Papers by Alan Scheller-wolf
arXiv (Cornell University), Jul 11, 2022
Motivated by the experiences of a healthcare service provider during the Covid-19 pandemic, we ai... more Motivated by the experiences of a healthcare service provider during the Covid-19 pandemic, we aim to study the decisions of a provider that operates both an Emergency Department (ED) and a medical Clinic. Patients contact the provider through a phone call or may present directly at the ED; patients can be COVID (suspected/confirmed) or non-COVID, and have different severities. Depending on severity, patients who contact the provider may be directed to the ED (to be seen in a few hours), be offered an appointment at the Clinic (to be seen in a few days), or be treated via phone or telemedicine, avoiding a visit to a facility. All patients make joining decisions based on comparing their own risk perceptions versus their anticipated benefits: They then choose to enter a facility only if it is beneficial enough. Also, after initial contact, their severities may evolve, which may change their decision. The hospital system's objective is to allocate service capacity across facilities so as to minimize costs from patients deaths or defections. We model the system using a fluid approximation over multiple periods, possibly with different demand profiles. While the feasible space for this problem can be extremely complex, it is amenable to decomposition into different sub-regions that can be analyzed individually; the global optimal solution can be reached via provably parsimonious computational methods over a single period and over multiple periods with different demand rates. Our analytical and computational results indicate that endogeneity results in non-trivial and non-intuitive capacity allocations that do not always prioritize high severity patients, for both single and multi-period settings.
ACM SIGMETRICS Performance Evaluation Review, 2017
We consider optimal job scheduling where each job consists of multiple tasks, each of unknown dur... more We consider optimal job scheduling where each job consists of multiple tasks, each of unknown duration, with precedence constraints between tasks. A job is not considered complete until all of its tasks are complete. Traditional heuristics, such as favoring the job of shortest expected remaining processing time, are suboptimal in this setting. Furthermore, even if we know which job to run, it is not obvious which task within that job to serve. In this paper, we characterize the optimal policy for a class of such scheduling problems and show that the policy is simple to compute.
Performance evaluation review, Jun 12, 2018
We consider an extremely broad class of M/G/1 scheduling policies called SOAP: Schedule Ordered b... more We consider an extremely broad class of M/G/1 scheduling policies called SOAP: Schedule Ordered by Age-based Priority. The SOAP policies include almost all scheduling policies in the literature as well as an infinite number of variants which have never been analyzed, or maybe not even conceived. SOAP policies range from classic policies, like first-come, first-serve (FCFS), foregroundbackground (FB), class-based priority, and shortest remaining processing time (SRPT); to much more complicated scheduling rules, such as the famously complex Gittins index policy and other policies in which a job's priority changes arbitrarily with its age. While the response time of policies in the former category is well understood, policies in the latter category have resisted response time analysis. We present a universal analysis of all SOAP policies, deriving the mean and Laplace-Stieltjes transform of response time. The full version of this work appears in POMACS [6]. CCS CONCEPTS • General and reference → Performance; • Mathematics of computing → Queueing theory; • Software and its engineering → Scheduling; • Computing methodologies → Model development and analysis; • Theory of computation → Scheduling algorithms; KEYWORDS M/G/1; exact response time analysis; Gittins index; shortest expected remaining processing time (SERPT)
Queueing Systems, May 25, 2022
Social Science Research Network, 2020
We consider the rostering decisions of a long-term care facility that assigns a set of interchang... more We consider the rostering decisions of a long-term care facility that assigns a set of interchangeable caregivers working a particular shift to units, and evaluate whether part-time or full-time workers should have higher priority to work in their “home” units. The facility’s objective is to minimize the monthly inconsistency level – i.e., a widely promoted quality metric representing the number of different caregivers working in each unit. We introduce simple rostering heuristics that prioritize part-time or full-time workers, and present a stochastic model of the repeated rostering problem to analytically compare their performance. This analysis supports prioritizing the assignment of part-time workers to their home units, while flexibly assigning full-time workers to minimize the inconsistency level. Using data from over 15,000 shifts worked by certified nursing assistants at three nursing homes, we compare the actual schedules to the consistency-maximizing schedules using hindsight optimization and test the performance of our rostering heuristics via trace-based simulation. This reinforces the superiority of prioritizing part-time workers, observing reductions in the inconsistency level between 20% and 30% in trace-based simulations of historical schedules. We also establish an upper bound for a threshold on the time horizon above which a policy giving assignment priority to part-time workers outperforms one giving priority to full-time workers.
