Denis Sauré

Time-of-Use pricing policies for offering Cloud Computing as a service

We study a reservation system with finite computing resources over an infinite horizon, where a set of incumbent users submit reservation requests for computing resources ahead in time. Computing resources may be purchased in exchange for tokens. We use the Multinomial Logit (MNL) framework to model customer substitution behavior. Given user requests, the objective is to maximize system performance, defined as the proportion of customers that obtain their preferred time slot, by adjusting resource prices in tokens per unit of time and per computing resource. We consider a class of pricing policies called Time-of-Use (ToU), and propose a simple and intuitive algorithm that is provably optimal for an approximation to our formulated problem. Our proposed solution has the appealing property of flattening demand over the horizon. We evaluate the performance of our approach numerically. For the set of problem instances that we consider, the optimal ToU policy outperforms single pricing strategies by 3–8 % for Customer Satisfaction, on average. We discuss the implementation of our proposed approach for Cloud Computing being developed by IBM at the King Abdullah University of Science and Technology (KAUST).

Dynamic Pricing Strategies in the Presence of Demand Shifts

Many factors introduce the prospect of changes in the demand environment that a firm faces, with the specifics of such changes not necessarily known in advance. If and when realized, such changes affect the delicate balance between demand and supply and thus current prices should account for these future possibilities. We study the dynamic pricing problem of a retailer facing the prospect of a change in the demand function during a finite selling season with no inventory replenishment opportunity. In particular, the time of the change and the postchange demand function are unknown upfront, and we focus on the fundamental trade-off between collecting revenues from current demand and doing so for postchange demand, with the capacity constraint introducing the main tension. We develop a formulation that allows for isolating the role of dynamic pricing in balancing inventory consumption throughout the horizon. We establish that, in many settings, optimal pricing policies follow a monotone path up to the change in demand. We show how one may compare upfront the attractiveness of pre- and postchange demand conditions and how such a comparison depends on the problem primitives. We further analyze the impact of the model inputs on the optimal policy and its structure, ranging from the impact of model parameter changes to the impact of different representations of uncertainty about future demand.

Sequential Shortest Path Interdiction with Incomplete Information

We study sequential interdiction when the interdictor has incomplete initial information about the network and the evader has complete knowledge of the network, including its structure and arc costs. In each time period, the interdictor blocks at most k arcs from the network observed up to that period, after which the evader travels along a shortest path between two (fixed) nodes in the interdicted network. By observing the evader’s actions, the interdictor learns about the network structure and arc costs and adjusts its actions to maximize the cumulative cost incurred by the evader. A salient feature of our work is that the feedback in each period is deterministic and adversarial. In addition to studying the regret minimization problem, we also discuss time stability of a policy, which is the number of time periods until the interdictor’s actions match those of an oracle interdictor with prior knowledge of the network. We propose a class of simple interdiction policies that have a finite regret and detect when the instantaneous regret reaches zero in real time. More importantly, we establish that this class of policies belongs to the set of efficient policies.

The Price of Nonabandonment: HIV in Resource-Limited Settings

The global fight against HIV/AIDS is hindered by a lack of drugs in the developing world. When patients in these countries initiate treatment, they typically remain on it until death; thus, policy makers and physicians follow nonabandonment policies. However, treated patients develop resistance to treatment, so in many cases untreated patients might benefit more from the drugs. In this paper we quantify the opportunity cost associated with restricting attention to nonabandonment policies. For this, we use an approximate dynamic programming framework to bound the benefit from allowing premature treatment termination. Our results indicate that in sub-Saharan Africa, the price associated with restricting attention to nonabandonment policies lies between 4.4% and 8.1% of the total treatment benefit. We also derive superior treatment allocation policies, which shed light on the role behavior and health progression play in prioritizing treatment initiation and termination.

Should Expectations about the Rate of New Antiretroviral Drug Development Impact the Timing of HIV Treatment Initiation and Expectations about Treatment Benefits

Background Many analyses of HIV treatment decisions assume a fixed formulary of HIV drugs. However, new drugs are approved nearly twice a year, and the rate of availability of new drugs may affect treatment decisions, particularly when to initiate antiretroviral therapy (ART). Objectives To determine the impact of considering the availability of new drugs on the optimal initiation criteria for ART and outcomes in patients with HIV/AIDS. Methods We enhanced a previously described simulation model of the optimal time to initiate ART to incorporate the rate of availability of new antiviral drugs. We assumed that the future rate of availability of new drugs would be similar to the past rate of availability of new drugs, and we estimated the past rate by fitting a statistical model to actual HIV drug approval data from 1982–2010. We then tested whether or not the future availability of new drugs affected the model-predicted optimal time to initiate ART based on clinical outcomes, considering treatment initiation thresholds of 200, 350, and 500 cells/mm3. We also quantified the impact of the future availability of new drugs on life expectancy (LE) and quality-adjusted life expectancy (QALE). Results In base case analysis, considering the availability of new drugs raised the optimal starting CD4 threshold for most patients to 500 cells/mm3. The predicted gains in outcomes due to availability of pipeline drugs were generally small (less than 1%), but for young patients with a high viral load could add as much as a 4.9% (1.73 years) increase in LE and a 8% (2.43 QALY) increase in QALE, because these patients were particularly likely to exhaust currently available ART regimens before they died. In sensitivity analysis, increasing the rate of availability of new drugs did not substantially alter the results. Lowering the toxicity of future ART drugs had greater potential to increase benefit for many patient groups, increasing QALE by as much as 10%. Conclusions The future availability of new ART drugs without lower toxicity raises optimal treatment initiation for most patients, and improves clinical outcomes, especially for younger patients with higher viral loads. Reductions in toxicity of future ART drugs could impact optimal treatment initiation and improve clinical outcomes for all HIV patients.

