Operations and Decision Technologies Abstracts

“Models for Drone Delivery of Medications and Other Healthcare Items”

Professor(s) Carlton Scott
Co-author(s): Judy E. Scott (PhD and MBA Alumna)
Accepted at: International Journal of Healthcare Information Systems and Informatics, May 2018
This article describes how a healthcare delivery drone has the potential for developing countries to leapfrog the development of traditional transportation infrastructure. Inaccessible roads no longer will prevent urgent delivery of blood, medications or other healthcare items. This article reviews the current status of innovative drone delivery with a particular emphasis on healthcare. The leading companies in this field and their different strategies are studied. Further, this article reviews the latest decision models that facilitate management decision making for operating a drone fleet. The contribution in this article of two new models associated with the design of a drone healthcare delivery networks will facilitate a more timely, efficient, and economical drone healthcare delivery service to potentially save lives.


“Coordinating Supply and Demand on an On-demand Service Platform with Impatient Customers”

Professor(s): Rick So
Co-author(s): Jiaru Bai (PhD Alumnus), Chris Tang, Xujun Chen, and Hai Wang 
Accepted at: Manufacturing and Service Operations Management, December 2017

We consider an on-demand service platform using earning sensitive independent providers with heterogeneous reservation price (for work participation) to serve its time and price sensitive customers with heterogeneous valuation of the service. As such, both the supply and demand are "endogenously'' dependent on the price the platform charges its customers and the wage the platform pays its independent providers. We present an analytical model with endogenous supply (number of participating agents) and endogenous demand (customer request rate) to study this on-demand service platform. To coordinate endogenous demand with endogenous supply, we include the steady-state waiting time performance based on a queueing model in the customer utility function to characterize the optimal price and wage rates that maximize the profit of the platform. We first analyze a base model that uses a fixed payout ratio (i.e., the ratio of wage over price), and then extend our model to allow the platform to adopt a time-based payout ratio. We find that it is optimal for the platform to charge a higher price when demand increases; however, the optimal price is not necessarily monotonic when the provider capacity or the waiting cost increases. Furthermore, the platform should offer a higher payout ratio as demand increases, capacity decreases or customers become more sensitive to waiting time. We also find that the platform should lower its payout ratio as it grows with the number of providers and customer demand increasing at about the same rate. We use a set of actual data from a large on-demand ride-hailing platform to calibrate our model parameters in numerical experiments to illustrate some of our main insights.

“Do Pictographs Affect Probability Comprehension and Risk Perception of Multiple-Risk Communications?”

Professor(s): Robin Keller
Co-author(s): James Leonhardt (PhD Alumnus)
Accepted at: Journal of Consumer Affairs, December 2017

Pictographs can be used to visually present probabilistic information using a matrix of icons. Previous research on pictographs has focused on single rather than multiple-risk options. The present research conducts a behavioral experiment to assess the effect of pictographs on probability comprehension and risk perception for single and multiple-risk options. The creation of the experimental stimuli is informed by a review of the Centers for Disease Control and Prevention’s vaccine information sheets. The results provide initial evidence that, in the context of childhood vaccines, the inclusion of pictographs alongside numeric (e.g. 1 in 5) probability information can result in higher probability comprehension and lower risk perception for multiple-risk options but not for single-risk options. These findings have implications for how health-related risks are communicated to the public.

“Improving Micro-Retailer and Consumer Welfare in Developing Economies: Replenishment Strategies and Market Entries”

Professor(s): Luyi Gui and Shuya Yin
Accepted at: Manufacturing & Service Operations Management, November 2017

