Raha Akhavan-Tabatabaei

OR models with stochastic components in disaster operations management: A literature survey

Abstract The increasing number of affected people due to disasters, the complexity and unpredictability of these phenomena and the different problems encountered in the planning and response in different scenarios, establish a need to find better measures and practices in order to reduce the human and economic loss in this kind of events. However this is not an easy task considering the great uncertainty these phenomena present including the multiple number of possible scenarios in terms of location, probability of occurrence and impact, the difficulty in estimating the demand and supply, the complexity of determining the number and type of resources both available and needed and the intricacy to establish the exact location of the demand, the supply and the possible damaged infrastructure, among many others. Disaster Operations Management has become very popular and, considering the properties of disasters, the use of tools and methodologies such as OR have been given a lot of attention in recent years. The present work provides a literature review on the OR models with some stochastic component applied to Disaster Operations Management (DOM), along with an analysis of these stochastic components and the techniques used by different authors to cope with them as well as a detailed database on the consulted papers, which differentiates this research from other reviews developed during the same period, in order to give an insight on the state of the art in the topic and determine possible future research directions.

On Modeling Stochastic Travel and Service Times in Vehicle Routing

Vehicle routing problems with stochastic travel and service times (VRPSTT) consist of designing transportation routes of minimal expected cost over a network where travel and service times are represented by random variables. Most of the existing approaches for VRPSTT are conceived to exploit the properties of the distributions assumed for the random variables. Therefore, these methods are tied to a given family of distributions and subject to strong modeling assumptions. We propose an alternative way to model travel and service times in VRPSTT without making many assumptions regarding such distributions. To illustrate our approach, we embed it into a state-of-the-art routing engine and use it to conduct experiments on instances with different travel and service time distributions.

A stochastic dynamic pricing model for the multiclass problems in the airline industry

In the airline industry, deciding the ticket price for each flight directly affects the number of people that in the future will try to buy a ticket. Depending on the willingness-to-pay of the customers the flight might take off with empty seats or seats sold at a lower price. Therefore, based on the behavior of the customers, a price must be fixed for each type of product in each period. We propose a stochastic dynamic pricing model to solve this problem, applying phase type distributions and renewal processes to model the inter-arrival time between two customers that book a ticket and the probability that a customer buys a ticket. We test this model in a real-world case where as a result the revenue is increased on average by 31 percent.

On the combined maintenance and routing optimization problem

This work focuses on the problem of planning and scheduling maintenance operations for a set of geographically distributed machines, subject to non-deterministic failures with a set of technicians that perform preventive maintenance and repair operations on the machines at the customer sites within a specific time window. This study presents a two-step iterative approach. In the first step, a maintenance model determines the optimal time until the next preventive maintenance operation, its frequency, and the time window for each customer, while minimizing the total expected maintenance costs. In the second step, a routing model assigns and schedules maintenance operations to each technician over the planning horizon within the workday. This two-step iterative process balances the maintenance cost, the failure probabilities, and waiting times at each customer. The novelty of this work lies in the integration of maintenance scheduling and a routing model that considers several machines.

Time and inventory dependent optimal maintenance policies for single machine workstations: An MDP approach

In this work the problem of obtaining an optimal maintenance policy for a single-machine, single-product workstation that deteriorates over time is addressed, using Markov Decision Process (MDP) models. Two models are proposed. The decision criteria for the first model is based on the cost of performing maintenance, the cost of repairing a failed machine and the cost of holding inventory while the machine is not available for production. For the second model the cost of holding inventory is replaced by the cost of not satisfying the demand. The processing time of jobs, inter-arrival times of jobs or units of demand, and the failure times are assumed to be random. The results show that in order to make better maintenance decisions the interaction between the inventory (whether in process or final), and the number of shifts that the machine has been working without restoration, has to be taken into account. If this interaction is considered, the long-run operational costs are reduced significantly. Moreover, structural properties of the optimal policies of the models are obtained after imposing conditions on the parameters of the models and on the distribution of the lifetime of a recently restored machine.

A Markov Chain Framework for Cycle Time Approximation of Toolsets

Cycle time is a key performance measure in semiconductor manufacturing. Currently, discrete event simulation and queueing theory are the most common approaches to estimating the cycle time of a fabrication facility. However, the performance of both approaches has been unsatisfactory due to many factors, including the inability to perform in an environment where informal and unwritten operational rules exist. Such rules create dependence between the arrival and service processes of a toolset, and, hence, render the classical queueing models inaccurate. We propose a Markov chain framework that attempts to approximate the cycle time of a toolset in the presence of informal operational rules, and we compare our approach with classical queueing models through a series of numerical examples.

Using discrete event simulation to evaluate the logistics of medical attention during the relief operations in an earthquake in Bogota

City of Bogotá the capital of Colombia, is located in a region with a high risk of natural disasters including earthquakes. Over the past few years the city officials have been developing high level emergency plans to cope with such disasters. However the current emergency plan lacks details on the logistics of medical attention. The motivation of this work is to evaluate the efficiency of the current emergency plan in attending the injured within the first four days of an earthquake. We present a simulation model to transfer the injured people to the temporary and permanent hospitals. The model takes into account the current capacity and occupation rate of the permanent hospitals, the current number of ambulances in the zone and the approximate duration of destructed routes among others. The model outcomes are used by the government agencies to reduce the uncertainty impact on planning the logistics of relief operations.

On the preventive management of sediment-related sewer blockages: a combined maintenance and routing optimization approach

In this work we tackle the problem of planning and scheduling preventive maintenance (PM) of sediment-related sewer blockages in a set of geographically distributed sites that are subject to non-deterministic failures. To solve the problem, we extend a combined maintenance and routing (CMR) optimization approach which is a procedure based on two components: (a) first a maintenance model is used to determine the optimal time to perform PM operations for each site and second (b) a mixed integer program-based split procedure is proposed to route a set of crews (e.g., sewer cleaners, vehicles equipped with winches or rods and dump trucks) in order to perform PM operations at a near-optimal minimum expected cost. We applied the proposed CMR optimization approach to two (out of five) operative zones in the city of Bogotá (Colombia), where more than 100 maintenance operations per zone must be scheduled on a weekly basis. Comparing the CMR against the current maintenance plan, we obtained more than 50% of cost savings in 90% of the sites.

Effective WIP dependent lot release policies: a discrete event simulation approach

In this paper we explore a lot release policy for wafer fabs that is based on the WIP threshold of the bottleneck station. Our results show that this policy is effective in cycle time improvement while keeping the same level of throughput compared with a case where no policy is applied. The application of this policy is practical and needs less considerations compared to policies that aim at keeping the WIP constant throughout the fab.

A method for cycle time estimation of semiconductor manufacturing toolsets with correlations

This paper proposes a cycle time estimation method for typical toolsets in Semiconductor Fabrication Facilities (Fabs). Due to sophisticated process flows and requirements of the process, queueing models for toolsets can become very complicated and their performance has been unsatisfactory due to the low accuracy of their results. In this paper, we first study the performance of classical queuing models using a high volume manufacturing toolset as our case study and discuss the potential causes for failure of classical models in predicting its cycle time. Then we propose a new approach for estimating the cycle time of toolsets that have inherent correlation between their arrival and service processes. Finally we apply this method to our case study toolset and show that the accuracy of cycle time estimation is improved significantly compared to use of classical queueing models.