Online Assortment Optimization with Reusable Resources

We consider an online assortment optimization problem where we have n substitutable products with fixed reusable capacities [Formula: see text]. In each period t, a user with some preferences (potentially adversarially chosen) who offers a subset of products, St, from the set of available products arrives at the seller’s platform. The user selects product [Formula: see text] with probability given by the preference model and uses it for a random number of periods, [Formula: see text], that is distributed i.i.d. according to some distribution that depends only on j generating a revenue [Formula: see text] for the seller. The goal of the seller is to find a policy that maximizes the expected cumulative revenue over a finite horizon T. Our main contribution is to show that a simple myopic policy (where we offer the myopically optimal assortment from the available products to each user) provides a good approximation for the problem. In particular, we show that the myopic policy is 1/2-competitive, that is, the expected cumulative revenue of the myopic policy is at least half the expected revenue of the optimal policy with full information about the sequence of user preference models and the distribution of random usage times of all the products. In contrast, the myopic policy does not require any information about future arrivals or the distribution of random usage times. The analysis is based on a coupling argument that allows us to bound the expected revenue of the optimal algorithm in terms of the expected revenue of the myopic policy. We also consider the setting where usage time distributions can depend on the type of each user and show that in this more general case there is no online algorithm with a nontrivial competitive ratio guarantee. Finally, we perform numerical experiments to compare the robustness and performance of myopic policy with other natural policies. This paper was accepted by Gabriel Weintraub, revenue management and analytics.

Allocation of COVID-19 Vaccines Under Limited Supply

Problem definition: This paper considers how to allocate COVID-19 vaccines to different age groups when limited vaccines are available over time. Academic/practical relevance: Vaccine is one of the most effective interventions to contain the ongoing COVID-19 pandemic. However, the initial supply of the COVID-19 vaccine will be limited. An urgent problem for the government is to determine who to get the first dose of the future COVID-19 vaccine. Methodology: We use epidemic data from New York City to calibrate an age-structured SAPHIRE model that captures the disease dynamics within and across various age groups. The model and data allow us to derive effective static and dynamic vaccine allocation policies minimizing the number of confirmed cases or the numbers of deaths. Results: The optimal static policies achieve a much smaller number of confirmed cases and deaths compared to other static benchmark policies including the pro rata policy. Dynamic allocation policies, including various versions of the myopic policy, significantly improve on static policies. Managerial implications: For static policies, our numerical study shows that prioritizing the older groups is beneficial to reduce deaths while prioritizing younger groups is beneficial to avert infections. For dynamic policies, the older groups should be vaccinated at early days and then switch to younger groups. Our analysis provides insights on how to allocate vaccines to the various age groups, which is tightly connected to the decision-maker's objective.

Transient-State Natural Gas Transmission in Gunbarrel Pipeline Networks

We study the energy consumption minimization problems of natural gas transmission in gunbarrel structured networks. In particular, we consider the transient-state dynamics of natural gas and the compressor’s nonlinear working domain and min-up-and-down constraints. We formulate the problem as a two-level dynamic program (DP), where the upper-level DP problem models each compressor station as a decision stage and each station’s optimization problem is further formulated as a lower-level DP by setting each time period as a stage. The upper-level DP faces the curse of high dimensionality. We propose an approximate dynamic programming (ADP) approach for the upper-level DP using appropriate basis functions and an exact approach for the lower-level DP by exploiting the structure of the problem. We validate the superior performance of the proposed ADP approach on both synthetic and real networks compared with the benchmark simulated annealing (SA) heuristic and the commonly used myopic policy and steady-state policy. On the synthetic networks (SNs), the ADP reduces the energy consumption by 5.8%–6.7% from the SA and 12% from the myopic policy. On the test gunbarrel network with 21 compressor stations and 28 pipes calibrated from China National Petroleum Corporation, the ADP saves 4.8%–5.1% (with an average of 5.0%) energy consumption compared with the SA and the currently deployed steady-state policy, which translates to cost savings of millions of dollars a year. Moreover, the proposed ADP algorithm requires 18.4%–61.0% less computation time than the SA. The advantages in both solution quality and computation time strongly support the proposed ADP algorithm in practice.

Dynamic scheduling with cancellations: an application to chemotherapy appointment booking

We study a dynamic scheduling problem that has the feature of due dates and time windows. This problem arises in chemotherapy scheduling where patients from different types have specific target dates along with time windows for appointment. We consider cancellation of appointments. The problem is modeled as a Markov Decision Process (MDP) and approximately solved using a direct-search based approximate dynamic programming (ADP) tehnique. We compare the performance of the ADP technique against the myopic policy under diverse scenarios. Our computational results reveal that the ADP technique outperforms the myopic policy on majority of problem sets we generated.