Distribution-Free Model for Ambulance Location Problem with Ambiguous Demand

Ambulance location problem is a key issue in Emergency Medical Service (EMS) system, which is to determine where to locate ambulances such that the emergency calls can be responded efficiently. Most related researches focus on deterministic problems or assume that the probability distribution of demand can be estimated. In practice, however, it is difficult to obtain perfect information on probability distribution. This paper investigates the ambulance location problem with partial demand information; i.e., only the mean and covariance matrix of the demands are known. The problem consists of determining base locations and the employment of ambulances, to minimize the total cost. A new distribution-free chance constrained model is proposed. Then two approximated mixed integer programming (MIP) formulations are developed to solve it. Finally, numerical experiments on benchmarks (Nickel et al., 2016) and 120 randomly generated instances are conducted, and computational results show that our proposed two formulations can ensure a high service level in a short time. Specifically, the second formulation takes less cost while guaranteeing an appropriate service level. Document type: Articl

Optimal Global Supply Chain and Warehouse Planning under Uncertainty

A manufacturing company\u27s inbound supply chain consists of various processes such as procurement, consolidation, and warehousing. Each of these processes is the focus of a different chapter in this dissertation. The manufacturer depends on its suppliers to provide the raw materials and parts required to manufacture a finished product. These suppliers can be located locally or overseas with respect to the manufacturer\u27s geographic location. The ordering and transportation lead times are shorter if the supplier is located locally. Just In Time (JIT) or Just In Sequence (JIS) inventory management methods could be practiced by the manufacturer to procure the raw materials and parts from the local supplier and control the inventory levels in the warehouse. In contrast, the lead time for the orders placed with an overseas supplier is usually long because sea-freight is often used as a primary mode of transportation. Therefore, the orders for the raw materials and parts (henceforth, we collectively refer to raw material and part by part) procured from overseas suppliers are usually placed using forecasted order quantities. In Chapter 2, we study the procurement process to reduce the overall expected cost and determine the optimal order quantities as well as the mode of transportation for procurement under forecast and inventory uncertainty. We formulate a two-stage stochastic integer programming model and solve it using the progressive hedging algorithm, a scenario-based decomposition method. Generally, the orders are placed with overseas suppliers using weekly or monthly forecasted demands, and the ordered part is delivered using sea-containers since sea-freight is the primary mode of transportation. However, the end manufacturing warehouse is usually designed to hold around one to two days of parts. To replenish the inventory levels, the manufacturer considered in this research unloads the sea-container that contains the part that needs to be restocked entirely. This may cause over-utilization of the manufacturer\u27s warehouse if an entire week\u27s supply of part is consolidated into a single sea-container. This problem is further aggravated if the manufacturer procures hundreds of different parts from overseas suppliers and stores them in its warehouse. In Chapter 3, we study the time-series forecasting models that help predict the manufacturing company\u27s daily demand quantities for parts with different characteristics. The manufacturer can use these forecasted daily demand quantities to consolidate the sea-containers instead of the weekly forecasted demand. In most cases, there is some discrepancy between the predicted and actual demands for parts, due to which the manufacturer can either have excess inventory or shortages. While excess inventory leads to higher inventory holding costs and warehouse utilization, shortages can result in substantially undesirable consequences, such as the total shutdown of production lines. Therefore, to avoid shortages, the manufacturer maintains predetermined safety stock levels of parts with the suppliers to fulfill the demands arising from shortages. We formulate a chance-constraint optimization model and solve it using the sample approximation approach to determine the daily safety stock levels at the supplier warehouse under forecast error uncertainty. Once the orders are placed with the local and overseas suppliers, they are consolidated into trailers (for local suppliers) and sea-containers (for overseas suppliers). The consolidated trailers and sea-containers are then delivered to the manufacturing plant, where they are stored in the yard until they are called upon for unloading. A detention penalty is incurred on a daily basis for holding a trailer or sea-container. Consolidating orders from different suppliers helps maximize trailer and sea-container space utilization and reduce transportation costs. Therefore, every sea-container and trailer potentially holds a mixture of parts. When a manufacturer needs to replenish the stocks of a given part, the entire sea-container or trailer that contains the required part is unloaded. Thus, some parts that are not imminently needed for production are also unloaded and stored inside the manufacturing warehouse along with the required parts. In Chapter 4, we study a multi-objective optimization model to determine the sea-containers and trailers to be unloaded on a given day to replenish stock levels such that the detention penalties and the manufacturing warehouse utilization are minimized. Once a sea-container or trailer is selected to replenish the warehouse inventory levels, its contents (i.e., pallets of parts) must be unloaded by the forklift operator and then processed by workers to update the stock levels and break down the pallets if needed. Finally, the unloaded and processed part is stored in the warehouse bins or shelves. In Chapter 5, we study the problem of determining the optimal team formation such that the total expected time required to unload, process, and store all the parts contained in the sea-containers and trailers selected for unloading on a given day is minimized

