Totally unimodular multistage stochastic programs

Sun, Ruichen; Shylo, Oleg V.; Schaefer, Andrew J.

doi:10.1016/j.orl.2014.11.003

Cited by 5 publications

(3 citation statements)

References 11 publications

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“…In contrast, integrality requirements in our problem are essential because we consider staff planning and, as shown in Table 1, the average number of anesthesiologists deployed in each service on a given day is small. Recent theoretical work on integer stochastic dynamic programs includes Kong et al (2013) and Sun et al (2015). Easton (2014) considers a two-stage problem to manage workforce allocation by incorporating the joint variability of attendance and demand.…”

Section: Literature Reviewmentioning

confidence: 99%

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Staff Planning for Hospitals with Implicit Cost Estimation and Stochastic Optimization

Rath

Rajaram

2022

Production and Operations Management

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W e consider the anesthesiologist staff planning problem for operating services departments in large multi-specialty hospitals without limit on anesthesiologist supply, where the planner makes monthly and daily decisions to minimize total costs. Each month the staff planner decides the number of anesthesiologists on regular duty and an on-call consideration list for each day of the following month. In addition, each day, the staff planner decides how many on-call anesthesiologists to call for the following day. Total costs consist of explicit and implicit costs. Explicit costs include the costs of calling an anesthesiologist and overtime costs. These costs are specified by the organization. Implicit costs encompass costs of not calling an on-call anesthesiologist and under-utilizing an anesthesiologist, and these have to be deduced from past decisions. We model the staff planning problem as a two-stage integer stochastic dynamic program. We develop structural properties of this model and use them in a sample average approximation algorithm constructed to solve this problem. We also develop a procedure to estimate the implicit costs, which are included in this model. Using data from the operating services department at the UCLA Ronald Reagan Medical Center, our model shows the potential to reduce overall costs by 16%. We provide managerial insights related to the relative scale of these costs, hiring decisions by service, sensitivity to cost parameters, and improvements in the prediction of the booked time durations.

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Section: Literature Reviewmentioning

confidence: 99%

“…(2013) and Sun et al. (2015). Easton (2014) considers a two‐stage problem to manage workforce allocation by incorporating the joint variability of attendance and demand.…”

Section: Introductionmentioning

confidence: 95%

Staff Planning for Hospitals with Implicit Cost Estimation and Stochastic Optimization

Rath

Rajaram

2022

Production and Operations Management

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“…Note that in (b-d), there is no restriction on matrices F j ω for j ∈ J and ω ∈ Ω. Moreover, we are considering TU matrices in the aforementioned structured CMIPs because of the following reasons: (1) In the literature on TSS-MILPs, researchers have considered two-stage stochastic mixed integer linear programs (TSS-MILPs) with TU recourse matrix [51] and extensive formulation of TSS-MILPs and multi-stage stochastic MIPs with TU constraint matrix [32,59]; (2) TU matrices also find their applications in deterministic problems such as two-commodity transportation problem [49], network flow model for nursing staffs' scheduling problems [27], and many more [42]; and (3) TSS-CMIPs and their distributionally robust variants (see Sect. 1.2) with these structured CMIPs have not been studied in the literature.…”

Section: Introductionmentioning

confidence: 99%

Scenario-based cuts for structured two-stage stochastic and distributionally robust p-order conic mixed integer programs

Bansal

Zhang

2021

J Glob Optim

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In this paper, we derive (partial) convex hull for deterministic multi-constraint polyhedral conic mixed integer sets with multiple integer variables using conic mixed integer rounding (CMIR) cut-generation procedure of Atamtürk and Narayanan (Math Prog 122:1-20, 2008), thereby extending their result for a simple polyhedral conic mixed integer set with single constraint and one integer variable. We then introduce two-stage stochastic p-order conic mixed integer programs (denoted by TSS-CMIPs) in which the second stage problems have sum of l p -norms in the objective function along with integer variables. First, we present sufficient conditions under which the addition of scenario-based nonlinear cuts in the extensive formulation of TSS-CMIPs is sufficient to relax the integrality restrictions on the second stage integer variables without impacting the integrality of the optimal solution of the TSS-CMIP. We utilize scenario-based CMIR cuts for TSS-CMIPs and their distributionally robust generalizations with structured CMIPs in the second stage, and prove that these cuts provide conic/linear programming equivalent or approximation for the second stage CMIPs. We also perform extensive computational experiments by solving stochastic and distributionally robust capacitated facility location problem and randomly generated structured TSS-CMIPs with polyhedral CMIPs and second-order CMIPs in the second stage, i.e. p = 1 and p = 2, respectively. We observe that there is a significant reduction in the total time taken to solve these problems after adding the scenario-based cuts. KeywordsTwo-stage stochastic p-order conic mixed integer program • Scenario-based cutting planes • Two-stage distributionally robust program • (Partial) convex hull • Conic mixed integer rounding • Multi-module capacitated facility location B Manish Bansal

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On the Value of Dual-Firing Power Generation Under Uncertain Gas Network Access

Defourny

2019

Springer Proceedings in Mathematics &Amp; Statistics

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Totally unimodular multistage stochastic programs

Cited by 5 publications

References 11 publications

Staff Planning for Hospitals with Implicit Cost Estimation and Stochastic Optimization

Staff Planning for Hospitals with Implicit Cost Estimation and Stochastic Optimization

Scenario-based cuts for structured two-stage stochastic and distributionally robust p-order conic mixed integer programs

On the Value of Dual-Firing Power Generation Under Uncertain Gas Network Access

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