Micro-retailers in remote rural areas in developing countries face high replenishment cost due to poor road infrastructure and the lack of formal distribution channels. This paper investigates the effectiveness of two innovative replenishment strategies (purchasing cooperatives and non-profit wholesaler) deployed by NGOs to reduce micro-retailers' replenishment cost and improve consumer welfare. The problem is relevant in practice as travel cost has been documented as a major cost burden that leads to meager earnings for the micro-retailers, few retailers in the market, and high prices to the consumers (due to less competition). Analyzing how these innovative strategies alleviate the above problems enable us to develop practical insights as well as fill an important gap in the literature. We adopt a stylized model that captures price competition, consumer welfare, and market entry decision of micro-retailers under the replenishment strategies considered. We compare the equilibrium retailer profit, consumer welfare, and the number of retailers entering the market under these strategies. We find that in a regulated market, a non-profit wholesaler creates supply chain inefficiency, and thus can lead to a higher retail price, which benefits the retailers yet harms the consumers. However, with free market entry (unregulated market), we show that under certain market conditions, both the cooperative and the non-profit wholesaler strategies can be Pareto improving. Yet between these two strategies, there typically exists a trade-off in both regulated and unregulated markets, i.e., the cooperative strategy enhances consumer welfare while the wholesaler strategy leads to higher retailer profits. Our results indicate that the policy maker needs to be mindful about the market conditions and the relative emphasis between the profit and market participation of micro-retailers and consumer welfare when choosing and implementing the purchasing cooperative and the non-profit wholesaler strategies.

“Designing Safety Regulations for High-Hazard Industries”

Professor(s): Robin Keller
Co-author(s): Committee for a Study of Performance-Based Safety Regulation
Accepted at: The National Academies Press, October 2017

TRB Special Report 324: Designing Safety Regulations for High-Hazard Industries, examines key factors relevant to government safety regulators when choosing among regulatory design types, particularly for preventing low-frequency, high consequence events. In such contexts, safety regulations are often scrutinized after an incident, but their effectiveness can be inherently difficult to assess when their main purpose is to reduce catastrophic failures that are rare to begin with. Nevertheless, regulators of high-hazard industries must have reasoned basis for making their regulatory design choices.

Asked to compare the advantages and disadvantages of so-called “prescriptive” and “performance-based” regulatory designs, the study committee explains how these labels are often used in an inconsistent and misleading manner that can obfuscate regulatory choices and hinder the ability of regulators to justify their choices. The report focuses instead on whether a regulation requires the use of a means or the attainment of some ends—and whether it targets individual components of a larger problem (micro-level) or directs attention to that larger problem itself (macro-level). On the basis of these salient features of any regulation, four main types of regulatory design are identified, and the rationale for and challenges associated with each are examined under different high-hazard applications.

Informed by academic research and by insights from case studies of the regulatory regimes of four countries governing two high-hazard industries, the report concludes that too much emphasis is placed on simplistic lists of generic advantages and disadvantages of regulatory design types. The report explains how a safety regulator will want to choose a regulatory design, or combination of designs, suited to the nature of the problem, characteristics of the regulated industry, and the regulator’s own capacity to promote and enforce compliance. This explanation, along with the regulatory design concepts offered in this report, is intended to help regulators of high-hazard industries make better informed and articulated regulatory design choices.

“Design Incentives under Collective Extended Producer Responsibility: A Network Perspective”

Professor(s): Luyi Gui
Co-author(s): Atalay Atasu, Ozlem Ergun, Beril Toktay
Accepted at: Management Science, July 2017

A key goal of Extended Producer Responsibility (EPR) legislation is to provide incentives for producers to design their products for recyclability. EPR is typically implemented in a collective system, where a network of recycling resources are coordinated to fulfill the EPR obligations of a set of producers, and the resulting system cost is allocated among these producers. Collective EPR is prevalent because of its cost efficiency advantages. However, it is considered to provide inferior design incentives compared to an individual implementation (where producers fulfill their EPR obligations individually). In this paper, we revisit this assertion and investigate its fundamental underpinnings in a network setting. To this end, we develop a new biform game framework that captures producers' independent design choices (non-cooperative stage) and recognizes the need to maintain the voluntary participation of producers for the collective system to be stable (cooperative stage). This biform game subsumes the network-based operations of a collective system and captures the interdependence between producers' product design and participation decisions. We then characterize the manner in which design improvement may compromise stability and vice versa. We establish that a stable collective EPR implementation can match and even surpass an individual implementation with respect to product design outcomes. In particular, we show that when the processing technology efficiency and product recyclability are substitutes (complements), a recycling network where processor capacity pooling leads to sufficiently low (high) cost reduction will lead to superior designs in the collective system and maintain its stability, and we propose cost allocation mechanisms to achieve this dual purpose.


