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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.16399 |
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| _version_ | 1866909944301748224 |
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| author | Fackrell, Mark Gupta, Hritika Taylor, Peter G. |
| author_facet | Fackrell, Mark Gupta, Hritika Taylor, Peter G. |
| contents | This paper addresses a fundamental and practically significant problem in call centre operations -- determining optimal call allocation policies that meet client service targets while minimising staffing costs. Motivated by a problem presented by an industry partner, we examine a real-world setting involving a relatively small call centre with hierarchical structure among agents. It is natural to model the operation of such a centre as a continuous-time Markov chain. To gain insight into the structure of optimal policies, we first (i) apply backward induction based on Bellman's equation to a finite-horizon discrete-time model, and (ii) derive stationary policies for an infinite-horizon continuous-time model with discounting. Subsequently, we evaluate the performance of these policies in the original finite-horizon continuous-time setting by computing the expected number of abandonments and the waiting time distributions of customers. This is achieved using first-step analysis combined with Laplace transform methods. The effectiveness of the proposed approach is illustrated through numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16399 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Performance Evaluation of Small Call Centres in a Transient Regime Fackrell, Mark Gupta, Hritika Taylor, Peter G. Probability This paper addresses a fundamental and practically significant problem in call centre operations -- determining optimal call allocation policies that meet client service targets while minimising staffing costs. Motivated by a problem presented by an industry partner, we examine a real-world setting involving a relatively small call centre with hierarchical structure among agents. It is natural to model the operation of such a centre as a continuous-time Markov chain. To gain insight into the structure of optimal policies, we first (i) apply backward induction based on Bellman's equation to a finite-horizon discrete-time model, and (ii) derive stationary policies for an infinite-horizon continuous-time model with discounting. Subsequently, we evaluate the performance of these policies in the original finite-horizon continuous-time setting by computing the expected number of abandonments and the waiting time distributions of customers. This is achieved using first-step analysis combined with Laplace transform methods. The effectiveness of the proposed approach is illustrated through numerical examples. |
| title | Performance Evaluation of Small Call Centres in a Transient Regime |
| topic | Probability |
| url | https://arxiv.org/abs/2403.16399 |