Decision dependent stochastic processes

Kirschenmann, Thomas; Popova, Elmira; Damien, Paul; Hanson, Timothy

doi:10.1016/j.ejor.2013.11.016

Cited by 9 publications

(3 citation statements)

References 13 publications

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“…In addition, we can utilize the posterior distributions from Bayesian inference within a Markov chain Monte Carlo (MCMC) simulation setting. Bayesian frameworks are also considered in Morton and Popova and Kirschenmann et al for sampling and estimation purposes prior to the solution of the optimization problem. Different from these approaches, APS involves transformation of the optimization problem into a grand simulation by treating the decision variable as random for computational purposes.…”

Section: Aps For Call Center Staffingmentioning

confidence: 99%

Stochastic call center staffing with uncertain arrival, service and abandonment rates: A Bayesian perspective

Aktekin

Ekin

2016

Naval Research Logistics

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In this article, we introduce staffing strategies for the Erlang‐A queuing system in call center operations with uncertain arrival, service, and abandonment rates. In doing so, we model the system rates using gamma distributions that create randomness in operating characteristics used in the optimization formulation. We divide the day into discrete time intervals where a simulation based stochastic programming method is used to determine staffing levels. More specifically, we develop a model to select the optimal number of agents required for a given time interval by minimizing an expected cost function, which consists of agent and abandonment (opportunity) costs, while considering the service quality requirements such as the delay probability. The objective function as well as the constraints in our formulation are random variables. The novelty of our approach is to introduce a solution method for the staffing of an operation where all three system rates (arrival, service, and abandonment) are random variables. We illustrate the use of the proposed model using both real and simulated call center data. In addition, we provide solution comparisons across different formulations, consider a dynamic extension, and discuss sensitivity implications of changing constraint upper bounds as well as prior hyper‐parameters. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 460–478, 2016

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Section: Aps For Call Center Staffingmentioning

confidence: 99%

Stochastic call center staffing with uncertain arrival, service and abandonment rates: A Bayesian perspective

Aktekin

Ekin

2016

Naval Research Logistics

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“…Lee, Homem-de Mello, and Kleywegt, (2012) provide a discussion of newsvendortype problems with decision dependent uncertainty. Following the early work of Jonsbraten, Wets, and Woodruff, (1998), a number of applications arise in operational planning of offshore gas development (Goel & Grossmann 2004), aggregate workforce planning (Fragnière, Gondzio, & Yang, 2010), reliability (Kirschenmann, Popova, Damien, & Hanson, 2014), project portfolio management (Solak, Clarke, Johnson, & Barnes, 2010;Colvin & Maravelias 2010) and scheduling (Morton & Popova 2004). Goel and Grossmann (2006) illustrate ways that decisions can influence uncertainty or stochastic evolution.…”

Section: Introductionmentioning

confidence: 99%

Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty

Ekin¹,

Polson

Soyer

2017

Naval Research Logistics

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We propose a novel simulation‐based approach for solving two‐stage stochastic programs with recourse and endogenous (decision dependent) uncertainty. The proposed augmented nested sampling approach recasts the stochastic optimization problem as a simulation problem by treating the decision variables as random. The optimal decision is obtained via the mode of the augmented probability model. We illustrate our methodology on a newsvendor problem with stock‐dependent uncertain demand both in single and multi‐item (news‐stand) cases. We provide performance comparisons with Markov chain Monte Carlo and traditional Monte Carlo simulation‐based optimization schemes. Finally, we conclude with directions for future research.

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“…Knowledge of the effect of repair is important for determining optimum maintenance policy (Scarf, 1997;Dekker & Scarf, 1998;Wang, 2002;Xiang, 2013;Zhong & Jin, 2014;Kirschenmann, Popova, Damien, & Hanson, 2014) and modelling the repair effect has attracted considerable research (e.g., Malik, 1979;Nakagawa, 1988;Kijima, 1989;Doyen & Gaudoin, 2004;Guo, Liao, Zhao, & Mettas, 2007;Wu & Zuo, 2010). The repair effect can be accommodated by a number of means, such as modification of the failure intensity or reduction of the virtual age of the system.…”

Section: Motivationmentioning

confidence: 99%

Decline and repair, and covariate effects

Scarf

2015

European Journal of Operational Research

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The failure processes of repairable systems may be impacted by operational and environmental stress factors. To accommodate such factors, reliability can be modelled using a multiplicative intensity function. In the proportional intensity model, the failure intensity is the product of the failure intensity function of the baseline system that quantifies intrinsic factors and a function of covariates that quantify extrinsic factors. The existing literature has extensively studied the failure processes of repairable systems using general repair concepts such as age-reduction when no covariate effects are considered. This paper investigates different approaches for modelling the failure and repair process of repairable systems in the presence of time-dependent covariates. We derive probabilistic properties of the failure processes for such systems.

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Decision dependent stochastic processes

Cited by 9 publications

References 13 publications

Stochastic call center staffing with uncertain arrival, service and abandonment rates: A Bayesian perspective

Stochastic call center staffing with uncertain arrival, service and abandonment rates: A Bayesian perspective

Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty

Decline and repair, and covariate effects

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