Scheduling the South American Qualifiers to the 2018 FIFA World Cup by integer programming

Every four years, the 10 national teams members of the South American Football Confederation (CONMEBOL) compete for one of the South American slots in the final phase of the FIFA World Cup. The qualifying competition consists of a double round robin tournament. The matches are scheduled in 9 closely spaced pairs known as double rounds. Every team plays twice in each double round. The tournament is spread over 2 years, so the double rounds are months apart. After using the same mirrored schedule for about twenty years, and persistent complaints from its members, CONMEBOL decided to change the schedule for the 2018 World Cup. Supported by one of CONMEBOL’s members, we used integer programmming to construct schedules that overcome the main drawbacks of the previous approach. After exploring many design criteria, we proposed a candidate schedule based on a French scheme. The main feature of the proposed schedule is that every team plays once at home and once away on each double round, a departure from traditional symmetric (mirrored) schemes. This proposal was unanimously approved by CONMEBOL members and is currently being used in the qualifier tournament for the 2018 FIFA World Cup in Russia.

Learning in Combinatorial Optimization: What and How to Explore

We study dynamic decision-making under uncertainty when, at each period, a decision-maker implements a solution to a combinatorial optimization problem. The objective coefficient vectors of said problem, which are unobserved prior to implementation, vary from period to period. These vectors, however, are known to be random draws from an initially unknown distribution with known range. By implementing different solutions, the decision-maker extracts information about the underlying distribution, but at the same time experiences the cost associated with said solutions. We show that resolving the implied exploration versus exploitation trade-off efficiently is related to solving a Lower Bound Problem (LBP), which simultaneously answers the questions of what to explore and how to do so. We establish a fundamental limit on the asymptotic performance of any admissible policy that is proportional to the optimal objective value of the LBP problem. We show that such a lower bound might be asymptotically attained by policies that adaptively reconstruct and solve LBP at an exponentially decreasing frequency. Because LBP is likely intractable in practice, we propose policies that instead reconstruct and solve a proxy for LBP, which we call the Optimality Cover Problem (OCP). We provide strong evidence of the practical tractability of OCP which implies that the proposed policies can be implemented in real-time. We test the performance of the proposed policies through extensive numerical experiments and show that they significantly outperform relevant benchmarks in the long-term and are competitive in the short-term.

A Dynamic Clustering Approach to Data-Driven Assortment Personalization

We consider an online retailer facing heterogeneous customers with initially unknown product preferences. Customers are characterized by a diverse set of demographic and transactional attributes. T...

HIV Treatment in Resource-Limited Environments: Treatment Coverage and Insights

BACKGROUND The effects of antiretroviral treatment on the HIV epidemic are complex. HIV-infected individuals survive longer with treatment, but are less likely to transmit the disease. The standard coverage measure improves with the deaths of untreated individuals and does not consider the fact that some individuals may acquire the disease and die before receiving treatment, making it susceptible to overestimating the long-run performance of antiretroviral treatment programs. OBJECTIVE The objective was to propose an alternative coverage definition to better measure the long-run performance of HIV treatment programs. METHODS We introduced cumulative incidence-based coverage as an alternative to measure an HIV treatment programs success. To numerically compare the definitions, we extended a simulation model of HIV disease and treatment to represent a dynamic population that includes uninfected and HIV-infected individuals. Also, we estimated the additional resources required to implement various treatment policies in a resource-limited setting. RESULTS In a synthetic population of 600,000 people of which 44,000 (7.6%) are infected, and eligible for treatment with a CD4 count of less than 500 cells/mm(3), assuming a World Health Organization (WHO)-defined coverage rate of 50% of eligible people, and treating these individuals with a single treatment regimen, the gap between the current WHO coverage definition and our proposed one is as much as 16% over a 10-year planning horizon. CONCLUSIONS Cumulative incidence-based definition of coverage yields a more accurate representation of the long-run treatment success and along with the WHO and other definitions of coverage provides a better understanding of the HIV treatment progress.