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Two-stage absolute semi-deviation mean-risk stochastic programming: An application to the supply chain replenishment problem

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COMPUTERS & OPERATIONS RESEARCH 2019年第Jun.期106卷 62-75页

作者： Venkatachalam, Saravanan Narayanan, Arunachalam Wayne State Univ Dept Ind & Syst Engn 4815 Fourth St Detroit MI 48202 USA Univ Houston Dept Decis & Informat Sci 334 Melcher Hall Houston TX 77204 USA

Conventionally, two-stage stochastic programs have been devised to minimize the expectation of recourse actions. However, in the presence of high data variability, the solutions from expected value models may not be robust, and hence weighted risk measures are introduced in the objective function. In this study, we consider a two-stage stochastic program with mean absolute semi-deviation (MASD) as a risk measure for an application in supply chain planning. Models with MASD lack block-angular structures;thus, they are not suitable for traditional decomposition algorithms and pose computational challenges. We therefore propose a heuristic procedure based on the expected excess risk measure for solving the model. Specifically, we propose a heuristic for a generic replenishment problem in supply chains with MASD risk measures. We evaluate the robustness of the MASD model solutions by comparing the fill rate for replenishment plans with the optimal solutions from deterministic and expected value models, and we demonstrate the efficacy of the heuristic based on extensive computational experiments. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： stochastic integer programming Mean absolute semi-deviation Risk measure Expected excess Replenishment problem Supply chain management

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Two-stage stochastic days-off scheduling of multi-skilled analysts with training options

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2019年第1期38卷 111-129页

作者： Altner, Douglas S. Mason, Erica K. Servi, Les D. Mitre Corp Operat Res Dept Mclean VA 20111 USA ThirdLove San Francisco CA 94107 USA

Motivated by a cybersecurity application, this paper studies a two-stage, stochastic days-off scheduling problem with (1) many types of jobs that require specialized training, (2) many multi-skilled analysts, (3) the ability to shape analyst skill sets through training decisions, and (4) a large number of possible future demand scenarios. We provide an integer linear program for this problem and show it can be solved with a direct feed into Gurobi with as many as 50 employees, 6 job types, and 50 demand scenarios per day without any decomposition techniques. In addition, we develop a matheuristicthat is, an integer-programming-based local search heuristicfor instances that are too large for a straightforward feed into a commercial solver. Computational results show our matheuristic can, on average, produce solutions within 4-7% of an upper bound of the optimal objective value.

关键词： Days-off scheduling Multi-skilled workforce stochastic integer programming Matheuristics Cybersecurity operations Training

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Mobility-Aware Relay Selection in 5G D2D Communication Using stochastic Model

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2019年第3期68卷 2837-2849页

作者： Singh, Durgesh Ghosh, Sasthi C. Indian Stat Inst Adv Comp & Microelect Unit Kolkata 700108 India

Challenges in relay selection for device-to-device (D2D) communication arise due to the mobility of nodes, which brings uncertainty in various network parameters. We first developed a network-assisted stochastic integer programming (SIP) model to incorporate uncertainty that predicts the network parameters for upcoming time instance based on information available at current time instance. We converted the SIP model to an equivalent deterministic mixed integer non-linear program (MINLP) model and proved its hardness result. By exploiting the constraints of MINLP, we developed a distributed greedy metric, termed as connectivity factor (CF), which is calculated locally at each node on per-hop basis. It captures the nodes mobility and, hence, takes care of link reliability that in turn controls packet loss and delay. It can be computed in O(n) time, where n is the number of transmitters interfering with the given link. Our approach is applicable to any mobility model with relevant distributions of mobility parameters known. We constructed perceived graph based on CF values to devise network-assisted and device-controlled relay selection algorithms for given source-destination pairs. Extensive simulation results show significant improvements in packet loss and average end-to-end delay by our approach over a recent implementation of an ad-hoc on-demand distance vector (AODV) based algorithm.

