Models and Methodologies to Address Emerging Needs in Network and Supply Chain Optimization

In this dissertation, we model three different security scenarios and propose solution methodologies to address each problem. Chapter 2 presents a large-scale optimization approach for solving a dynamic bi-level network interdiction problem (NIP) in which interdiction activities must be scheduled in order to minimize the cumulative maximum flow over a finite time horizon. A logic-based decomposition (LBD) approach is proposed that utilizes constraint programming to exploit the scheduling nature of this dynamic NIP. Chapter 3 considers a set of centers to which content (e.g., data or smuggled items), are assigned to ensure availability. An interdictor (e.g., border security officials) attempts to determine which centers (e.g., border\u27s checkpoints) to interdict in order to minimize the content availability. We present our efforts to model the problem as an Integer Programming formulation and show that the problem is NP-hard. We propose modeling improvements, which, in conjunction with a genetic algorithm is used to obtain quality solutions to the problem quickly. A comparison of the approaches is presented along with future research direction for the problem. Finally, Chapter 4 pursues a quantitative risk assessment of the complete poultry supply chain in China. This work is supported by collaborators in biological engineering, poultry science and numerous companies and universities throughout China. This effort considers contamination concerns from Salmonella for chicken broilers studied at the production steps in the supply chain as well as offering one of the first attempts to include the transportation, distribution, retail and consumption elements that complete the supply chain. Our quantitative risk assessment model makes use of preliminary data collected from a Chinese poultry company since Fall 2016

DiviML: A Module-based Heuristic for Mapping Neural Networks onto Heterogeneous Platforms

Datacenters are increasingly becoming heterogeneous, and are starting to include specialized hardware for networking, video processing, and especially deep learning. To leverage the heterogeneous compute capability of modern datacenters, we develop an approach for compiler-level partitioning of deep neural networks (DNNs) onto multiple interconnected hardware devices. We present a general framework for heterogeneous DNN compilation, offering automatic partitioning and device mapping. Our scheduler integrates both an exact solver, through a mixed integer linear programming (MILP) formulation, and a modularity-based heuristic for scalability. Furthermore, we propose a theoretical lower bound formula for the optimal solution, which enables the assessment of the heuristic solutions' quality. We evaluate our scheduler in optimizing both conventional DNNs and randomly-wired neural networks, subject to latency and throughput constraints, on a heterogeneous system comprised of a CPU and two distinct GPUs. Compared to na\"ively running DNNs on the fastest GPU, he proposed framework can achieve more than 3$\times$ times lower latency and up to 2.9$\times$ higher throughput by automatically leveraging both data and model parallelism to deploy DNNs on our sample heterogeneous server node. Moreover, our modularity-based "splitting" heuristic improves the solution runtime up to 395$\times$ without noticeably sacrificing solution quality compared to an exact MILP solution, and outperforms all other heuristics by 30-60% solution quality. Finally, our case study shows how we can extend our framework to schedule large language models across multiple heterogeneous servers by exploiting symmetry in the hardware setup. Our code can be easily plugged in to existing frameworks, and is available at https://github.com/abdelfattah-lab/diviml.Comment: accepted at ICCAD'2

Optimization of Healthcare Delivery System under Uncertainty: Schedule Elective Surgery in an Ambulatory Surgical Center and Schedule Appointment in an Outpatient Clinic

This work investigates two types of scheduling problems in the healthcare industry. One is the elective surgery scheduling problem in an ambulatory center, and the other is the appointment scheduling problem in an outpatient clinic. The ambulatory surgical center is usually equipped with an intake area, several operating rooms (ORs), and a recovery area. The set of surgeries to be scheduled are known in advance. Besides the surgery itself, the sequence-dependent setup time and the surgery recovery are also considered when making the scheduling decision. The scheduling decisions depend on the availability of the ORs, surgeons, and the recovery beds. The objective is to minimize the total cost by making decision in three aspects, number of ORs to open, surgery assignment to ORs, and surgery sequence in each OR. The problem is solved in two steps. In the first step, we propose a constraint programming model and a mixed integer programming model to solve a deterministic version of the problem. In the second step, we consider the variability of the surgery and recovery durations when making scheduling decisions and build a two stage stochastic programming model and solve it by an L-shaped algorithm. The stochastic nature of the outpatient clinic appointment scheduling system, caused by demands, patient arrivals, and service duration, makes it difficult to develop an optimal schedule policy. Once an appointment request is received, decision makers determine whether to accept the appointment and put it into a slot or reject it. Patients may cancel their scheduled appointment or simply not show up. The no-show and cancellation probability of the patients are modeled as the functions of the indirect waiting time of the patients. The performance measure is to maximize the expected net rewards, i.e., the revenue of seeing patients minus the cost of patients\u27 indirect and direct waiting as well as the physician\u27s overtime. We build a Markov Decision Process model and proposed a backward induction algorithm to obtain the optimal policy. The optimal policy is tested on random instances and compared with other heuristic policies. The backward induction algorithm and the heuristic methods are programmed in Matlab

Stochastic Optimization Approaches for an Operating Room and Anesthesiologist Scheduling Problem

