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作者： Woodaman, Ronald F. A. George Mason University

学位级别：Ph.D.

This thesis describes the research conducted to support the optimal selection of a portfolio of military solutions during wartime. During peacetime, the United States military selects a portfolio of military solutions holistically as part of an annual budgetary planning cycle supported by long-term planning. During wartime, this annual review and decision process is not responsive to the rapid cycles of battlefield adaptation and the resulting exploitation of opposing capability gaps by adversaries. The long-running vulnerability of U.S. forces in Iraq and Afghanistan to Improvised Explosive Device (IED) attacks, as the threat's tactics and techniques evolved during these conflicts, provides a poignant example. During conflict, opportunities to improve the force arrive irregularly over time and are difficult to anticipate. When potential solutions are identified, these must be rapidly pursued, subject to resource constraints. Bad decisions early rob resources from better opportunities that arrive later, while good opportunities unduly delayed may lead to lost opportunities on the battlefield. We develop quantitative methods to support decision makers in the optimal selection of solutions in this context, employing as our motivating case study the challenges faced by the United States Department of Defense's Joint Improvised Explosive Device Defeat Organization (JIEDDO). For example, in fiscal year 2013, the JIEDDO budget was $1.6 billion. This organization had to make counter-IED solution selection decisions continuously as these arrived, without knowing precisely what other opportunities might occur in the future months. Two key aspects of this problem are how to measure the military value of potential solutions, and how to make the best choices as opportunities arrive. Correspondingly, this dissertation examines these two sides: valuation of war-fighting solutions in an uncertain and time-sensitive context, and, given a valuation method, methods for optimal sequen

关键词： Operations research Statistics Computer science approximate dynamic programming dynamic stochastic knapsack problem multi-objective decision analysis sequential decision analysis stochastic integer programming stochastic optimization

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A Polynomial-Time Algorithm for Optimizing over N-Fold 4-Block Decomposable integer Programs

A Polynomial-Time Algorithm for Optimizing over <i>N</i>-Fol...

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14th International Conference integer programming and Combinatorial Optimization

作者： Hemmecke, Raymond Koeppe, Matthias Weismantel, Robert Tech Univ Munich D-8000 Munich Germany Univ Calif Davis CA USA ETH Zurich Switzerland

ISBN: (纸本)9783642130359

In this paper we generalize N-fold integer programs and two-stage integer programs with AT scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time solvable for any linear objective. Moreover, we present a polynomial-time computable optimality certificate for the case of fixed blocks, variable N and any convex separable objective function. We conclude with two sample applications, stochastic integer programs with second-order dominance constraints and stochastic integer multi-commodity flows, which (for fixed blocks) can be solved in polynomial time in the number of scenarios and commodities and in the binary encoding length of the input data. In the proof of our main theorem we combine several non-trivial constructions from the theory of Graver bases. We are confident that our approach paves the way for further extensions.

关键词： N-fold integer programs Graver basis augmentation algorithm polynomial-time algorithm stochastic multi-commodity flow stochastic integer programming

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Block-based outpatient clinic appointments scheduling under open-access policy

Block-based outpatient clinic appointments scheduling under ...

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作者： Fu, Yu Texas A&M University

学位级别：Ph.D.

Outpatient clinic appointment scheduling is an important topic in OR/IE studies. Open-access policy shows its strength in improving patient access and satisfaction, as well as reducing no-show rate. The traditional far-in-advance scheduling plays an important role in handling chronic and follow-up care. This dissertation discusses a hybrid policy under which a clinic deals with three types of patients. The first type of patients are those who request their appointments before the visit day. The second type of patients schedule their appointment on the visit day. The third type of patients are walk-in patients who go to the clinic without appointments and wait to see the physician in turn. In this dissertation, the online scheduling policy is addressed for the Type 2 and Type 3 patients, and the offline scheduling policy is used for the Type 1 patients. For the online scheduling policy, two stochastic integer programming (SIP) models are built under two different sets of assumptions. The first set of assumptions ignores the endogenous uncertainty in the problem. An aggregate assigning method is proposed with the deterministic equivalent problem (DEP) model. This method is demonstrated to be better than the traditional one-at-a-time assignment through both overestimation and underestimation numerical examples. The DEP formulations are solved using the proposed bound-based sampling method, which provides approximated solutions and reasonable sample size with the least gap between lower and upper bound of the original objective value. On the basis of the first set of assumptions and the SIP model, the second set of assumptions considers patient no-shows, preference, cancellations and lateness, which introduce endogenous uncertainty into the SIP model. A modified L-shaped method and aggregated multicut L-shaped method are designed to handle the model with decision dependent distribution parameter. Distinctive optimality cut generation schemes are proposed for three types

关键词： appointment scheduling open-access policy stochastic integer programming endogenous uncertainty L-shaped method aggregated multicut L-shaped method job shop maximum independent set bin packing GRASP simulated annealing Thesis

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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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Decomposition methods for stochastic integer programs with dominance constraints 8

Decomposition methods for stochastic integer programs with d...

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8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2009

作者： Schultz, Rüdiger Department of Mathematics University of Duisburg-Essen Lotharstr. 65 DuisburgD-47048 Germany

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Models and Methods for Multiple Resource Constrained Job Scheduling under Uncertainty

Models and Methods for Multiple Resource Constrained Job Sch...