Comparing with the traditional retailers, online retailers are playing quite important roles in t... more Comparing with the traditional retailers, online retailers are playing quite important roles in the contemporary retailing channels. They offer more options for their customers, like flexible delivery, pricing, etc. In this paper, we consider an inventory system where customers may have different priorities under the retailer's capacity. A single supplier who must invest in capacity to manufacturer and sell products to buyers having different priorities. The buyers can place pre-orders before their demand is observed, and can also issue additional orders upon observing demand information. Since the supplier guarantees delivery of pre-ordered goods (these are not constrained by the supplier's capacity), buyers with lower priorities may consider pre-ordering in order to secure inventory. We derive optimal policies for the supplier and buyers. We show surprisingly that it is optimal for the supplier to set the pre-order price so high that pre-ordering will not be used much even though pre-ordering should be of benefit to the supplier due to risk sharing. We also show that the supplier can make a pricing decision using an aggregate model.
Manufacturing & Service Operations Management, 2022
Utility regulators are grappling to devise compensation schemes for customers who sell rooftop so... more Utility regulators are grappling to devise compensation schemes for customers who sell rooftop solar generation back to the grid, balancing environmental interests and the financial interests of utilities, solar system installers, and retail customers. This is difficult: Regulatory changes made in Nevada in 2015 to protect Nevada's utility induced SolarCity, the market leader in solar systems, to suspend local operations. We show that the choice of tariff structure is crucial to achieving socially desirable objectives. (2) Academic/Practical Relevance: It is important for regulators to understand how tariff structure interacts with social objectives. This has implications for consumers, regulators and industry. (3) Methodology: We use a sequential game to analyze the regulator's social welfare maximization problem in a market with a regulated utility, an unregulated, price-setting, profit-maximizing solar system installer, and customers who endogenously determine whether to adopt solar or not, based on utility tariffs, solar prices and their heterogeneous usage profiles and generation potentials. (4) Results: We illustrate that the effectiveness of tariff structures is not governed simply by the number of free tariff parameters, but by the functions these parameters serve. In particular, an effective tariff must discriminate among customer usage tiers and between customers with and without rooftop solar to achieve socially desirable outcomes. We present a tariff structure with these two characteristics and show how it can be implemented as a simple buy-all, sell-all tariff while retaining its favorable properties. We illustrate our findings numerically using data from Nevada and New Mexico, two states grappling with this issue. (5) Managerial Implications: Many utilities in the U.S. operate tariff structures that are missing at least one of the two identified features. Regulators must overhaul these tariff structures to adequately safeguard all stake-holders.
Performance evaluation review, Oct 11, 2017
arXiv (Cornell University), May 7, 2020
We study a single station two-stage reneging queue with Poisson arrivals, exponential services, a... more We study a single station two-stage reneging queue with Poisson arrivals, exponential services, and two levels of exponential reneging behaviors, extending the popular Erlang A model that assumes a constant reneging rate. We derive approximate analytical formulas representing performance measures for our twostage queue following the Markov chain decomposition approach. Our formulas not only give accurate results spanning the heavy-traffic to the light-traffic regimes, but also provide insight into capacity decisions.
Performance evaluation review, Sep 1, 2005
A common problem in multiserver systems is deciding how to allocate resources among jobs so as to... more A common problem in multiserver systems is deciding how to allocate resources among jobs so as to minimize mean response time. Since good parameter settings typically depend on environmental conditions such as system loads, an allocation policy that is optimal in one environment may provide poor performance when the environment changes, or when the prediction of the environment is wrong. We say that such a policy is not robust. In this paper, we analytically compare the robustness of several threshold-based allocation policies, in a dual server beneficiary-donor model. We introduce two types of robustness: static robustness , which measures robustness against mis-estimation of the true load, and dynamic robustness , which measures robustness against fluctuations in the load. We find that policies employing multiple thresholds offer significant benefit over single threshold policies with respect to static robustness. Yet they surprisingly offer much less benefit with respect to dynamic robustness.