We propose combined allocation, assignment, sequencing, and scheduling problems under uncertainty involving multiple operation rooms (ORs), anesthesiologists, and surgeries, as well as methodologies for solving such problems. Specifically, given sets of ORs, regular anesthesiologists, on-call anesthesiologists, and surgeries, our methodologies solve the following decision-making problems simultaneously: (1) an allocation problem that decides which ORs to open and which on-call anesthesiologists to call in, (2) an assignment problem that assigns an OR and an anesthesiologist to each surgery, and (3) a sequencing and scheduling problem that determines the order of surgeries and their scheduled start times in each OR. To address uncertainty of each surgery's duration, we propose and analyze stochastic programming (SP) and distributionally robust optimization (DRO) models with both risk-neutral and risk-averse objectives. We obtain near-optimal solutions of our SP models using sample average approximation and propose a computationally efficient column-and-constraint generation method to solve our DRO models. In addition, we derive symmetry-breaking constraints that improve the models' solvability. Using real-world, publicly available surgery data and a case study from a health system in New York, we conduct extensive computational experiments comparing the proposed methodologies empirically and theoretically, demonstrating where significant performance improvements can be gained. Additionally, we derive several managerial insights relevant to practice

On the Scalability of Constraint Solving for Static/Off-Line Real-Time Scheduling

Recent papers have reported on successful application of constraint solving techniques to off-line real-time scheduling problems, with realistic size and complexity. Success allegedly came for two reasons: major recent advances in solvers efficiency and use of optimized, problem-specific constraint representations. Our current objective is to assess further the range of applicability and the scalability of such constraint solving techniques based on a more general and agnostic evaluation campaign. For this, we have considered a large number of synthetic scheduling problems and a few real-life ones, and attempted to solve them using 3 state-of-the-art solvers, namely CPLEX, Yices2, and MiniZinc/G12. Our findings were that, for all problems considered, constraint solving does scale to a certain limit, then diverges rapidly. This limit greatly depends on the specificity of the scheduling problem type. All experimental data (synthetic task systems, SMT/ILP models) are provided so as to allow experimental reproducibility

On the Scalability of Constraint Solving for Static/Off-Line Real-Time Scheduling

International audienceRecent papers have reported on successful application of constraint solving techniques to off-line real-time scheduling problems, with realistic size and complexity. Success allegedly came for two reasons: major recent advances in solvers efficiency and use of optimized, problem-specific constraint representations. Our current objective is to assess further the range of applicability and the scalability of such constraint solving techniques based on a more general and agnostic evaluation campaign. For this, we have considered a large number of synthetic scheduling problems and a few real-life ones, and attempted to solve them using 3 state-of-the-art solvers, namely CPLEX, Yices2, and MiniZinc/G12. Our findings were that, for all problems considered, constraint solving does scale to a certain limit, then diverges rapidly. This limit greatly depends on the specificity of the scheduling problem type. All experimental data (synthetic task systems, SMT/ILP models) are provided so as to allow experimental reproducibility

A stochastic programming approach for chemotherapy appointment scheduling

Chemotherapy appointment scheduling is a challenging problem due to the uncertainty in pre-medication and infusion durations. In this paper, we formulate a two-stage stochastic mixed integer programming model for the chemotherapy appointment scheduling problem under limited availability and number of nurses and infusion chairs. The objective is to minimize the expected weighted sum of nurse overtime, chair idle time, and patient waiting time. The computational burden to solve real-life instances of this problem to optimality is significantly high, even in the deterministic case. To overcome this burden, we incorporate valid bounds and symmetry breaking constraints. Progressive hedging algorithm is implemented in order to solve the improved formulation heuristically. We enhance the algorithm through a penalty update method, cycle detection and variable fixing mechanisms, and a linear approximation of the objective function. Using numerical experiments based on real data from a major oncology hospital, we compare our solution approach with several scheduling heuristics from the relevant literature, generate managerial insights related to the impact of the number of nurses and chairs on appointment schedules, and estimate the value of stochastic solution to assess the significance of considering uncertainty

Combinatorial optimisation for sustainable cloud computing

Enabled by both software and hardware advances, cloud computing has emerged as an efficient way to leverage economies of scale for building large computational infrastructures over a global network. While the cost of computation has dropped significantly for end users, the infrastructure supporting cloud computing systems has considerable economic and ecological costs. A key challenge for sustainable cloud computing systems in the near future is to maintain control over these costs. Amid the complexity of cloud computing systems, a cost analysis reveals a complex relationship between the infrastructure supporting actual computation on a physical level and how these physical assets are utilised. The central question tackled in this dissertation is how to best utilise these assets through efficient workload management policies. In recent years, workload consolidation has emerged as an effective approach to increase the efficiency of cloud systems. We propose to address aspects of this challenge by leveraging techniques from the realm of mathematical modeling and combinatorial optimisation. We introduce a novel combinatorial optimisation problem suitable for modeling core consolidation problems arising in workload management in data centres. This problem extends on the well-known bin packing problem. We develop competing models and optimisation techniques to solve this offline packing problem with state-of-the-art solvers. We then cast this newly defined combinatorial optimisation problem in an semi-online setting for which we propose an efficient assignment policy that is able to produce solutions for the semi-online problem in a competitive computational time. Stochastic aspects, which are often faced by cloud providers, are introduced in a richer model. We then show how predictive methods can help decision makers dealing with uncertainty in such dynamic and heterogeneous systems. We explore a similar but relaxed problem falling within the scope of proactive consolidation. This is a relaxed consolidation problem in which one decides which, when and where workload should be migrated to retain minimum energy cost. Finally, we discuss ongoing efforts to model and characterise the combinatorial hardness of bin packing instances, which in turn will be useful to study the various packing problems found in cloud computing environments