A Method for Staffing Large Call Centers Based on Stochastic Fluid Models | Massachusetts Institute of Technology - Edubirdie

University:
Massachusetts Institute of Technology
Course:
15.992 | S-Lab: Laboratory for Sustainable Business
Academic year:

2023
Views:

118

Pages:

11
Author:

gandujadqtrdj

A Method for Staffing Large Call Centers Based on Stochastic Fluid Models Outline Motivation and Problem Proposed Model Supporting Logic Numerical Examples Comments and Discussion Motivation Large-Scale Call Centers Example: AT&T, Verizon Local Phone, DSL, Cell Phone, etc. Billing, Technical Support, Termination, etc. Different Agents/Servers for different types of calls Other examples: Banks, Insurance Companies, Dell, IBM and many others Model 1 1 2 3 2 r m m customer classes r agent pools bi agents in pool i Service time depends on customer class and service pool Tasks Staff Scheduling/ Capacity Planning* 1. Number and types of agent pools # of agents in each pools Dynamic Routing 2. Customer arrival -> serve/buffer Service Completion -> server idle/another customer Assumptions Scale is large enough to treat variables as continuous variables The capacity is determined in advance and cannot be revised Demand is doubly stochastic Poisson All other uncertainty and variability are negligible compared to demand, i.e., assume everything else constant Doubly Stochastic Poisson Model Λ (t ) = (Λ1 (t ),..., Λ m (t )),0 ≤ t ≤ T Given Λ(t ) = (λ1 ,..., λm ) conditional distribution of arrivals in different classes immediately after t are independent Poisson processes Objective Cost ck per agent in pool k Penalty pi per abandonment call per customer for class I Want to select bk to minimize m r ∑c b + ∑ p q k =1 k k i =1 i i Problem: Difficult to find qi the total expected abandonment call per class Proposed Method Given λ ∈ \ m+ b ∈ \ r+ π * (λ , b) = minimize π = p ⋅ (λ − Rx) subject to: Rx ≤ λ , Ax ≤ b, x ≥ 0 ⎧⎪ T * ⎫⎪ Objective: minimize c ⋅ b + Ε ⎨ ∫ π (Λ (t ), b)dt ⎬ ⎩⎪ 0 ⎭⎪ T Let 1 F (λ ) := ∫ Ρ {Λ (t ) ≤ λ } dt for λ ∈ \ m+ T 0 minimize c ⋅ b + T ∫ π * (λ , b)dF (λ ) =: φ (b) R+m Proposed Method Proposition r φ (b) is a convex function on R + Convex Optimization problem Gradient-descent method combined with Monte Carlo simulation to find the numerical solution Comments and Critiques Well written paper with interesting under-research topic Proposed a model for skill-based routing Major Criticism: Assume no variability in service time Neglect the dependence between optimal policy and routing method -> most routing methods may only get a cost far above optimal given the theoretical policy Would be more interesting if they provide some interesting results using their methods

Related Documents

A Method for Staffing Large Call Centers Based on Stochastic Fluid Models

A Method for Staffing Large Call Centers Based on Stochastic Fluid Models - Page 1

A Method for Staffing Large Call Centers Based on Stochastic Fluid Models - Page 2

A Method for Staffing Large Call Centers Based on Stochastic Fluid Models - Page 3

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A Method for Staffing Large Call Centers Based on Stochastic Fluid Models - Page 5

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