Production and Operations Management, Nov 26, 2018
We investigate the management of a merchant wind energy farm co-located with a grid-level storage... more We investigate the management of a merchant wind energy farm co-located with a grid-level storage facility and connected to a market through a transmission line. We formulate this problem as a Markov decision process (MDP) with stochastic wind speed and electricity prices. Consistent with most deregulated electricity markets, our model allows these prices to be negative. As this feature makes it difficult to characterize any optimal policy of our MDP, we show the optimality of a stage-and partialstate-dependent-threshold policy when prices can only be positive. We extend this structure when prices can also be negative to develop heuristic one (H1) that approximately solves a stochastic dynamic program. We then simplify H1 to obtain heuristic two (H2) that relies on a price-dependent-threshold policy and derivative-free deterministic optimization embedded within a Monte Carlo simulation of the random processes of our MDP. We conduct an extensive and data-calibrated numerical study to assess the performance of these heuristics and variants of known ones against the optimal policy, as well as to quantify the effect of negative prices on the value added by and environmental benefit of storage. We find that (i) H1 computes an optimal policy and on average is about 17 times faster to execute than directly obtaining an optimal policy; (ii) H2 has a near optimal policy (with a 2.86% average optimality gap), exhibits a two orders of magnitude average speed advantage over H1, and outperforms the remaining considered heuristics; (iii) storage brings in more value but its environmental benefit falls as negative electricity prices occur more frequently in our model.
Manufacturing & Service Operations Management, Mar 1, 2023
Problem definition: We consider the rostering decisions—that is, the assignment of workers schedu... more Problem definition: We consider the rostering decisions—that is, the assignment of workers scheduled for a shift to units—of a long-term care facility. The facility’s objective is to minimize the monthly inconsistency level, a widely promoted quality metric representing the number of different caregivers working in each unit over one month. Methodology/results: We introduce simple rostering heuristics that prioritize either part-time or full-time workers and present a stochastic model of the repeated rostering problem to compare the performance of different strategies analytically. Our analysis shows that in order to minimize the inconsistency level, part-time workers should receive higher priority than full-time workers for assignment to their home units. We also establish an analytical upper bound for a threshold on the time horizon above which a policy giving assignment priority to part-time workers is guaranteed to outperform one giving priority to full-time workers. Using data from more than 15,000 shifts worked by nursing assistants at three nursing homes, we compare the actual rosters to the hindsight optimal consistency-maximizing schedules, demonstrating a significant opportunity for improvement. We then compare the performance of our rostering heuristics via trace-based simulation of the historical schedules. This reinforces the superiority of prioritizing part-time workers, yielding reductions in the inconsistency level between 20% and 30% compared with the historical rosters. Managerial implications: Contrary to popular guidance, our results show that managers should focus on part-time workers and assign them as consistently as possible. Even if some full-time workers are always assigned to their home units (because of preferences or work rules), assignment flexibility among the remaining full-time workers still enables significant improvements in the consistency of care. This flexibility among full-time workers helps because their higher work frequency tends to make a reassignment away from their home unit contribute less to inconsistency, because they are able to work multiple shifts in these nonhome units. Supplemental Material: The e-companion is available at https://doi.org/10.1287/msom.2022.1174 .
arXiv (Cornell University), Dec 3, 2017
We consider an extremely broad class of M/G/1 scheduling policies called SOAP: Schedule Ordered b... more We consider an extremely broad class of M/G/1 scheduling policies called SOAP: Schedule Ordered by Agebased Priority. The SOAP policies include almost all scheduling policies in the literature as well as an infinite number of variants which have never been analyzed, or maybe not even conceived. SOAP policies range from classic policies, like first-come, first-serve (FCFS), foreground-background (FB), class-based priority, and shortest remaining processing time (SRPT); to much more complicated scheduling rules, such as the famously complex Gittins index policy and other policies in which a job's priority changes arbitrarily with its age. While the response time of policies in the former category is well understood, policies in the latter category have resisted response time analysis. We present a universal analysis of all SOAP policies, deriving the mean and Laplace-Stieltjes transform of response time. CCS Concepts: • General and reference → Performance; • Mathematics of computing → Queueing theory; • Software and its engineering → Scheduling; • Computing methodologies → Model development and analysis; • Theory of computation → Scheduling algorithms;
Manufacturing & Service Operations Management, Jul 1, 2015
Merchants operations involves valuing and hedging the cash flows of commodity and energy conversi... more Merchants operations involves valuing and hedging the cash flows of commodity and energy conversion assets as real options based on stochastic models that inevitably embed model error. In this paper we quantify how empirically calibrated model errors about the futures price term structure affect the valuation and hedging of commodity storage assets, specifically the storage of natural gas, an important energy source. We also explore ways to mitigate the impact of these errors. Our analysis demonstrates the differential impact of term structure model error on natural gas storage valuation versus hedging. We also propose an effective approach to deal with the negative effect of such model error on factor hedging, a specific hedging approach. More generally, our work suggests managerial principles for option valuation and hedging in the presence of term structure model error. These principles should have relevance for the merchant management of other commodity conversion assets and for the management of financial options that also depend on term structure dynamics.
