Supply chain network design under uncertainty and risk

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.We consider the research problem of quantitative support for decision making in supply chain network design (SCND). We first identify the requirements for a comprehensive SCND as (i) a methodology to select uncertainties, (ii) a stochastic optimisation model, and (iii) an appropriate solution algorithm. We propose a process to select a manageable number of uncertainties to be included in a stochastic program for SCND. We develop a comprehensive two-stage stochastic program for SCND that includes uncertainty in demand, currency exchange rates, labour costs, productivity, supplier costs, and transport costs. Also, we consider conditional value at risk (CV@R) to explore the trade-off between risk and return. We use a scenario generator based on moment matching to represent the multivariate uncertainty. The resulting stochastic integer program is computationally challenging and we propose a novel iterative solution algorithm called adaptive scenario refinement (ASR) to process the problem. We describe the rationale underlying ASR, validate it for a set of benchmark problems, and discuss the benefits of the algorithm applied to our SCND problem. Finally, we demonstrate the benefits of the proposed model in a case study and show that multiple sources of uncertainty and risk are important to consider in the SCND. Whereas in the literature most research is on demand uncertainty, our study suggests that exchange rate uncertainty is more important for the choice of optimal supply chain strategies in international production networks. The SCND model and the use of the coherent downside risk measure in the stochastic program are innovative and novel; these and the ASR solution algorithm taken together make contributions to knowledge

Virtual power plant models and electricity markets - A review

In recent years, the integration of distributed generation in power systems has been accompanied by new facility operations strategies. Thus, it has become increasingly important to enhance management capabilities regarding the aggregation of distributed electricity production and demand through different types of virtual power plants (VPPs). It is also important to exploit their ability to participate in electricity markets to maximize operating profits. This review article focuses on the classification and in-depth analysis of recent studies that propose VPP models including interactions with different types of energy markets. This classification is formulated according to the most important aspects to be considered for these VPPs. These include the formulation of the model, techniques for solving mathematical problems, participation in different types of markets, and the applicability of the proposed models to real case studies. From the analysis of the studies, it is concluded that the most recent models tend to be more complete and realistic in addition to featuring greater diversity in the types of electricity markets in which VPPs participate. The aim of this review is to identify the most profitable VPP scheme to be applied in each regulatory environment. It also highlights the challenges remaining in this field of study

Robust Optimization Framework to Operating Room Planning and Scheduling in Stochastic Environment

Arrangement of surgical activities can be classified as a three-level process that directly impacts the overall performance of a healthcare system. The goal of this dissertation is to study hierarchical planning and scheduling problems of operating room (OR) departments that arise in a publicly funded hospital. Uncertainty in surgery durations and patient arrivals, the existence of multiple resources and competing performance measures are among the important aspect of OR problems in practice. While planning can be viewed as the compromise of supply and demand within the strategic and tactical stages, scheduling is referred to the development of a detailed timetable that determines operational daily assignment of individual cases. Therefore, it is worthwhile to put effort in optimization of OR planning and surgical scheduling. We have considered several extensions of previous models and described several real-world applications. Firstly, we have developed a novel transformation framework for the robust optimization (RO) method to be used as a generalized approach to overcome the drawback of conventional RO approach owing to its difficulty in obtaining information regarding numerous control variable terms as well as added extra variables and constraints into the model in transforming deterministic models into the robust form. We have determined an optimal case mix planning for a given set of specialties for a single operating room department using the proposed standard RO framework. In this case-mix planning problem, demands for elective and emergency surgery are considered to be random variables realized over a set of probabilistic scenarios. A deterministic and a two-stage stochastic recourse programming model is also developed for the uncertain surgery case mix planning to demonstrate the applicability of the proposed RO models. The objective is to minimize the expected total loss incurred due to postponed and unmet demand as well as the underutilization costs. We have shown that the optimum solution can be found in polynomial time. Secondly, the tactical and operational level decision of OR block scheduling and advance scheduling problems are considered simultaneously to overcome the drawback of current literature in addressing these problems in isolation. We have focused on a hybrid master surgery scheduling (MSS) and surgical case assignment (SCA) problem under the assumption that both surgery durations and emergency arrivals follow probability distributions defined over a discrete set of scenarios. We have developed an integrated robust MSS and SCA model using the proposed standard transformation framework and determined the allocation of surgical specialties to the ORs as well as the assignment of surgeries within each specialty to the corresponding ORs in a coordinated way to minimize the costs associated with patients waiting time and hospital resource utilization. To demonstrate the usefulness and applicability of the two proposed models, a simulation study is carried utilizing data provided by Windsor Regional Hospital (WRH). The simulation results demonstrate that the two proposed models can mitigate the existing variability in parameter uncertainty. This provides a more reliable decision tool for the OR managers while limiting the negative impact of waiting time to the patients as well as welfare loss to the hospital

A MILP model for an integrated project scheduling and multi-skilled workforce allocation with flexible working hours

