Research

(Contact: Vasiliki Kostami)

For the most popular rides in Disneyland, visitors have a choice. They can either wait in a line or obtain a FASTPASS. The FASTPASS specifies a time at which the visitor can take the ride, making it possible for the customer to visit other parts of the park instead of waiting in a line. The FASTPASS also benefits Disneyland because FASTPASS ("offline") customers may spend money on food or entertainment while they wander around the park. Hence, the offline queue benefits both Disneyland and its customers. In practice, we observe many different implementations of the offline idea. For example, many restaurants give their patrons wireless devices that signal when a table becomes available. In call centres, the idea of giving customers a call-back option has been studied. Cruises and all-inclusive resorts often allow customers to wander while they wait for space to become available in a desired activity. Student health-care clinics may offer noncritical drop-in patients who face a long delay in seeing a doctor or nurse the option of returning later in the day.

In some settings, such as a restaurant, where the server is able to communicate with customers, incorrect waiting time estimates can be corrected. However, in other settings, such as Disneyland or any other amusement park, where communication with offline customers is prohibitively difficult, accurately estimating waiting times is essential. Most amusement parks have hundreds of customers arriving per hour for popular rides that last only minutes. Furthermore, almost every departing train has customers in every available seat. To operate such a system, the service provider must:  1. make an upfront static decision on how to allocate capacity between the inline and the offline queue, and  2. provide arriving customers with waiting time estimates in real time for both the inline and offline queue, when there are costs associated with customer abandonments and inline queueing and an assumed revenue per customer in the offline queue. The upfront static capacity allocation decision is motivated by the amusement park setting, in which seats on each ride are allocated in predetermined proportions to the inline and the offline queue. We further dynamically derive wait time estimates that depend on that allocation decision. The difficulty inherent in making such estimates accurately is complicated by the presence of customers in the offline queue who may abandon, and it is not a priori clear that a simple scheme can work. This work has been published in Manufacturing & Service Operations Management (joint work with A.R. Ward).

Long lines in amusement parks

(Contact: Nitin Bakshi)

Countries such as the United States perceive a threat from the possible use of maritime containers by terrorists to smuggle "dirty bombs" or even nuclear material. To mitigate this threat, the containers can be inspected at the ports of origin or entry using sophisticated, but time consuming, scanning devices. Although security can be enhanced by more intensive scanning, it can be detrimental to members of the trading fraternity through the resulting congestion and increased lead times. The goal of this research effort was to identify sensible inspection and security policies that minimize adverse impact on the maritime supply chain. Its findings have been presented to staff of the Homeland Security committees of the U.S. House and Senate. Articles citing this work have appeared in the Economist, Business Strategy Review and numerous other practitioner-oriented publications, and this research has resulted in two research papers published in the journal Management Science.
Inspecting containers requires a trade-off between security and congestion

(Contact: Victor DeMiguel)

The Nobel laureate Harry Markowitz showed that an investor who cares only about the mean and variance of portfolio returns should hold a portfolio on the efficient frontier. To implement these portfolios in practice, one needs to estimate the means and covariances of asset returns. Traditionally, the sample means and covariances have been used for this purpose. But due to estimation error, the portfolios that rely on the sample estimates typically perform poorly out of sample. For instance, in the paper "Optimal versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy?'', Review of Financial Studies (2009), we evaluate the out-of-sample performance of the mean-variance model and its various extensions relative to the benchmark strategy of investing a fraction 1/N of wealth in each of the N assets available. Of the fourteen models of optimal portfolio choice that we evaluate across seven empirical datasets, we find that none is consistently better than the 1/N rule in terms of Sharpe ratio, certainty-equivalent return, or turnover. This finding indicates that, out of sample, the gain from optimal diversification is more than offset by estimation error.

The main insight from the 1/N paper is that the mean-variance portfolio and its extensions perform poorly out of sample---indeed they fail to outperform the simple 1/N rule. To address this issue, in the paper "Improving Performance By Constraining Portfolio Norms: A Generalized Approach to Portfolio Optimization'', Management Science (2009), we provide a general framework for identifying portfolios that relies on solving the traditional minimum-variance problem but subject to the additional constraint that the norm of the portfolio-weight vector be smaller than a given threshold. We show that our unifying framework nests as special cases several portfolio selection approaches proposed in the literature. We also use our general framework to propose several new portfolio strategies. For these new portfolios, we provide a moment-shrinkage interpretation and also a Bayesian interpretation where the investor has a prior belief on portfolio weights rather than on moments of asset returns. Finally, we compare empirically (in terms of portfolio variance, Sharpe ratio, and turnover), the out-of-sample performance of the new portfolios we propose to ten strategies in the existing literature across five datasets. We find that the norm-constrained portfolios we propose often have a lower variance and a higher Sharpe ratio than several benchmark portfolios from the literature.

The 1/N paper was awarded the "Best Paper Prize" from the Institute of Quantitative Investment Research, and it has also been quoted among the top 10 "Hot Papers in Economics and Business" by the Times Educational Supplement. Portfolio selection is a very active area of research where Management Scientists can contribute by bringing methodologies from Optimization, Statistics, and Applied Probability to design portfolios that perform well in practice.