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作者： Keller, Brian University of Arizona

学位级别：master

We consider a scheduling problem where each job requires multiple classes of resources, which we refer to as the multiple resource constrained scheduling problem(MRCSP). Potential applications include team scheduling problems that arise in service industries such as consulting and operating room scheduling. We focus on two general cases of the problem. The first case considers uncertainty of processing times, due dates, and resource availabilities consumption, which we denote as the stochastic MRCSP with uncertain parameters (SMRCSP-U). The second case considers uncertainty in the number of jobs to schedule, which arises in consulting and defense contracting when companies bid on future contracts but may or may not win the bid. We call this problem the stochastic MRCSP with job bidding (SMRCSP-JB).We first provide formulations of each problem under the framework of two-stage stochastic programming with recourse. We then develop solution methodologies for both problems. For the SMRCSP-U, we develop an exact solution method based on the L-shaped method for problems with a moderate number of scenarios. Several algorithmic enhancements are added to improve efficiency. Then, we embed the L-shaped method within a sampling-based solution method for problems with a large number of scenarios. We modify a sequential sampling procedure to allowfor approximate solution of integer programs and prove desired properties. The sampling-based method is applicable to two-stage stochastic integer programs with integer first-stage variables. Finally, we compare the solution methodologies on a set of test *** SMRCSP-JB, we utilize the disjunctive decomposition (D2 ) algorithm for stochastic integer programs with mixed-binary subproblems. We develop several enhancements to the D2 algorithm. First, we explore the use of a cut generation problem restricted to a subspace of the variables, which yields significant computational savings. Then, we examine generating alternative disjunc

关键词： disjunctive decomposition sampling stochastic integer programming stochastic scheduling

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Single Period Profit Maximization Problem for Intermediaries in Telecommunication Networks Under stochastic Bandwidth Demand

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JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING 2013年第3-4期21卷 287-315页

作者： Turan, Hasan Huseyin Kasap, Nihat Serarslan, Mehmet Nahit Univ Yalova Dept Ind Engn TR-77100 Yalova Turkey Sabanci Univ Sch Management TR-34956 Istanbul Turkey Istanbul Tech Univ Dept Ind Engn TR-34367 Istanbul Turkey

During the last decade telecommunications market has become a very competitive environment, with a great many vendors, carriers, and services provided. The Intermediaries are one of the main players in the telecom network market, and they may acquire network capacity from a set of telecommunication Backbone Providers that offer different pricing and quality of service schemes and sell purchased capacity to end-users in order to make a profit. Unfortunately, the bandwidth demands of customers are not known in advance. Therefore, Intermediaries may end up having either slack capacity or unsatisfied customer demands. In this paper, to overcome these problems, a two-stage stochastic integer programming approach is proposed. The performance of suggested method is validated on several randomly generated scenarios. In addition, the effects of different bandwidth demand distributions are examined by using well-known measures such as Expected Value of Perfect Information (EVPI) and Value of stochastic Solution (VSS). The robustness of methodology is evaluated by carrying out sensitivity analysis on different problem parameters.

关键词： telecommunication intermediaries stochastic integer programming pricing schemes quality of service

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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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Resource distribution under spatiotemporal uncertainty of disease spread: stochastic versus robust approaches

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COMPUTERS & OPERATIONS RESEARCH 2023年 149卷

作者： Basciftci, Beste Yu, Xian Shen, Siqian Univ Iowa Tippie Coll Business Dept Business Analyt Iowa City IA 52242 USA Ohio State Univ Dept Integrated Syst Engn Columbus OH USA Univ Michigan Ann Arbor Dept Ind & Operat Engn Ann Arbor MI USA

We consider the problem of optimizing locations of distribution centers (DCs) and plans for distributing resources such as test kits and vaccines, under spatiotemporal uncertainties of disease spread and demand for the resources. We aim to balance the operational cost (including costs of deploying facilities, shipping, and storage) and quality of service (reflected by demand coverage), while ensuring equity and fairness of resource distribution across multiple populations. We compare a sample-based stochastic programming (SP) approach with a distributionally robust optimization (DRO) approach using a moment-based ambiguity set. Numerical studies are conducted on instances of distributing COVID-19 vaccines in the United States and test kits, to compare SP and DRO models with a deterministic formulation using estimated demand and with the current resource distribution plans implemented in the US. We demonstrate the results over distinct phases of the pandemic to estimate the cost and speed of resource distribution depending on scale and coverage, and show the "demand-driven"properties of the SP and DRO solutions. Our results further indicate that if the worst-case unmet demand is prioritized, then the DRO approach is preferred despite of its higher overall cost. Nevertheless, the SP approach can provide an intermediate plan under budgetary restrictions without significant compromises in demand coverage.

关键词： COVID-19 pandemic Vaccine distribution Resource allocation stochastic integer programming Distributionally robust optimization Multi-objective optimization

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Heterogeneous Multi-resource Planning and Allocation Under stochastic Demand

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INFORMS JOURNAL ON COMPUTING 2023年第5期35卷 929-951页

作者： Baxter, Arden Keskinocak, Pinar Singh, Mohit Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA Georgia Inst Technol Ctr Hlth & Humanitarian Syst Atlanta GA 30332 USA

We study the capacity planning and allocation decisions for multiple heterogeneous resources, considering potential demand scenarios, where each demand requests a subset of the available resource types simultaneously at a specified time, location, and duration (smRmD). We model this problem as a two-stage stochastic integer program and consider two variants for the objective function: (a) maximize the expected reward of demands met over all scenarios, subject to a budget B for resources, and (b) maximize the expected reward of demands met over all scenarios minus the cost of resources. Contributions of this work include (i) a thorough complexity analysis of smRmD and its variants, (ii) analysis of structural properties, (iii) development of various approximation algorithms using the unique structural properties of smRmD and its variants, and (iv) an extensive computational study to explore the ease with which exact and approximate solutions may be found.

关键词： stochastic integer programming resource allocation resource planning approximation algorithms

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