Stochastic Programming and Distributionally Robust Optimization Approaches for Location and Inventory Prepositioning of Disaster Relief Supplies

In this paper, we study the problem of disaster relief inventory prepositioning under uncertainty. Specifically, we aim to determine where to open warehouses and how much relief item inventory to preposition in each, pre-disaster. During the post-disaster phase, prepositioned items are distributed to demand nodes, and additional items are procured and distributed as needed. There is uncertainty in the (1) disaster level, (2) locations of affected areas, (3) demand of relief items, (4) usable fraction of prepositioned items post-disaster, (5) procurement quantity, and (6) arc capacity. We propose and analyze two-stage stochastic programming (SP) and distributionally robust optimization (DRO) models, assuming known and unknown uncertainty distributions, respectively. The first and second stages correspond to pre- and post-disaster phases, respectively. We propose a Monte Carlo Optimization procedure to solve the SP and a decomposition algorithm to solve the DRO model. To illustrate potential applications of our approaches, we conduct extensive experiments using a hurricane season and an earthquake as case studies. Our results demonstrate the (1) the robustness and superior post-disaster operational performance of the DRO decisions under various distributions compared to SP decisions, especially under misspecified distributions and high variability, (2) the trade-off between considering distributional ambiguity and following distributional belief, and (3) computational efficiency of our approaches

Reliable multi-product multi-vehicle multi-type link logistics network design: A hybrid heuristic algorithm

Abstract This paper considers the reliable multi-product multi-vehicle multi-type link logistics network design problem (RMLNDP) with system disruptions, which is concerned with facilities locating, transshipment links constructing, and also allocating them to the customers in order to satisfy their demand with minimum expected total cost (including locating costs, link constructing costs, and also expected transshipment costs in normal and disruption conditions). The motivating application of this class of problem is in multi-product, multi-vehicle, and multitype link logistics network design regarding to system disruptions simultaneously. In fact, the decision makers in this area are not only concerned with the facility locating costs, link constructing costs, and logistical costs of the system but also by focusing on the several system disruption states in order to be able to provide a reliable sustainable multi configuration logistic network system. All facility location plans, link construction plans and also link transshipment plans of demands in the problem must be efficiently determined while considering the several system disruptions. The problem is modeled as a mixed integer programming (MIP) model. Also, a hybrid heuristic, based on linear programming (LP) relaxation approach, is proposed. Computational experiments illustrate that the provided algorithm will be able to substantially outperform the proposed integer programming model in terms of both finding and verifying the efficient optimal (or near optimal) solution at a reasonable processing time

Design of a reliable logistics network with hub disruption under uncertainty

In this study, we design a reliable logistics network based on a hub location problem, which is less sensitive to disruption and it performs efficiently when disruption occurs. A new mixed-integer programming model is proposed to minimize the total sum of the nominal and expected failure costs. This model considers complete and partial disruption at hubs. In addition, we propose a new hybrid meta-heuristic algorithm based on genetic and imperialist competitive algorithms. We compare the performance of the proposed al- gorithm with a new lower bound method in terms of the CPU time and solution quality. Furthermore, we conclude that a considerable improvement in the reliability of the net- work can be achieved with only a slight increase in the total cost. Finally, we demonstrate that the networks designed using our model are less conservative and more robust to dis- ruption compared with those designed based on other robustness measures

Responsive Contingency Planning for Supply Chain Disruption Risk Mitigation

Contingent sourcing from a backup resource is an effective risk mitigation strategy under major disruptions. The production volumes and speeds of the backup resource are important protection design considerations, as they affect recovery. The objective of this dissertation is to show that cost-effective protection of existing supply networks from major disruptions result from planning appropriate volume and response speeds of a backup production facility prior to the disruptive event by considering operational aspects such as congestion that may occur at facilities. Contingency strategy are more responsive and disruption recovery periods can be shortened through such prior planning. The dissertation focuses on disruption risk arising from intelligent or pre-meditated attacks on supply facilities. An intelligent attacker has the capability to create worst case loss depending on the protection strategy of a given network. Since the attacker seeks the maximum loss and the designer tries to identify the protection scheme which minimizes this maximum loss, there exists an interdependence between attack and protection decisions. Ignoring this characteristic leads to suboptimal mitigation solutions under such disruptions. We therefore develop a mathematical model which utilizes a game theoretic framework of attack and defense involving nested optimization problems. The model is used to decide optimal selection of backup production volume and the response speeds, the facilities to build such capability within the available budget. The reallocation of demands from a disrupted facility to an undisrupted facility in a contingency strategy leads to congestion of the undisrupted facility, which may result in longer lead times and reduced throughput during disruption periods, thereby limiting the effectiveness of a contingency strategy. In the second part of the dissertation, we therefore analyze congestion effects in responsive contingency planning. The congestion cost function is modeled and integrated into the mathematical model of responsive contingency planning developed in the first part of the dissertation. The main contribution of this dissertation is that a decision tool has been developed to plan protection of an existing supply networks considering backup sourcing through gradual capacity acquisition. The solution methodology involving recursive search tree has been implemented which allows exploring protection solutions under a given budget of protection and multiple combinations of response speeds and production capacities of a backup facility. The results and analysis demonstrate the value of planning for responsive contingency in supply chains subject to risks of major disruptions and provide insights to aid managerial decision making

Resource Allocation Models in Healthcare Decision Making

We present models for allocating limited healthcare resources efficiently among target populations in order to maximize society's welfare and/or minimize the expected costs. In general, this thesis is composed of two major parts. Firstly, we formulate a novel uncapacitated fixed-charge location problem which considers the preferences of customers and the reliability of facilities simultaneously. A central planner selects facility locations from a set of candidate sites to minimize the total cost of opening facilities and providing service. Each customer has a strict preference order over a subset of the candidate sites, and uses her most preferred available facility. If that facility fails due to a disruptive event, the customer attends her next preferred available facility. This model bridges the gap between the location models that consider the preferences of customers and the ones that consider the reliability of facilities. It applies to many healthcare settings, such as preventive care clinics, senior centers, and disaster response centers. In such situations, patient (or customer) preferences vary significantly. Therefore, there could be a large number of subgroups within the population depending on their preferences of potential facility sites. In practice, solving problems with large numbers of population subgroups is very important to increase granularity when considering diverse preferences of several different customer types. We develop a Lagrangian branch-and-bound algorithm and a branch-and-cut algorithm. We also propose valid inequalities to tighten the LP relaxation of the model. Our numerical experiments show that the proposed solution algorithms are efficient, and can be applied to problems with extremely large numbers of customers. Secondly, we study the allocation of colorectal cancer (CRC) screening resources among individuals in a population. CRC can be early-detected, and even prevented, by undergoing periodic cancer screenings via colonoscopy. Current guidelines are based on existing medical evidence, and do not explicitly consider (i) all possible alternative screening policies, and (ii) the effect of limited capacity of colonoscopy screening on the economic feasibility of the screening program. We consider the problem of allocating limited colonoscopy capacity for CRC screening and surveillance to a population composed of patients of different risk groups based on risk factors including age, CRC history, etc. We develop a mixed integer program that maximizes the quality-adjusted life years for a given patient population considering the population's demographics, CRC progression dynamics, and relevant constraints on the system capacity and the screening program effectiveness. We show that the current guidelines are not always optimal. In general, when screening capacity is high, the optimal screening programs recommend higher screening rates than the current guidelines, and the optimal screening policies change with age and gender. This shows the significance of incorporating screening capacity into the decisions of optimal screening policies