EURO 2024 Copenhagen
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2138. A bivariate two-moments fit and its application in appointment scheduling

Invited abstract in session WB-34: Stochastic Optimization: Advanced Applications, stream Stochastic, Robust and Distributionally Robust Optimization.

Wednesday, 10:30-12:00
Room: 43 (building: 303A)

Authors (first author is the speaker)

1. Bharti Bharti
Korteweg-de Vries Institute for Mathematics, University of Amsterdam
2. Michel Mandjes
University of Amsterdam
3. René Bekker
Vrije Universiteit

Abstract

The optimization of appointment scheduling within parallel server systems is important for enhancing operational efficiency and customer satisfaction in diverse service industries, ranging from healthcare and telecommunications to transportation and manufacturing. In this context, we tackle the challenge of appointment scheduling in systems where clients are served by two correlated servers operating in parallel, with given distribution. We devise a stochastic optimization framework to minimize a comprehensive loss function that balances clients' waiting times, server idle times, and the effects of individual client's sojourn times. To capture the diverse operational scenarios encountered in practice, we introduce novel metrics, including maximum and minimum sojourn times, reflecting real-world constraints and priorities and redefine the scheduling objective solely in terms of sojourn times, facilitating the application of standard optimization methodologies. To accurately model the distributions of sojourn times, we propose a bivariate extension of the conventional two-moments fit using Weibull distribution and leverage the Frechet bounds for bivariate distributions with fixed marginals to get bounds on correlation between the two queues. Finally we conduct a series of numerical experiments to illustrate the efficiency of our method. We compare our method with simulated results and examine the effect for both negative and positive correlations with different distributions.

Keywords

Status: accepted

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