关键词： stochastic integer programming mobility of devices relay selection 5G D2D communication packet loss and end to end delay

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A stochastic model for scheduling elective surgeries in a cyclic Master Surgical Schedule

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COMPUTERS & INDUSTRIAL ENGINEERING 2019年 129卷 156-168页

作者： M'Hallah, Rym Visintin, Filippo Kuwait Univ Dept Stat & Operat Res Coll Sci Safat Kuwait Univ Florence IBIS Lab Dept Ind Engn Florence Italy

In this study we propose a stochastic model that determines the number and type of surgeries to schedule in a two-week planning horizon where each operating session is assigned to a surgical specialty according to a fixed grid (Master Surgical Schedule). Our model considers surgery times, intensive care unit times and post-surgery lengths of stays stochastic and accounts for the availability of both intensive care unit beds and post-surgery beds. It aims to maximise the expected operating theatre's throughput. The assignment problem, modelled as a stochastic problem, is solved via a sample average approximation. It gets an estimate of the optimum expected throughput for each specialty and of the operating theatre. We illustrate the application of the model on a real case study with real data from a leading European Children's Hospital, study the sensitivity of obtained results to the two-week planned grid, and highlight the importance of considering the stochastic nature of the problem.

关键词： Sample average approximation stochastic integer programming Length of stay Post-surgery beds Operating room

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Modeling Ground Firefighting Resource Activities to Manage Risk Given Uncertain Weather

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FORESTS 2019年第12期10卷 1077页

作者： Belval, Erin J. Wei, Yu Bevers, Michael Colorado State Univ Dept Forest & Rangeland Stewardship Ft Collins CO 80523 USA Rist Canyon Consulting LLC POB 65 Bellvue CO 80512 USA

Wildland firefighting requires managers to make decisions in complex decision environments that hold many uncertainties;these decisions need to be adapted dynamically over time as fire behavior evolves. Models used in firefighting decisions should also have the capability to adapt to changing conditions. In this paper, detailed line construction constraints are presented for use with a stochastic mixed integer fire growth and behavior program. These constraints allow suppression actions to interact dynamically with stochastic predicted fire behavior and account for many of the detailed line construction considerations. Such considerations include spatial restrictions for fire crew travel and operations. Crew safety is also addressed;crews must keep a variable safety buffer between themselves and the fire. Fireline quality issues are accounted for by comparing control line capacity with fireline intensity to determine when a fireline will hold. The model assumes crews may work at varying production rates throughout their shifts, providing flexibility to fit work assignments with the predicted fire behavior. Nonanticipativity is enforced to ensure solutions are feasible for all modeled weather scenarios. Test cases demonstrate the model's utility and capability on a raster landscape.

关键词： wildland fire suppression stochastic integer programming fireline construction safety

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Higher-order total variation bounds for expectations of periodic functions and simple integer recourse approximations

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COMPUTATIONAL MANAGEMENT SCIENCE 2018年第3-4期15卷 325-349页

作者： van der Laan, Niels Romeijnders, Ward van der Vlerk, Maarten H. Univ Groningen Dept Operat POB 800 NL-9700 AV Groningen Netherlands

We derive bounds on the expectation of a class of periodic functions using the total variations of higher-order derivatives of the underlying probability density function. These bounds are a strict improvement over those of Romeijnders et al. (Math Program 157:3-46, 2016b), and we use them to derive error bounds for convex approximations of simple integer recourse models. In fact, we obtain a hierarchy of error bounds that become tighter if the total variations of additional higher-order derivatives are taken into account. Moreover, each error bound decreases if these total variations become smaller. The improved bounds may be used to derive tighter error bounds for convex approximations of more general recourse models involving integer decision variables.

关键词： stochastic integer programming Convex approximations Error bounds

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An adaptive model with joint chance constraints for a hybrid wind-conventional generator system

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COMPUTATIONAL MANAGEMENT SCIENCE 2018年第3-4期15卷 563-582页

作者： Singh, Bismark Morton, David P. Santoso, Surya Univ Texas Austin Grad Program Operat Res & Ind Engn Austin TX 78712 USA Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA Univ Texas Austin Dept Elect & Comp Engn Austin TX 78701 USA

We analyze scheduling a hybrid wind-conventional generator system to make it dispatchable, with the aim of profit maximization. Our models ensure that with high probability we satisfy the day-ahead power promised by the model, using combined output of the conventional and wind generators. We consider two scenarios, which differ in whether the conventional generator must commit to its schedule prior to observing the wind-power realizations or has the flexibility to adapt in near real-time to these realizations. We investigate the synergy between the conventional generator and wind farm in these two scenarios. Computationally, the non-adaptive model is relatively tractable, benefiting from a strong extended-variable formulation as an integer program. The adaptive model is a two-stage stochastic integer program with joint chance constraints. Such models have seen limited attention in the literature because of the computational challenges they pose. However, we develop an iterative regularization scheme in which we solve a sequence of sample average approximations under a growing sample size. This reduces computational effort dramatically, and our empirical results suggest that it heuristically achieves high-quality solutions. Using data from a wind farm in Texas, we demonstrate that the adaptive model significantly outperforms the non-adaptive model in terms of synergy between the conventional generator and the wind farm, with expected profit more than doubled.

