warehouses and recharging stations through the development of a stochastic mixed-integer model, resulting in improving the coverage and reliability of the supply chain network. Due to the computational complexity of the scenario-based mixed-integer model, this research improves the performance of the genetic algorithm by considering each scenario independently in one of the steps of the algorithm to significantly improve the computational time need to find the solutions. Computational results demonstrate that the proposed algorithm is efficiently capable of solving large-scale problems. Finally, this dissertation analyzes tradeoffs related to charging strategies for recharging stations which can be viewed as warehouses in last-mile logistics with capacity constraints and stochastic lead times. To enhance delivery time, this research assumes that extra batteries are available at the recharging station where individual drones land when they run out of power and swap empty batteries with fully charged ones. Stochastic Markov decision models are formulated to handle stochasticity in the problem and determine the optimal policy for decision-makers by applying a policy iteration algorithm. To overcome of computational challenges, a novel approximation method called the decomposition-based approach is proposed to split the original Markov decision problem for the system with N states into N independent Markov chain processes. Through numerical studies, this dissertation demonstrates that the proposed solution algorithm is not only capable of solving large-scale problems, but also avoids long run times. It is also demonstrated how different stochastic rate like flight or demand, and inventory and backorder costs can affect the optimal decisions

MULTI-VEHICLE ROUTE PLANNING FOR CENTRALIZED AND DECENTRALIZED SYSTEMS

Multi-vehicle route planning is the problem of determining routes for a set of vehicles to visit a set of locations of interest. In this thesis, we describe a study of a classical multi-vehicle route planning problem which compared existing solutions methods on min-sum (minimizing total distance traveled) and min-max (minimizing maximum distance traveled) cost objectives. We then extended the work in this study by adapting approaches tested to generate robust solutions to a failure-robust multi vehicle route planning problem in which a potential vehicle failure may require modifying the solution, which could increase costs. Additionally, we considered a decentralized extension to the multi-vehicle route planning problem, also known as the decentralized task allocation problem. The results of a computational study show that our novel genetic algorithm generated better solutions than existing approaches on larger instances with high communication quality

Optimization Approaches for Mobility and Service Sharing

Mobility and service sharing is undergoing a fast rise in popularity and industrial growth in recent years. For example, in patient-centered medical home care, services are delivered to patients at home, who share a group of medical staff riding together in a vehicle that also carries shared medical devices; companies such as Amazon and Meijer have been investing tremendous human effort and money in grocery delivery to customers who share the use of delivery vehicles and staff. In such mobility and service sharing systems, decision-makers need to make a wide range of system design and operational decisions, including locating service facilities, matching supplies with demand for shared mobility services, dispatching vehicles and staff, and scheduling appointments. The complexity of the linking decisions and constraints, as well as the dimensionality of the problems in the real world, pose challenges in finding optimal strategies efficiently. In this work, we apply techniques from Operations Research to investigate the optimal and practical solution approaches to improve the quality of service, cost-effectiveness, and operational efficiency of mobility and service sharing in a variety of applications. We deploy stochastic programming, integer programming, and approximation algorithms to address the issues in decision-making for seeking fast and reliable solutions for planning and operations problems. This dissertation contains four main chapters. In Chapter 2, we consider a class of vehicle routing problems (VRPs) where the objective is to minimize the longest route taken by any vehicle as opposed to the total distance of all routes. In such a setting, the traditional decomposition approach fails to solve the problem effectively. We investigate the hardness result of the problem and develop an approximation algorithm that achieves the best approximation ratio. In Chapter 3, we focus on developing an efficient computational algorithm for the elementary shortest path problem with resource constraints, which is solved as the pricing subproblem of the column generation-based approach for many VRP variants. Inspired by the color-coding approach, we develop a randomized algorithm that can be easily implemented in parallel. We also extend the state-of-the-art pulse algorithm for elementary shortest path problem with a new bounding scheme on the load of the route. In Chapter 4, we consider a carsharing fleet location design problem with mixed vehicle types and a restriction on CO2 emission. We use a minimum-cost flow model on a spatial-temporal network and provide insights on fleet location, car-type design, and their environmental impacts. In Chapter 5, we focus on the design and operations of an integrated car-and-ride sharing system for heterogeneous users/travelers with an application of satisfying transportation needs in underserved communities. The system aims to provide self-sustained community-based shared transportation. We address the uncertain travel and service time in operations via a stochastic integer programming model and propose decomposition algorithms to solve it efficiently. Overall, our contributions are threefold: (i) providing mathematical models of various complex mobility and service sharing systems, (ii) deriving efficient solution algorithms to solve the proposed models, (iii) evaluating the solution approaches via extensive numerical experiments. The models and solution algorithms that we develop in this work can be used by practitioners to solve a variety of mobility and service sharing problems in different business contexts, and thus can generate significant societal and economic impacts.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155115/1/miaoyu_1.pd

The location-routing problem with multi-compartment and multi-trip: formulation and heuristic approaches

The location-routing problem with multi-compartment and multi-trip is an extension to the standard location-routing problem. In this problem, depots are used to deliver different products using heterogeneous vehicles with several compartments. Each compartment has a limited capacity and is dedicated to a single type of product. The problem is formulated as a mixed integer program. A constructive heuristic and a hybrid genetic algorithm (HGA) are proposed. Numerical experiments show that both heuristics can efficiently determine the optimal solutions on small size instances. For larger ones, the HGA outperforms the constructive heuristic with relatively more computational time. Managerial insights have been obtained from sensitivity analyses which would be helpful to improve the performance of the supply network