Stochastic programming approaches to stochastic scheduling

Birge, John R.; Dempstert, M. A. H.

doi:10.1007/bf00121682

Cited by 47 publications

(25 citation statements)

References 26 publications

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“…These linear models are more aggregate than the integer-constrained shift scheduling models we consider here. For stochastic programming approaches to hierarchical scheduling, see Birge and Dempster (1996).…”

Section: Literature Reviewmentioning

confidence: 99%

Workforce planning at USPS mail processing and distribution centers using stochastic optimization

2007

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Service organizations that operate outside the normal 8-hour day and face wide fluctuations in demand constantly struggle to optimize the size and composition of their workforce. Recent research has shown that improved personnel scheduling methods that take demand uncertainty into account can lead to significant reductions in labor costs. This paper addresses a staff planning and scheduling problem that arises at United States Postal Service (USPS) mail processing & distribution centers (P&DCs) and develops a two-stage stochastic integer program with recourse for the analysis. In the first stage, before the demand is known, the number of full-time and part-time employees is determined for the permanent workforce. In the second stage, the demand is revealed and workers are assigned to specific shifts during the week. When necessary, overtime and casual labor are used to satisfy demand. This paper consists of two parts: (1) the analysis of the demand distribution in light of historical data, and (2) the development and analysis of the stochastic integer programming model. Using weekly demand for a three-year period, we first investigate the possibility that there exists an end-of-month effect, i.e., the week at the end of month has larger volume than the other weeks. We show that the data fail to indicate that this is the case.In the computational phase of the work, three scenarios are considered: high, medium, and low demand. The stochastic optimization problem that results is a large-scale integer program that embodies the full set of contractual agreements and labor rules governing the design of the workforce at a P&DC. The usefulness of the model is evaluated by solving a

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Section: Literature Reviewmentioning

confidence: 99%

Workforce planning at USPS mail processing and distribution centers using stochastic optimization

2007

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“…These are shown in Fig. 1 and denoted by (1), (2), (3) and (4). The probability of occurrence of each of these scenarios is 0.25, which is obtained by multiplying the probabilities of the uncertain parameter values in each scenario.…”

Section: Approximation Strategymentioning

confidence: 99%

“…There is an abundance of literature in the area of optimization under uncertainty involving several applications. Some of these include: production planning (Clay and Grossmann, 1997;Cheng et al, 2003), scheduling (Birge and Dempster, 1996; Balasubramanian and Grossmann, 2002), optimal chemical process synthesis (Acevedo and Pistikopoulos, 1998;Liu and Sahinidis, 1996;Rooney and Biegler, 2003), electricity production (Takriti et al, 1996;Nowak et al, 2005). Usually problems with uncertainty are represented as stochastic programming problems (Birge and Louveaux, 1997) or as deterministic flexibility problems (Grossmann et al, 1983).…”

Section: Introductionmentioning

confidence: 99%

A simple heuristic for reducing the number of scenarios in two-stage stochastic programming

Karuppiah

Martı́n

Grossmann

2010

Computers & Chemical Engineering

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In this work we address the problem of solving multiscenario optimization models that are deterministic equivalents of two-stage stochastic programs. We present a heuristic approximation strategy where we reduce the number of scenarios and obtain an approximation of the original multiscenario optimization problem. In this strategy, a subset of the given set of scenarios is selected based on a proposed criterion and probabilities are assigned to the occurrence of the reduced set of scenarios. The original stochastic programming model is converted into a deterministic equivalent using the reduced set of scenarios. A mixed-integer linear program (MILP) is proposed for the reduced scenario selection. We apply this practical heuristic strategy to four numerical examples and show that reformulating and solving the stochastic program with the reduced set of scenarios yields an objective value close to the optimum of the original multiscenario problem.

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“…Some relevant research on duality gaps in stochastic programming is contained in [5,30,31]. The authors of [5,31] try to establish quantitative estimates for the duality gap arising when the scenario decomposition approach is applied to solving mixed-integer multistage stochastic programs. The relative duality gap per scenario term is estimated in [31].…”

Section: A T T (ζ T )X T + a T T−1 (ζ T )X T−1 ≥ C T (ζ T )mentioning

confidence: 99%

“…The relative duality gap per scenario term is estimated in [31]. In [5] the authors state sufficient conditions that lead to the vanishing of the duality gap in the scenario decomposition if the number of scenarios tends to infinity. However, an example with non-vanishing duality gap while increasing the number of scenarios is constructed in [30].…”

Section: A T T (ζ T )X T + a T T−1 (ζ T )X T−1 ≥ C T (ζ T )mentioning

confidence: 99%

Duality gaps in nonconvex stochastic optimization

Dentcheva

Römisch

2004

Math. Program., Ser. A

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Abstract. We consider multistage stochastic optimization models containing nonconvex constraints, e.g., due to logical or integrality requirements. We study three variants of Lagrangian relaxations and of the corresponding decomposition schemes, namely, scenario, nodal and geographical decomposition. Based on convex equivalents for the Lagrangian duals, we compare the duality gaps for these decomposition schemes. The first main result states that scenario decomposition provides a smaller or equal duality gap than nodal decomposition. The second group of results concerns large stochastic optimization models with loosely coupled components. The results provide conditions implying relations between the duality gaps of geographical decomposition and the duality gaps for scenario and nodal decomposition, respectively.

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Stochastic programming approaches to stochastic scheduling

Cited by 47 publications

References 26 publications

Workforce planning at USPS mail processing and distribution centers using stochastic optimization

Workforce planning at USPS mail processing and distribution centers using stochastic optimization

A simple heuristic for reducing the number of scenarios in two-stage stochastic programming

Duality gaps in nonconvex stochastic optimization

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