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Three Essays on Data-Driven Optimization for Scheduling in Manufacturing and Healthcare
This dissertation consists of three essays on data-driven optimization for scheduling in manufacturing and healthcare. In Chapter 1, we briefly introduce the optimization problems tackled in these essays. The first of these essays deals with machine scheduling problems. In Chapter 2, we compare the effectiveness of direct positional variables against relative positional variables computationally in a variety of machine scheduling problems and we present our results. The second essay deals with a scheduling problem in healthcare: the team primary care practice. In Chapter 3, we build upon the two-stage stochastic integer programming model introduced by Alvarez Oh (2015) to solve this challenging scheduling problem of determining patient appointment times to minimize a weighted combination of patient wait and provider idle times for the team practice. To overcome the computational complexity associated with solving the problem under the large set of scenarios required to accurately capture uncertainty in this setting, our approach relies on a lower bounding technique based on solving an exhaustive and mutually exclusive group of scenario subsets. Our computational results identify the structure of optimal schedules and quantify the impact of nurse flexibility, patient crossovers and no-shows. We conclude with practical scheduling guidelines for team primary care practices. The third essay deals with another scheduling problem observed in a manufacturing setting similar to first essay, this time in aerospace industry. In Chapter 4, we propose mathematical models to optimize scheduling at a tactical and operational level in a job shop at an aerospace parts manufacturer and implement our methods using real-life data collected from this company. We generalize the Multi-Level Capacitated Lot-Sizing Problem (MLCLSP) from the literature and use novel computational techniques that depend on the data structure observed to reduce the size of the problem and solve realistically-sized instances in this chapter. We also provide a sensitivity analysis of different modeling techniques and objective functions using key performance indicators (KPIs) important for the manufacturer. Chapter 5 proposes extensions of models and techniques that are introduced in Chapters 2, 3 and 4 and outlines future research directions. Chapter 6 summarizes our findings and concludes the dissertation
Minimizing sum of completion times on a single machine with sequence-dependent family setup times
This paper presents a branch-and-bound (B&B) algorithm for minimizing the sum of completion times in a singlemachine scheduling setting with sequence-dependent family setup times. The main feature of the B&B algorithm is a new lower bounding scheme that is based on a networkformulation of the problem. With extensive computational tests, we demonstrate that the B&B algorithm can solve problems with up to 60 jobs and 12 families, where setup and processing times are uniformly distributed in various combinations of the [1,50] and [1,100] ranges
Minimizing value-at-risk in the single-machine total weighted tardiness problem
The vast majority of the machine scheduling literature focuses on deterministic
problems, in which all data is known with certainty a priori. This may be a reasonable assumption when the variability in the problem parameters is low. However, as variability in the parameters increases incorporating this uncertainty explicitly into a scheduling model is essential to mitigate the resulting adverse effects. In this paper, we consider the celebrated single-machine total weighted tardiness (TWT) problem in the presence of uncertain problem parameters. We impose a probabilistic constraint on the random TWT and introduce a risk-averse stochastic programming model. In particular, the objective of the proposed model is to find a non-preemptive static job processing sequence that minimizes the value-at-risk (VaR) measure on the random
TWT at a specified confidence level. Furthermore, we develop a lower bound on the optimal VaR that may also benefit alternate solution approaches in the future. In this study, we implement a tabu-search heuristic to obtain reasonably good feasible solutions and present results to demonstrate the effect of the risk parameter and the value of the proposed model with respect to a corresponding risk-neutral approach
An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging
This paper proposes two new mixed integer programming models for capacitated multi-level lot-sizing problems with backlogging, whose linear programming relaxations provide good lower bounds on the optimal solution value. We show that both of these strong formulations yield the same lower bounds. In addition to these theoretical results, we propose a new, effective optimization framework that achieves high quality solutions in reasonable computational time. Computational results show that the proposed optimization framework is superior to other well-known approaches on several important performance dimensions
Better Unrelated Machine Scheduling for Weighted Completion Time via Random Offsets from Non-Uniform Distributions
In this paper we consider the classic scheduling problem of minimizing total
weighted completion time on unrelated machines when jobs have release times,
i.e, using the three-field notation. For this
problem, a 2-approximation is known based on a novel convex programming (J. ACM
2001 by Skutella). It has been a long standing open problem if one can improve
upon this 2-approximation (Open Problem 8 in J. of Sched. 1999 by Schuurman and
Woeginger). We answer this question in the affirmative by giving a
1.8786-approximation. We achieve this via a surprisingly simple linear
programming, but a novel rounding algorithm and analysis. A key ingredient of
our algorithm is the use of random offsets sampled from non-uniform
distributions.