关键词： stochastic integer programming Chance-constrained optimization Wind power Hybrid renewable system

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Mixed-integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty

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MANAGEMENT SCIENCE 2017年第7期63卷 2073-2091页

作者： Bodur, Merve Luedtke, James R. Univ Toronto Dept Mech & Ind Engn Toronto ON M5S 3G8 Canada Univ Wisconsin Dept Ind & Syst Engn Madison WI 53706 USA

We study server scheduling in multiclass service systems under uncertainty in the customer arrival volumes. Common practice in such systems is to first identify staffing levels and then determine schedules for the servers that cover these levels. We propose a new stochastic integer programming (SIP) model that integrates these two decisions, which can yield lower scheduling costs by exploiting the presence of alternative server configurations that yield similar quality of service. We find that a branch-and-cut algorithm based on Benders decomposition may fail due to the weakness of the relaxation bound. We propose a novel application of mixed-integer rounding to improve the Benders cuts used in this algorithm, a technique that is applicable to any SIP with integer first-stage decision variables. Numerical examples illustrate the computational efficiency of the proposed approach and the potential benefit of solving the integrated model compared to considering the staffing and scheduling problems separately.

关键词： service-system scheduling stochastic integer programming mixed-integer rounding

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Single-ratio fractional integer programs with stochastic right-hand sides

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IISE TRANSACTIONS 2017年第6期49卷 579-592页

作者： Zhang, Junlong Ozaltin, Osman Y. North Carolina State Univ Edward P Fitts Dept Ind & Syst Engn Raleigh NC 27695 USA

We present an equivalent value function reformulation for a class of single-ratio Fractional integer Programs (FIPs) with stochastic right-hand sides and propose a two-phase solution approach. The first phase constructs the value functions of FIPs in both stages. The second phase solves the reformulation using a global branch-and-bound algorithm or a level-set approach. We derive some basic properties of the value functions of FIPs and utilize them in our algorithms. We show that in certain cases our approach can solve instanceswhose extensive forms have the same order ofmagnitude as the largest stochastic quadratic integer programs solved in the literature.

关键词： Fractional integer programming stochastic integer programming value functions superadditive duality

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Platelet Inventory Management in Blood Supply Chains

Platelet Inventory Management in Blood Supply Chains

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作者： Rajendran, Suchithra PennState University Libraries

学位级别：Doctor of Philosophy

It has been shown that a significant amount of platelets is wasted due to their short life after collection, just 5 days. Most of the previous work develop inventory policies based on a known demand pattern over a finite time horizon. Further, they assume that the entire platelet units received by the hospitals from the blood center are fresh (with all 3 days of transfusable life remaining). However, in practice, nearly 50% of the incoming platelets have one day shelf life. This research develops inventory models for the hospitals and the blood center under realistic settings (demand uncertainty, platelets with varying shelf life, finite supply at the blood center) with the objective of minimizing platelet shortage and wastage (due to outdating).In this dissertation, single objective deterministic inventory model is first developed to determine the number of platelet units to order and time between orders at the hospital. The model is extended to multiple objective inventory models at the hospital. The deterministic models are later extended stochastic programming models under demand uncertainty for hospital inventory management. Finally, inventory management along the entire blood supply chain is studied and platelet ordering policies are developed under demand *** to the computational complexity of the stochastic programming model developed for hospital inventory management, three heuristic rules are proposed for determining the platelet ordering policy at the hospital. The performance of these three ordering policies is compared against that of the traditional periodic review order-up-to policy, using real-life data obtained from a medical center. The shelf life of arriving platelets, coefficient of variation of demand and cost parameters are varied, and their impact is analyzed on the performance measures and the best rule with respect to each setting is determined. Based on the hospital setting and cost prioritization, the decision maker can decide

关键词： Platelet wastage stochastic integer programming heuristic ordering policies blood supply chain genetic algorithm

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