We consider a principal (e.g., a ridesharing platform such as Uber or Lyft) who receives two types of jobs (e.g., passengers requesting solo or shared rides) according to a Poisson process. The principal first decides which jobs to admit and then assigns an agent (e.g., driver) to perform them. The agent who is assigned the job has preference between the two types of jobs. The agent can independently decide whether to accept or reject a job which is assigned to them. The principal and the agent receive different rewards from each job thus resulting in incentives misalignment. The research questions are: (1) which job(s) should the principal admit? (2) How much should the principal pay the agent? To answer these questions, we model the agent as an M / M / 1 loss system. Using a Markov decision process and dynamic programming, we find the optimal wage the principal should pay the agent and a threshold admission policy (also known as trunk-reservation or switching-curve policy). Prior literature did not consider two players (agent and principal) with misaligned objectives and each making dynamic decisions. We contribute to the literature by adding another layer of decision making and by introducing server (agent) independence wherein the servers have preferences regarding the type of job they wish to perform.
| Published in | American Journal of Operations Management and Information Systems (Volume 6, Issue 3) |
| DOI | 10.11648/j.ajomis.20210603.11 |
| Page(s) | 29-34 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2021. Published by Science Publishing Group |
Revenue Management, Queueing, Principal-Agent, Stochastic
| [1] | Eitan Altman, Tania Jim´enez, and Ger Koole. On optimal call admission control in resource-sharing system. IEEE Transactions on Communications, 49 (9): 1659–1668, 2001. |
| [2] | Eitan Altman and Ger Koole. On submodular value functions and complex dynamic programming. Stochastic Models, 14 (5): 1051–1072, 1998. |
| [3] | Christian Borgs, Jennifer T Chayes, Sherwin Doroudi, Mor Harchol-Balter, and Kuang Xu. The optimal admission threshold in observable queues with state dependent pricing. Probability in the Engineering and Informational Sciences, 28 (1): 101–119, 2014. |
| [4] | Noah Gans and Sergei Savin. Pricing and capacity rationing for rentals with uncertain durations. Management Science, 53 (3): 390–407, 2007. |
| [5] | Mark E Lewis, Hayriye Ayhan, and Robert D Foley. Bias optimal admission control policies for a multiclass nonstationary queueing system. Journal of Applied Probability, 39 (1): 20–37, 2002. |
| [6] | Steven A Lippman. Applying a new device in the optimization of exponential queuing systems. Operations Research, 23 (4): 687–710, 1975. |
| [7] | Steven A Lippman and Sheldon M Ross. The streetwalkers’ dilemma: A job shop model. SIAM Journal on Applied Mathematics, 20 (3): 336–342, 1971. |
| [8] | Bruce L Miller. A queueing reward system with several customer classes. Management Science, 16 (3): 234–245, 1969. |
| [9] | Srimathy Mohan, Ferdous M Alam, John W Fowler, Mohan Gopalakrishnan, and Antonios Printezis. Capacity planning and allocation for web-based applications. Decision Sciences, 45 (3): 535–567, 2014. |
| [10] | E Lerzan Ormeci and Jan van der Wal. Admission policies for a two class loss system with general interarrival times. Stochastic Models, 22 (1): 37–53, 2006. |
| [11] | EL Ormeci, A Burnetas, and J van der Wal. Admission policies for a two class loss system. Stochastic Models, 17 (4): 513–539, 2001. |
| [12] | Martin L Puterman. Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley & Sons, 1994. |
| [13] | Sergei V Savin, Morris A Cohen, Noah Gans, and Ziv Katalan. Capacity management in rental businesses with two customer bases. Operations Research, 53 (4): 617–631, 2005. |
| [14] | Richard F Serfozo. An equivalence between continuous and discrete time Markov decision processes. Operations Research, 27 (3): 616–620, 1979. |
| [15] | Shaler Stidham. Optimal control of admission to a queueing system. IEEE Transactions on Automatic Control, 30 (8): 705–713, 1985. |
| [16] | Julie Leanne Vile, Jonathan William Gillard, Paul R Harper, and Vincent A Knight. A queueing theoretic approach to set staffing levels in time-dependent dual-class service systems. Decision Sciences, 48 (4): 766–794, 2017. |
| [17] | Utku Yildirim and John J Hasenbein. Admission control and pricing in a queue with batch arrivals. Operations Research Letters, 38 (5): 427–431, 2010. |
| [18] | Seunghwan Yoon and Mark E Lewis. Optimal pricing and admission control in a queueing system with periodically varying parameters. Queueing Systems, 47 (3): 177–199, 2004. |