“Information Presentation in Decision and Risk Analysis: Answered, Partly Answered, and Unanswered Questions”

Professor(s) Robin Keller 
Co-author(s): YiTong Wong, PhD Alumnus
Accepted at: Risk Analysis, September 2016 

For the last thirty years, researchers in risk analysis, decision analysis, and economics have consistently proven that decision makers employ different processes for evaluating and combining anticipated and actual losses, gains, delays and surprises. While rational models generally prescribe a consistent response, people’s heuristic processes will sometimes lead them to be inconsistent in the way they respond to information presented in theoretically equivalent ways. We point out several promising future research directions by listing and detailing a series of answered, partly answered, and unanswered questions.

“Mixed Planar and Network Single-Facility Location Problems”

Professor(s) Carlton Scott and John Turner 
Co-author(s): Zvi Drezner
Accepted at: Networks, August 2016 

We consider the problem of optimally locating a single facility anywhere in a network to serve both on-network and off-network demands. Off-network demands occur in a Euclidean plane, while on-network demands are restricted to a network embedded in the plane. On-network demand points are serviced using shortest-path distances through links of the network (e.g., on-road travel), whereas demand points located in the plane are serviced using more expensive Euclidean distances. Our base objective minimizes the total weighted distance to all demand points. We develop several extensions to our base model, including: (i) a threshold distance model where if network distance exceeds a given threshold, then service is always provided using Euclidean distance, and (ii) a minimax model that minimizes worst-case distance. We solve our formulations using the “Big Segment Small Segment” global optimization method, in conjunction with bounds tailored for each problem class. Computational experiments demonstrate the effectiveness of our solution procedures. Solution times are very fast (often under one second), making our approach a good candidate for embedding within existing heuristics that solve multi-facility problems by solving a sequence of single-facility problems.

“Markov Chain Models in Practice: A Review of Low Cost Software Options”

Professor(s) Robin Keller 
Co-author(s): Jiaru Bai (PhD Student) and Cristina del Campo
Accepted at: Investigación Operacional, July 2016 

Markov processes (or Markov chains) are used for modeling a phenomenon in which changes over time of a random variable comprise a sequence of values in the future, each of which depends only on the immediately preceding state, not on other past states. A Markov process (PM) is completely characterized by specifying the finite set S of possible states and the stationary probabilities (i.e. time-invariant) of transition between these states. The software most used in medical applications is produced by TreeAge, since it offers many advantages to the user. But, the cost of the TreeAge software is relatively high. Therefore in this article two software alternatives are presented: Sto Tree and the zero cost add-in program "markovchain" implemented in R. An example of a cost-effectiveness analysis of two possible treatments for advanced cervical cancer, previously conducted with the Treeage software, is re-analyzed with these two low cost software packages. This paper was also written in Spanish to facilitate communication with Spanish-speaking scholars in Cuba and elsewhere, who aim to conduct Markov cost effectiveness analyses and would benefit from low cost software alternatives.

