Outsourcing a Two-Level Service Process

Abstract

This paper studies outsourcing decisions for a two-level service process in which the first level serves as a gatekeeper for a second level of experts. The objective of the system operator (the client) is to minimize the sum of staffing costs, customer waiting costs, and mistreatment costs due to unsuccessful attempts by a gatekeeper to solve the customer's problem. The client may outsource all or part of the process to a vendor, and first-best contracts exist when the client outsources only gatekeepers or experts. When the client outsources the entire system as a two-level process, a client-optimal contract may not exist unless the exogenous system parameters satisfy a particular (and unlikely) coordination condition. In addition, optimal incentive-compatible contracts exist when the vendor's structure choice (one-level or two-level) can deviate from the client's preference.Finally, we numerically examine how vendor structure choice and labor cost advantages influence the client's optimal outsourcing option.

Managing the Outsourcing of Two-Level Service Processes: Literature Review and Integration

“…The cases in which it is significantly differs from the optimal are those cases in which it is optimal to operate a one-level system of experts anyway. [21] show that for a large class of treatment functions the optimal treatment threshold asymptotically approaches the deterministic one for large systems. In particular the optimal threshold is described by:…”

“…Therefore, we have made two sets of approximations: that each queue is an M/M/N system, and that each operates in the QED regime. Experiments in [4], [13], [15], and [21] show that both of these approximations are extremely accurate. For example, experiments in [21] demonstrate that over a wide variety of parameters, the mean error for the total time in system is less than 1%, and for large systems (over 250 servers), the maximum error is 3.5% or less.…”

“…Experiments in [4], [13], [15], and [21] show that both of these approximations are extremely accurate. For example, experiments in [21] demonstrate that over a wide variety of parameters, the mean error for the total time in system is less than 1%, and for large systems (over 250 servers), the maximum error is 3.5% or less. In addition, the largest errors are not caused directly by the approximations, but rather by the rounding of staffing levels (the QED approximation and squareroot staffing rule lead to a continuous staffing level, while the test simulation in [21] requires integer staffing levels).…”

“…[15] and [21] extend the deterministic model of [31] to a stochastic setting. With stochastic customer arrivals and service times it is necessary to model the system as a queuing system and to take into account customer waiting costs and staffing levels.…”

“…For example, experiments in [21] demonstrate that over a wide variety of parameters, the mean error for the total time in system is less than 1%, and for large systems (over 250 servers), the maximum error is 3.5% or less. In addition, the largest errors are not caused directly by the approximations, but rather by the rounding of staffing levels (the QED approximation and squareroot staffing rule lead to a continuous staffing level, while the test simulation in [21] requires integer staffing levels). Likewise, experiments in [15] show that the error in the total cost of the system due to the approximation is consistently less than 1% and that staffing decisions made under the approximation are consistently identical to, or within 1 server, of the exact optimal solution.…”