(Contact: Jérémie Gallien)

Zara's supply chain consists of two primary warehouses located in Spain which periodically receive shipments of finished clothes from suppliers, and ship replenishment inventory directly to every Zara store in the world twice a week. A key associated challenge is to determine the exact number of units of each size (up to 8) of each article (up to 3,000 at any time) that should be included in each shipment to each store (more than 1,500) -  this is the bloodstream of Zara's merchandise to its primary sales channel. Until 2007, the process used by Zara for determining those shipments involved the examination by a large team of warehouse employees of shipment requests sent by every store, which presented an opportunity to improve both scalability and revenues.

As part of a collaborative research project with Zara, we developed an alternative decision process relying on novel forecasting algorithms, stochastic analysis and a large-scale mixed-integer programming model. Its implementation presented many technical difficulties, including the need to capture forecast uncertainty and store-level inventory policies, the live integration of a complex mathematical model with many large databases, and the development of the software and hardware infrastructure necessary to solve thousands of optimization problems in just a couple of hours every day. Deployment was completed in 2008 however, and a controlled field implementation experiment demonstrated that the new system increased revenues during each selling season by 3-4%, amounting to about $50M of additional net income for Zara in 2009. Descriptions of this work were published in the journals Operations Research and Interfaces, it was referenced in numerous general press articles, and this project was a laureate in the 2009 Franz Edelman Competition of INFORMS (joint work with F. Caro, M. Díaz, J. García, J. M. Corredoira, M. Montes, J. A. Ramos and J. Correa)

Zara's Distribution Control Centre

Distribution-related communications with a Zara store

(Contact: Song Alex Yang)

As an integrated part of a supply contract, trade credit is a type of credit sellers extend to buyers, allowing the latter to purchase goods from the former without immediate payment. Empirical evidence shows that trade credit is an extremely important source of external financing.  According to Financial Times, in 2007, 90% of world merchandize trade is financed by trade credit, with a value of about 25 trillion USD. Trade credit has intrinsic connections with supply chain contracting and inventory management, two very important areas in operations management. The goal of this research is to understand how trade credit mitigates inefficiencies in supply chain, what the optimal trade credit contract is, how firms finance their production activities and inventory when trade credit is offered, and whether there are other financing contracts that could over-perform trade credit. The results show that when offering trade credit, the supplier balances its impact on operational profit and costs of financial distress. Facing a trade credit contract, the retailer finances inventory using a portfolio of cash, trade credit, and short-term debt, where the structure of portfolio depends on the retailer's financing needs and bargaining power. Using a sample of firm-level data, we find that the inventory financing pattern our model predicts exists in a wide range of firms.

(Contact: Nicos Savva )

In recent years hospitals have been faced with ever-increasing pressure from governments as well as managed care organizations to cut costs. Since personnel accounts for a very large portion of expenses, the response in many instances has been reductions of medical staff leading to an increase in staff workloads. Workloads have been further increased by shorter hospital lengths-of-stay (LOS) and increasing use of outpatient procedures, resulting in sicker hospitalized patients who require more care. In two related papers we investigate the impact of this workload increase on different aspects of hospital performance by combining both empirical and analytical (optimization) methods.

The problem of determining nurse staffing levels in a hospital environment is a complex task due to variable patient census levels and uncertain service capacity caused by nurse absenteeism.  According to the US Bureau of Labor Statistics, in 2008 they exhibited 12.5 incidents of illness or occupational injury per 100 full-time employees, second only to construction workers, as well as the highest number of cases involving days away from work. In the paper "Nursevendor Problem": Personnel Staffing in the Presence of Endogenous Absenteeism we combine an empirical investigation of the factors affecting nurse absenteeism rates with an analytical treatment of nurse staffing decisions.  Using data from the emergency department of a large urban hospital, we find that absenteeism rates are consistent with nurses exhibiting an aversion to higher levels of anticipated workload. Using our empirical findings we analyse a single-period nurse staffing problem considering both the case of constant absenteeism rate (exogenous absenteeism) as well as an absenteeism rate which is a function of the number of scheduled nurses (endogenous absenteeism). We provide characterizations of the optimal staffing levels in both situations and show that the failure to incorporate absenteeism as an endogenous effect results in understaffing.

Turning to physicians, in the paper "Physician workload and hospital reimbursement", we utilise a detailed data set from the trauma department of a major urban hospital to show that the more discharge summaries a physician compiles in a given day, the less likely they are to provide all the necessary documentation for their patients to be classified as high severity for reimbursement purposes. In addition to having implications for follow-up care, incomplete discharge summaries have severe revenue implications for the hospital. Patients classified as high severity result, on average, in a 47.8% higher reimbursement payment. We estimate that workload induced incorrect coding deprives the trauma department 1.1% of annual revenue. This effect persists after we control for a number of systematic differences in patient characteristics, condition and time of discharge. Furthermore, we show that it is unlikely to be caused by selection bias or endogeneity in either discharge timing or allocation of discharges to physicians. This observation suggests that hospitals need to redesign their discharge process to mitigate the impact of workload.