“Group Selling, Product Durability and Consumer Behavior”

Professor(s) Shuya Yin 
Co-author(s): Yuhong He (Ph.D. Alumna) and Saibal Ray
Accepted at: Production and Operations Management, May 2016 

Firms producing complementary goods often strategically form groups and jointly sell their products to better coordinate their decisions. For consumer durables, decisions about such collaboration might be complicated due to two factors. Because of their durability and presence of used goods markets, such products engender “future” price competition between new and used goods. On the other hand, consumers of such products might be forward-looking and patient, both of which affect their purchasing behavior. In this paper, we study how the above product and consumer characteristics interact to affect the group selling decisions of complementary firms. We do so through a two-period model consisting of a value chain with two upstream manufacturers and a downstream retailer. When consumers are relatively impatient and reluctant to wait to buy later, group selling by manufacturers will take place only when the end product is relatively perishable, i.e., product durability is low. However, if consumers are patient, i.e., willing to wait, collaboration happens only when the end product is quite durable; for relatively perishable products the manufacturers sell their products separately. We also comment on how our results are affected by factors like manufacturers directly selling to end consumers or there being multiple opportunities to decide whether or not to use group selling strategy.

“Managing a Closed-Loop Supply System with Random Returns and a Cyclic Delivery Schedule”

Professor(s) Rick So 
Co-author(s): Candice Huyhn (Ph.D. Alumna) and Haresh Gurnani
Accepted at: European Journal of Operational Research, May 2016 

Motivated by an industry example, we develop a mathematical framework to address the inventory replenishment and capacity planning problem for a closed-loop supply system with random returns. The provider needs to deliver new or refurbished products to a group of clients under a fixed cyclic schedule, and also collects back a random portion of the used products in the subsequent delivery cycle for refurbishment. We first address the product replenishment strategy, in which only a random portion of the delivered products will be returned for refurbishment and the supplier must regularly purchase new products to replace the lost units. We then analyze the capacity decision problem where the provider uses his facility to refurbish the returned products for reuse, and the provider could incur extra refurbishing cost to handle the returned product at the end of each cycle due to insufficient capacity. Our models provide a simple decision support tool for making effective replenishment and capacity decisions in managing such a closed-loop supply system.

“The Value of Demand Forecast Updates in Managing Component Procurements for Assembly Systems”

Professor(s) Rick So 
Co-author(s): James Cao (Ph.D. Alumnus)
Accepted at: IIE Transactions, May 2016 

This paper examines the value of demand forecast updates in an assembly system where a single assembler must order components from independent suppliers with different lead-times. By staggering each ordering time, the assembler can utilize the latest market information, as it is developed, to form a better forecast over time. The updated forecast can subsequently be used to decide the following procurement decision. The objective of this research is to understand the specific operating environment under which demand forecast updates are most beneficial. Using a uniform demand adjustment model, we are able to derive analytical results that allow us to quantify the impact of demand forecast updates. We show that forecast updates can drastically improve profitability by reducing the mismatch cost caused by demand uncertainty.

“Thinking Styles Affect Reactions to Brand Crisis Apologies”

Professor(s) Robin Keller 
Co-author(s): Shijian Wang , Liangyan Wang (Ph.D. Alumna) and Jie Li
Accepted at: European Journal of Marketing, April 2016 

Purpose – This article examines how a person’s thinking style, specifically holistic versus analytic, and a firm’s crisis apology with the remedial solution framed in “why” (vs. “how”) terms can interactively impact consumers’ perceived efficacy of the firm to respond to the crisis and their impression or evaluation of the brand. Design/methodology/approach – Hypotheses were tested through three experimental studies involving 308 participants recruited in China. Participants answered survey questions investigating the interactive effects from consumers’ thinking style (culture as a proxy in study 1, measured in study 2 or primed in study 3) and a brand’s crisis apology with the remedial solution framed in “why” (vs. “how”) terms on consumers’ perceived efficacy and evaluation of the firm. Findings – The frame of the remedial solution resulting in a higher evaluation improvement depended on a consumer’s thinking style. For holistic thinkers, a “why” (vs. “how”) framed remedial solution resulted in a higher evaluation improvement; however, for analytic thinkers, a “how” (vs. “why”) framed remedial solution resulted in a higher evaluation improvement. Additionally, the results showed that a consumer’s perceived efficacy of the brand being able to successfully respond to the crisis mediated the interactive effects of the remedial solution framing and thinking styles on the evaluation improvement. Research limitations/implications – Different ways of framing the remedial solution in a firm’s apology will have different impacts on people with different thinking styles. Participants in studies 2 and 3 were recruited from samples on campus in China. Additionally, the automobile brand used in this study is fictional to avoid prior brand name or brand commitment impact. Practical implications – Our findings provide evidence that framing of the remedial solution can be leveraged as a tool to reduce negative impact resulting from a brand crisis. Specifically, our results suggest that companies may do well to employ a “why” framed remedial solution, particularly in cases where consumers are likely to process information holistically. Conversely, a “how” framed remedial solution may be effective in situations where consumers are likely to process information analytically. Originality/value – This research contributes to the literature, being among the first to consider how the remedial solution framing in a firm’s apology can enhance people’s evaluation of the brand and decrease the perceived negative impact resulting from the brand crisis.