Management Science, Mar 1, 2016
Electricity cannot yet be stored on a large scale, but technological advances leading to cheaper ... more Electricity cannot yet be stored on a large scale, but technological advances leading to cheaper and more efficient industrial batteries make grid-level storage of electricity surpluses a natural choice. Because electricity prices can be negative, it is unclear how the presence of negative prices might affect the storage policy structure known to be optimal when prices are only non-negative, or even how important it is to consider negative prices when managing an industrial battery. For fast storage (a storage facility that can both be fully emptied and filled up in one decision period), we show analytically that negative prices can substantially alter the optimal storage policy structure, e.g., all else being equal, it can be optimal to empty an almost empty storage facility and fill up an almost full one. For more typical slow grid-level electricity storage, we numerically establish that ignoring negative prices could result in a considerable loss of value when negative prices occur more than 5% of the time. Negative prices raise another possibility: rather than storing surpluses, a merchant might buy negatively priced electricity surpluses and dispose of them, e.g., using load banks. We find that the value of such disposal strategy is substantial, e.g., about 118 $/kW-year when negative prices occur 10% of the time, but smaller than that of the storage strategy, e.g., about 391 $/kW-year using a typical battery. However, devices for disposal are much cheaper than those for storage. Our results thus have ramifications for merchants as well as policy makers.
arXiv (Cornell University), Dec 5, 2021
The Erlang A model-an M/M/s queue with exponential abandonment-is often used to represent a servi... more The Erlang A model-an M/M/s queue with exponential abandonment-is often used to represent a service system with impatient customers. For this system, the popular square-root staffing rule determines the necessary staffing level to achieve the desirable QED (quality-and-efficiency-driven) service regime; however, the rule also implies that properties of large systems are highly sensitive to parameters. We reveal that the origin of this high sensitivity is due to the operation of large systems at a point of singularity in a phase diagram of service regimes. We can avoid this singularity by implementing a congestion-based control (CBC) scheme-a scheme that allows the system to change its arrival and service rates under congestion. We analyze a modified Erlang A model under the CBC scheme using a Markov chain decomposition method, derive non-asymptotic and asymptotic normal representations of performance indicators, and confirm that the CBC scheme makes large systems less sensitive than the original Erlang A model.
We consider the scenario of two processors, each serving its own workload, where one of the proce... more We consider the scenario of two processors, each serving its own workload, where one of the processors (known as the "donor") can help the other processor (known as the "beneficiary") with its jobs, during times when the donor processor is idle. That is the beneficiary processor "steals idle cycles" from the donor processor. We assume that both donor jobs and beneficiary jobs may have generally-distributed service requirements. We assume that there is a switching cost required for the donor processor to start working on the beneficiary jobs, as well as a switching cost required for the donor processor to return to working on its own jobs. We also allow for threshold constraints, whereby the donor processor only initiates helping the beneficiary if both the donor is idle and the number of jobs at the beneficiary exceeds a certain threshold. We analyze the mean response time for the donor and beneficiary processors. Our analysis is approximate, but can be made as accurate as desired, and is validated via simulation. Results of the analysis illuminate several interesting principles with respect to the general benefits of cycle stealing and the design of cycle stealing policies.
European Journal of Operational Research, Aug 1, 2016
The problem is Case II of Point 4 in the proof of Lemma 4.1. Specifically, one of the parameters ... more The problem is Case II of Point 4 in the proof of Lemma 4.1. Specifically, one of the parameters used in the proof, b , could be negative, thus rendering an appeal to strong CK-convexity invalid. The proof may be corrected as follows: Proof. Case II: H(y + z) = G (y + z) , H(y − a − b) = ˜ G (y − a − b) = K + G (y − a − b) for some b − C ≤ b < b.
Social Science Research Network, 2016
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Papers by Alan Scheller-wolf