We also consider the preemptive version of the problem, i.e, . We again use the idea of sampling offsets from non-uniform
distributions to give the first better than 2-approximation for this problem.
This improvement also requires use of a configuration LP with variables for
each job's complete schedules along with more careful analysis. For both
non-preemptive and preemptive versions, we break the approximation barrier of 2
for the first time.Comment: 24 pages. To apper in FOCS 201
The Iray Light Transport Simulation and Rendering System
While ray tracing has become increasingly common and path tracing is well
understood by now, a major challenge lies in crafting an easy-to-use and
efficient system implementing these technologies. Following a purely
physically-based paradigm while still allowing for artistic workflows, the Iray
light transport simulation and rendering system allows for rendering complex
scenes by the push of a button and thus makes accurate light transport
simulation widely available. In this document we discuss the challenges and
implementation choices that follow from our primary design decisions,
demonstrating that such a rendering system can be made a practical, scalable,
and efficient real-world application that has been adopted by various companies
across many fields and is in use by many industry professionals today
Resource-constrained project scheduling.
Abstract: Resource-constrained project scheduling involves the scheduling of project activities subject to precedence and resource constraints in order to meet the objective(s) in the best possible way. The area covers a wide variety of problem types. The objective of this paper is to provide a survey of what we believe are important recent in the area . Our main focus will be on the recent progress made in and the encouraging computational experience gained with the use of optimal solution procedures for the basic resource-constrained project scheduling problem (RCPSP) and important extensions. The RCPSP involves the scheduling of a project its duration subject to zero-lag finish-start precedence constraints of the PERT/CPM type and constant availability constraints on the required set of renewable resources. We discuss recent striking advances in dealing with this problem using a new depth-first branch-and-bound procedure, elaborating on the effective and efficient branching scheme, bounding calculations and dominance rules, and discuss the potential of using truncated branch-and-bound. We derive a set of conclusions from the research on optimal solution procedures for the basis RCPSP and subsequently illustrate how effective and efficient branching rules and several of the strong dominance and bounding arguments can be extended to a rich and realistic variety of related problems. The preemptive resource-constrained project scheduling problem (PRCPSP) relaxes the nonpreemption condition of the RCPSP, thus allowing activities to be interrupted at integer points in time and resumed later without additional penalty cost. The generalized resource-constrained project scheduling (GRCPSP) extends the RCPSP to the case of precedence diagramming type of precedence constraints (minimal finish-start, start-start, start-finish, finish-finish precedence relations), activity ready times, deadlines and variable resource availability's. The resource-constrained project scheduling problem with generalized precedence relations (RCPSP-GPR) allows for start-start, finish-start and finish-finish constraints with minimal and maximal time lags. The MAX-NPV problem aims at scheduling project activities in order to maximize the net present value of the project in the absence of resource constraints. The resource-constrained project scheduling problem with discounted cash flows (RCPSP-DC) aims at the same non-regular objective in the presence of resource constraints. The resource availability cost problem (RACP) aims at determining the cheapest resource availability amounts for which a feasible solution exists that does not violate the project deadline. In the discrete time/cost trade-off problem (DTCTP) the duration of an activity is a discrete, non-increasing function of the amount of a single nonrenewable resource committed to it. In the discrete time/resource trade-off problem (DTRTP) the duration of an activity is a discrete, non-increasing function of the amount of a single renewable resource. Each activity must then be scheduled in one of its possible execution modes. In addition to time/resource trade-offs, the multi-mode project scheduling problem (MRCPSP) allows for resource/resource trade-offs and constraints on renewable, nonrenewable and doubly-constrained resources. We report on recent computational results and end with overall conclusions and suggestions for future research.Scheduling; Optimal;
Scheduling to Minimize Total Weighted Completion Time via Time-Indexed Linear Programming Relaxations
We study approximation algorithms for scheduling problems with the objective
of minimizing total weighted completion time, under identical and related
machine models with job precedence constraints. We give algorithms that improve
upon many previous 15 to 20-year-old state-of-art results. A major theme in
these results is the use of time-indexed linear programming relaxations. These
are natural relaxations for their respective problems, but surprisingly are not
studied in the literature.
We also consider the scheduling problem of minimizing total weighted
completion time on unrelated machines. The recent breakthrough result of
[Bansal-Srinivasan-Svensson, STOC 2016] gave a -approximation for the
problem, based on some lift-and-project SDP relaxation. Our main result is that
a -approximation can also be achieved using a natural and
considerably simpler time-indexed LP relaxation for the problem. We hope this
relaxation can provide new insights into the problem
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