“Trust Antecedents, Trust and Online Microsourcing Adoption: An Empirical Study from the Resource Perspective”

Professor(s) Robin Keller 
Co-author(s): Baozhou Lu, Tao Zhang, and Liangyan Wang (Ph.D. Alumna)
Accepted at: Decision Support Systems, April 2016 

The online microsourcing marketplace is a new form of outsourcing that is organized over online platforms for the performance of relatively small service tasks. Microsourcing offers a more flexible way to hire contract workers or to outsource. Prior research indicates the importance of individual-level trust when choosing providers in online sourcing marketplaces. We argue that institution-based trust is also crucial for online microsourcing adoptions. Drawing on a trust framework adapted from prior literature, this paper uncovers the trust-building mechanisms in online microsourcing marketplaces, as well as the marketplace-related attributes for online microsourcing adoption. The proposed research model is tested with a data set collected from the clients of a typical marketplace in China – The findings suggest that perceptions of resource-based attributes of a marketplace, together with the perceived effectiveness of its intermediary role, can help to build trust towards the marketplace, enhancing trust towards the community of providers and driving the intent to adopt online microsourcing. Thus, this paper confirms the roles of online marketplaces as both the resource pool and the transaction intermediary from the perspective of clients. Finally, this paper not only indicates the relevance of resource theories in understanding this new trend in outsourcing, but also suggests the importance of trusted relational governance in governing online microsourcing transactions.

“A Queueing Model for Managing Small Projects under Uncertainties”

Professor(s) Rick So and Ph.D. Student Jiaru Bai 
Co-author(s): Chris Tang
Accepted at: European Journal of Operation Research, March 2016 

We consider a situation in which a home improvement project contractor has a team of regular crew members who receive compensation even when they are idle. Because both projects arrivals and the completion time of each project are uncertain, the contractor needs to manage the utilization of his crews carefully. One common approach adopted by many home improvement contractors is to accept multiple projects to keep his crew members busy working on projects to generate positive cash flows. However, this approach has a major drawback because it causes "intentional" (or foreseeable) project delays. Intentional project delays can inflict explicit and implicit costs on the contractor when frustrating customers abandon their projects and/or file complaints or lawsuits. In this paper, we present a queueing model to capture uncertain customer (or project) arrivals and departures, along with the possibility of customer abandonment. Also, associated with each admission policy (i.e., the maximum number of projects that the contractor will accept), we model the underlying tradeoff between accepting too many projects (that can increase customer dissatisfaction) and accepting too few projects (that can reduce crew utilization). We examine this tradeoff analytically so as to determine the optimal admission policy and the optimal number of crew members. We further apply our model to analyze other issues including worker productivity and project pricing. Finally, our model can be extended to allow for multiple classes of projects with different types of crew members.