| [19] | Gabriel Zayas-Cab´an and Mark E Lewis. Admission control in a two-class loss system with periodically varying parameters and abandonments. Queueing Systems, 94 (1-2): 175–210, 2020. |
APA Style
Jagan Jacob. (2021). A Note on Principal-Agent Problem in a Stochastic System. American Journal of Operations Management and Information Systems, 6(3), 29-34. https://doi.org/10.11648/j.ajomis.20210603.11
ACS Style
Jagan Jacob. A Note on Principal-Agent Problem in a Stochastic System. Am. J. Oper. Manag. Inf. Syst. 2021, 6(3), 29-34. doi: 10.11648/j.ajomis.20210603.11
AMA Style
Jagan Jacob. A Note on Principal-Agent Problem in a Stochastic System. Am J Oper Manag Inf Syst. 2021;6(3):29-34. doi: 10.11648/j.ajomis.20210603.11
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Download@article{10.11648/j.ajomis.20210603.11,
author = {Jagan Jacob},
title = {A Note on Principal-Agent Problem in a Stochastic System},
journal = {American Journal of Operations Management and Information Systems},
volume = {6},
number = {3},
pages = {29-34},
doi = {10.11648/j.ajomis.20210603.11},
url = {https://doi.org/10.11648/j.ajomis.20210603.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajomis.20210603.11},
abstract = {We consider a principal (e.g., a ridesharing platform such as Uber or Lyft) who receives two types of jobs (e.g., passengers requesting solo or shared rides) according to a Poisson process. The principal first decides which jobs to admit and then assigns an agent (e.g., driver) to perform them. The agent who is assigned the job has preference between the two types of jobs. The agent can independently decide whether to accept or reject a job which is assigned to them. The principal and the agent receive different rewards from each job thus resulting in incentives misalignment. The research questions are: (1) which job(s) should the principal admit? (2) How much should the principal pay the agent? To answer these questions, we model the agent as an M / M / 1 loss system. Using a Markov decision process and dynamic programming, we find the optimal wage the principal should pay the agent and a threshold admission policy (also known as trunk-reservation or switching-curve policy). Prior literature did not consider two players (agent and principal) with misaligned objectives and each making dynamic decisions. We contribute to the literature by adding another layer of decision making and by introducing server (agent) independence wherein the servers have preferences regarding the type of job they wish to perform.},
year = {2021}
}
TY - JOUR T1 - A Note on Principal-Agent Problem in a Stochastic System AU - Jagan Jacob Y1 - 2021/08/11 PY - 2021 N1 - https://doi.org/10.11648/j.ajomis.20210603.11 DO - 10.11648/j.ajomis.20210603.11 T2 - American Journal of Operations Management and Information Systems JF - American Journal of Operations Management and Information Systems JO - American Journal of Operations Management and Information Systems SP - 29 EP - 34 PB - Science Publishing Group SN - 2578-8310 UR - https://doi.org/10.11648/j.ajomis.20210603.11 AB - We consider a principal (e.g., a ridesharing platform such as Uber or Lyft) who receives two types of jobs (e.g., passengers requesting solo or shared rides) according to a Poisson process. The principal first decides which jobs to admit and then assigns an agent (e.g., driver) to perform them. The agent who is assigned the job has preference between the two types of jobs. The agent can independently decide whether to accept or reject a job which is assigned to them. The principal and the agent receive different rewards from each job thus resulting in incentives misalignment. The research questions are: (1) which job(s) should the principal admit? (2) How much should the principal pay the agent? To answer these questions, we model the agent as an M / M / 1 loss system. Using a Markov decision process and dynamic programming, we find the optimal wage the principal should pay the agent and a threshold admission policy (also known as trunk-reservation or switching-curve policy). Prior literature did not consider two players (agent and principal) with misaligned objectives and each making dynamic decisions. We contribute to the literature by adding another layer of decision making and by introducing server (agent) independence wherein the servers have preferences regarding the type of job they wish to perform. VL - 6 IS - 3 ER -
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