Amazon sized contact centers with mathematical programming, cutting cost per contact

By the mid-2000s Amazon.com's success depended on high-quality customer service, delivered through a hybrid network: contact centers the company ran itself, plus externally managed centers handling overflow. The decisions were intertwined — how many agents to hire and train in-house, and how much voice and e-mail volume to send to vendors — yet sizing them in isolation wastes money on one side and degrades service on the other.

Keblis and Chen developed a mathematical-programming approach that Amazon.com uses to plan this capacity. The model schedules hiring and training at internal centers and allocates voice and e-mail volumes across external providers, so the whole network is planned as a single system rather than a collection of separately managed call centers.

The reported outcome is the combination that naive setups almost never achieve: the approach reduced the average cost of handling a customer contact and, at the same time, increased the service level provided to customers. Cost usually buys quality in service operations; planning the joint allocation is how you get both.

The case is a template for any business with a mixed in-house/outsourced service network — logistics, IT support, back offices. The leverage is not in a better forecast of call volume but in making hiring, training and routing decisions together instead of channel by channel.

One optimization plan for hiring, training and routing

The dumb alternative sizes each center separately and renews vendor contracts by habit, ignoring that in-house hires take months of lead time while vendor volume flexes.

Training lead times make agent capacity sticky; deciding hiring without a plan for routing next season's volume either strands trained agents or buries vendors in overflow they price back.

Mathematical programming suits this structure: linear trade-offs between staffing costs and vendor fees under service-level constraints, with the optimum shifting as demand grows.

An e-commerce contact base spikes seasonally; a joint plan reallocates that peak between internal and external capacity instead of paying every center to be sized for its worst week.

Service quality is a capacity-planning problem. Sizing centers separately leaves you overstaffed somewhere, understaffed elsewhere; plan hiring, training and routing in one optimization.

The work appeared in Interfaces in 2006 as part of INFORMS' practice literature, and the paper states Amazon.com used the approach in planning capacity. It remains a reference case for optimizing hybrid contact-center networks.