“Intention-Behavior Discrepancy of Foreign versus Domestic Brands in Emerging Markets: The Relevance of Consumer Prior Knowledge”

Professor(s) Robin Keller 
Co-author(s): Luping Sun, Xiaona Zheng, and Meng Su
Accepted at: Journal of International Marketing, November 2016 

Most research on the performance of foreign versus domestic brands in emerging markets examines measures of product evaluation or purchase intention. However, consumers intending to buy a product may switch to competing brands, displaying an intention-behavior discrepancy (IBD). Drawing upon literature on country associations and dual process theory, we examine the difference in IBD of foreign versus domestic brands in emerging markets and the moderating role of prior knowledge. We conducted an intention survey followed by a post-purchase survey in the Chinese automobile and smartphone industries. We found that foreign brands have an advantage on IBD relative to domestic brands, indicating that they have the dual advantage of higher evaluations and lower IBDs. Furthermore, foreign brands’ advantage on IBD is smaller for consumers with inaccurate prior knowledge, as they are more likely to systematically reprocess information and discount foreign brands’ favorable country associations. For these consumers, overestimating the product reduces foreign brands’ advantage to a smaller degree than underestimating it due to confirmation bias. These findings provide implications for brands in emerging markets.

“A Unified Framework for the Scheduling of Guaranteed Targeted Display Advertising under Reach and Frequency Requirements”

Professor(s) John Turner 
Co-author(s): Ali Hojjat (Ph.D. Alumnus), Suleyman Cetintas, Jian Yang
Accepted at: Operations Research, October 2016 

Motivated by recent trends in online advertising and advancements made by online publishers, we consider a new form of contract which allows advertisers to specify the number of unique individuals that should see their ad (reach), and the minimum number of times each individual should be exposed (frequency ). We develop an optimization framework that aims for minimal under-delivery and proper spread of each campaign over its targeted demographics. As well, we introduce a pattern-based delivery mechanism which allows us to integrate a variety of interesting features into a website’s ad allocation optimization problem which have not been possible before. For example, our approach allows publishers to implement any desired pacing of ads over time at the user level or control the number of competing brands seen by each individual. We develop a two-phase algorithm that employs column generation in a hierarchical scheme with three parallelizable components. Numerical tests with real industry data show that our algorithm produces high-quality solutions and has promising run-time and scalability. Several extensions of the model are presented, e.g., to account for multiple ad positions on the webpage, or randomness in the website visitors’ arrival process.


“Impact of an ‘Online-to-Store’ Channel on Demand Allocation, Online Pricing and Profitability”

Professor(s): Shuya Yin
Co-authors: James Cao (PhD Alumnus) and Rick So
Accepted at: European Journal of Operational Research, September 2015
The growth of e-commerce in the past decade has opened the door to a new and exciting opportunity for retailers to better target different segments of the customer population. In this paper, we develop an analytical framework to study the impact of an “online-to-store” channel on the demand allocations and profitability of a retailer who sells products to customers through multiple distribution channels. This new channel can help the retailer tap new customer segments and generate additional demand, but may also hurt the retailer by cannibalizing existing channels and increasing operating costs. The analytical model allows us to evaluate these fundamental tradeoffs and provide useful managerial insights regarding the specific product and market characteristics that are most conducive for increasing profitability. Our analysis provides some simple conditions under which adding an online-to-store channel would lead to higher profits for products that are only available online. If the product is also available in-store, the analysis becomes more complex. In this case, we performed numerical experiments to generate insights on when the OS channel should be used. Our results imply that the retailer needs to carefully select the set of products to be offered through the online-to-store channel.