Dynamic temporary blood facility location-allocation during and post-disaster periods

The key objective of this study is to develop a tool (hybridization or integration of different techniques) for locating the temporary blood banks during and post-disaster conditions that could serve the hospitals with minimum response time. We have used temporary blood centers, which must be located in such a way that it is able to serve the demand of hospitals in nearby region within a shorter duration. We are locating the temporary blood centres for which we are minimizing the maximum distance with hospitals. We have used Tabu search heuristic method to calculate the optimal number of temporary blood centres considering cost components. In addition, we employ Bayesian belief network to prioritize the factors for locating the temporary blood facilities. Workability of our model and methodology is illustrated using a case study including blood centres and hospitals surrounding Jamshedpur city. Our results shows that at-least 6 temporary blood facilities are required to satisfy the demand of blood during and post-disaster periods in Jamshedpur. The results also show that that past disaster conditions, response time and convenience for access are the most important factors for locating the temporary blood facilities during and post-disaster periods

Large-scale optimization under uncertainty: applications to logistics and healthcare

Many decision making problems in real life are affected by uncertainty. The area of optimization under uncertainty has been studied widely and deeply for over sixty years, and it continues to be an active area of research. The overall aim of this thesis is to contribute to the literature by developing (i) theoretical models that reflect problem settings closer to real life than previously considered in literature, as well as (ii) solution techniques that are scalable. The thesis focuses on two particular applications to this end, the vehicle routing problem and the problem of patient scheduling in a healthcare system. The first part of this thesis studies the vehicle routing problem, which asks for a cost-optimal delivery of goods to geographically dispersed customers. The probability distribution governing the customer demands is assumed to be unknown throughout this study. This assumption positions the study into the domain of distributionally robust optimization that has a well developed literature, but had so far not been extensively studied in the context of the capacitated vehicle routing problem. The study develops theoretical frameworks that allow for a tractable solution of such problems in the context of rise-averse optimization. The overall aim is to create a model that can be used by practitioners to solve problems specific to their requirements with minimal adaptations. The second part of this thesis focuses on the problem of scheduling elective patients within the available resources of a healthcare system so as to minimize overall years of lives lost. This problem has been well studied for a long time. The large scale of a healthcare system coupled with the inherent uncertainty affecting the evolution of a patient make this a particularly difficult problem. The aim of this study is to develop a scalable optimization model that allows for an efficient solution while at the same time enabling a flexible modelling of each patient in the system. This is achieved through a fluid approximation of the weakly-coupled counting dynamic program that arises out of modeling each patient in the healthcare system as a dynamic program with states, actions, transition probabilities and rewards reflecting the condition, treatment options and evolution of a given patient. A case-study for the National Health Service in England highlights the usefulness of the prioritization scheme obtained as a result of applying the methodology developed in this study.Open Acces

An integer L-shaped algorithm for the integrated location and network restoration problem in disaster relief

Being prepared for potential disaster scenarios enables government agencies and humanitarian organizations to respond effectively once the disaster hits. In the literature, the two-stage stochastic programming models are commonly employed to develop preparedness plans before anticipated disasters. These models can be very difficult to solve as the complexity increases by several sources of uncertainty and interdependent decisions. In this study, we propose an integer L-shaped algorithm to solve the integrated location and network restoration model, which is a two-stage stochastic programming model determining the number and locations of the emergency response facilities and restoration resources under uncertainty. Our algorithm accommodates the second-stage binary decision variables which are required to indicate undamaged and restored roads of the network that can be used for relief distribution. Our computational results show that our algorithm outperforms CPLEX for the larger number of disaster scenarios as the solution time of our algorithm increases only linearly as the number of scenarios increases

Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition

In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer formulation, we derive its linear counterparts and show that they could be stronger than existing linear formulations. We also develop a variant of Jensen's inequality that extends the one for stochastic program. To solve this challenging problem, we present a variant of Benders decomposition method in bilinear form, which actually provides an easy-to-use algorithm framework for further improvements, along with a few enhancement strategies based on structural properties or Jensen's inequality. Computational study shows that the presented Benders decomposition method, jointly with appropriate enhancement techniques, outperforms a commercial solver by an order of magnitude on solving chance constrained program or detecting its infeasibility