Spatial Capacity Planning

60 Pages Posted: 13 Dec 2018 Last revised: 19 Feb 2019

See all articles by Omar Besbes

Omar Besbes

Columbia Business School - Decision Risk and Operations

Francisco Castro

Columbia Business School - Decision Risk and Operations

Ilan Lobel

New York University (NYU)

Date Written: November 26, 2018

Abstract

We study the relationship between capacity and performance for a service firm with spatial operations, in the sense that requests arrive with origin-destination pairs. An example of such a system is a ride-hailing platform in which each customer arrives in the system with the need to travel from an origin to a destination. We propose a state-dependent queueing model that captures spatial frictions as well as spatial economies of scale through the service rate. In a classical M/M/n queueing model, the square root safety (SRS) staffing rule is known to balance server utilization and customer wait times. By contrast, we find that the SRS rule does not lead to such a balance in spatial systems. In a spatial environment, pickup times increase the load in the system; furthermore, they are an endogenous source of extra workload that leads the system to only operate efficiently if there is sufficient imbalance between supply and demand. In heavy traffic, we derive the mapping from load to regimes of interest and establish that to obtain a balance of utilization and wait times, the service firm should use a higher safety factor, proportional to the offered load to the power of 2/3. We discuss implications of these results for general systems.

Keywords: heavy traffic, queueing, capacity sizing, staffing, spatial operations, QED regime, ride-hailing, ride-sharing, asymptotic analysis

JEL Classification: C6

Suggested Citation

Besbes, Omar and Castro, Francisco and Lobel, Ilan, Spatial Capacity Planning (November 26, 2018). Available at SSRN: https://ssrn.com/abstract=3292651 or http://dx.doi.org/10.2139/ssrn.3292651

Omar Besbes

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Francisco Castro

Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

Ilan Lobel (Contact Author)

New York University (NYU) ( email )

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