“Joint Selling of Complementary Components under Brand and Retail Competition”

Professor(s): Shuya Yin
Co-authors: Yuhong He (PhD Alumna)
Accepted at: Manufacturing and Service Operations Management, February 2015
Suppliers of complementary goods often package their items together when selling to downstream retailers. One motivation behind this behavior is to reduce double marginalization through coordinated pricing so that system efficiency is improved and individual members can also benefit. The objective of this paper is to understand how competition in supply chains would impact such joint selling partnerships among complementary suppliers. We first model competition at the supply level, which is generated from the existence of multiple partially substitutable brands (or suppliers) for a particular component. We then extend the analysis to a model which also involves retail competition that is caused by decentralization among retailers who assemble suppliers’ components into final products and sell to customers. The analysis of a model with two complementary components, one of which has multiple brands, indicates that the supply level competition discourages joint selling of complementary goods. That is, when competing brands become more alike (or substitutable), complementary suppliers act more independently in pricing and selling their items. However, retail competition leads to an opposite effect: Competition among retailers would actually encourage complementary suppliers to package their goods together and act jointly.

“Efficient Implementation of Collective Extended Producer Responsibility Legislation”

Professor(s) Luyi Gui  
Co-author(s): Atalay Atasu, Ozlem Ergun and Beril Toktay
Accepted at: Management Science, January 2015

Extended Producer Responsibility (EPR) is a policy tool that holds producers financially responsible for the post-use collection, recycling and disposal of their products. Many EPR implementations are collective – a large collection and recycling network (CRN) handles multiple producers’ products in order to benefit from scale and scope economies. The total cost is then allocated to producers based on metrics such as their return shares by weight. Such weight-based proportional allocation mechanisms are criticized in practice for not taking into account the heterogeneity in the costs imposed by different producers’ products. The consequence is cost allocations that impose higher costs on certain producer groups than they can achieve independently, which may lead some producers to break away from collective systems, resulting in fragmented systems with higher total cost. Yet cost efficiency is a key legislative and producer concern. To address this concern, this paper develops cost allocation mechanisms that induce participation in collective systems and maximize cost efficiency. The cost allocation mechanisms we propose consist of adjustments to the widely used return share method, and include the weighing of return shares based on processing costs and the rewarding of capacity contributions to collective systems. Researchers validate their theoretical results using Washington state EPR implementation data and provide insights as to how these mechanisms can be implemented in practice.


“Simultaneous Location of Trauma Centers and Helicopters for Emergency Medical Service Planning”

Professor(s) John Turner 
Co-author(s): Soo-Haeng Cho, Hoon Jang and Taesik Lee
Accepted at: Journal of Operations Research, May 2014

This paper studies the problem of simultaneously locating trauma centers and helicopters. The standard approach to locating helicopters involves the use of helicopter busy fractions to model the random availability of helicopters. However, busy fractions cannot be estimated a priority in our problem because the demand for each helicopter cannot be determined until the trauma center locations are selected. To overcome this challenge, we endogenize the computation of busy fractions within an optimization problem. The resulting formulation has non-convex bilinear terms in the objective, for which we develop an integrated method that iteratively solves a sequence of problem relaxations and restrictions. Specifically, we devise a specialized algorithm, called the Shifting Quadratic Envelopes algorithm that 1) generates tighter outer-approximations than linear McCormick envelopes, and 2) outperforms a Benders-like cut generation scheme. We apply our integrated method to the design of a nationwide trauma care system in Korea. By running a trace-based simulation on a full year of patient data, we find that the solutions generated by our model outperform several benchmark heuristics by up to 20%, as measured by an industry-standard metric: the proportion of patients successfully transported to a care facility within one hour. Our results have helped the Korean government to plan its nationwide trauma care system. More generally, our method can be applied to a class of optimization problems that aim to find the locations of both fixed and mobile servers when service needs to be carried out within a certain time threshold.

“Approximate and Exact Formulas for the (Q r) Inventory Model”

Professor(s) Carlton Scott 
Co-author(s): Zvi Drezner
Accepted at: Journal of Industrial and Management Optimization, January 2014

In this paper, new results are derived for the (Q, r) stochastic inventory model. We derive approximate formulas for the particular case of an exponential demand distribution. The approximate solution is within 0.29% of the optimal value. We also derive simple formulas for a Poisson demand distribution. The original expression consists of double summation. We simplify the formula and are able to calculate the exact value of the objective function in O(1) time with no need for any summations.