In this paper, we integrate two decision problems arising in various applications such as production planning and project management: the project scheduling problem, which consists in scheduling a set of precedence-constrained tasks, where each task requires executing a set of skills to be performed, and the workforce allocation problem which includes assigning workers as scarce resources to the skills of each task. These two problems are interrelated as the tasks durations are not predefined, but depend on the number of workers assigned to that task as well as their skill levels. We here present a mixed integer linear programming model that considers important real life aspects related to the flexibility in the use of human resources, such as multi-skilled workers whose skill levels are different and measured by their efficiencies. Hence, execution times of the same workload by different workers vary according to these efficiencies. Moreover, the model considers the flexible working time of employees; i.e. the daily and weekly workload of a given worker may vary from one period to another according to the work required. Furthermore, efficient team building is incorporated in this model; i.e. assigning an expert worker and one or more apprentice worker(s) together with the purpose of skill development thanks to knowledge transfer. A numerical example is provided to check the performance of the model

Interdisciplinary Space Logistics Optimization Framework for Large-Scale Space Exploration

As low-cost rocket launch technologies and space resource utilization systems emerge, human space exploration is attracting increasing interest from industry, government, and academia. To extend the domain of human activity beyond the low-Earth orbit and maintain a long-term human presence in cislunar space and eventually Mars, we need to build a sustainable and affordable interplanetary space transportation system. It requires a campaign-level perspective for space mission design in addition to the conventional mission-level perspective. This thesis first proposes an integrated space logistics framework to enable concurrent optimization of space transportation scheduling, spacecraft sizing, space infrastructure design and deployment. Then, a periodic time-expanded network is built to resolve the scalability issue in the time dimension for long-term space exploration missions. After establishing efficient space logistics optimization frameworks, we switch our focus to space infrastructure technology trade studies to consider space infrastructure design from the subsystem-level. A multi-fidelity optimization method is introduced to guarantee optimization accuracy while improving computational efficiency. Finally, a flexibility management framework is proposed to handle uncertainties in space mission planning and operations. Multiple case studies for human lunar and Mars exploration campaigns are conducted leveraging the proposed methods and frameworks to demonstrate their values and potential impacts. This research resolves the grand challenge of space logistics mission design for future large-scale multi-mission space campaigns.Ph.D

Optimal staffing under an annualized hours regime using Cross-Entropy optimization

This paper discusses staffing under annualized hours. Staffing is the selection of the most cost-efficient workforce to cover workforce demand. Annualized hours measure working time per year instead of per week, relaxing the restriction for employees to work the same number of hours every week. To solve the underlying combinatorial optimization problem this paper develops a Cross-Entropy optimization implementation that includes a penalty function and a repair function to guarantee feasible solutions. Our experimental results show Cross-Entropy optimization is efficient across a broad range of instances, where real-life sized instances are solved in seconds, which significantly outperforms an MILP formulation solved with CPLEX. In addition, the solution quality of Cross-Entropy closely approaches the optimal solutions obtained by CPLEX. Our Cross-Entropy implementation offers an outstanding method for real-time decision making, for example in response to unexpected staff illnesses, and scenario analysis

River Basin Water Quality Management Models: A State-of-the-Art Review

With the increasing human activities within river basins, the problem of water quality management is becoming increasingly important. Quality management can be achieved through control/prevention measures that have various economic and water quality implications. To facilitate the analysis of available management options, decision models are needed which represent the many facets of the problem. Such models must be capable of adequately depicting the hydrological, chemical and biological processes occurring in the river; while incorporating social, economic and political considerations within the decision framework. Management analyses can be performed using simulation, optimization, or both, depending on the management goal and the size and type of the problem. The critical issues in a management model are the nonlinearities, uncertainties, multiple pollutant nature of waste discharges, multiple objectives, and the spatial and temporal distribution of management actions. Literature on various management models were reviewed under the headings of linear, nonlinear and dynamic programming approaches; their stochastic counterparts, and combined or miscellaneous approaches. Dynamic programming was found to be an attractive methodology which can exploit the sequential decision problem pertaining to river basin water quality problems (downstream control actions do not influence water quality upstream). DP handles discrete decision variables which represent discrete management alternatives, and it is generic in the sense that both linear and non-linear water quality models expressing the relation between emissions and ambient quality levels can be incorporated. An example problem is presented which demonstrates the application of a DP-based management model to formulate least-cost strategies for the Nitra River basin in Slovakia. However, it is hardly possible for a single model to represent all the aspects of a complex decision problem. Different types of management models (e.g. deterministic vs stochastic models) have different capabilities and limitations. The only way to compensate for the deficiencies is to perform the analysis in a sensitivity style. The necessity for sensitivity analyses is further implied due to the fact that water quality problems are rather loosely formulated with respect to the quality and economic goals

The value of flexibility for pulp mills investing in energy efficiency and future biorefinery concepts

Changing conditions in biomass and energy markets require the pulp and paper industry to improve energy efficiency and find new opportunities in biorefinery implementation. Considering the expected changes in the pulp mill environment and the variety of potential technology pathways, flexibility should be a strong advantage for pulp mills. In this context, flexibility is defined as the ability of the pulp mill to respond to changing conditions. The aim of this article is to show the potential value of flexibility in the planning of pulp mill energy and biorefinery projects and to demonstrate how this value can be incorporated into models for optimal strategic planning of such investments. The paper discusses the requirements on the optimization models in order to adequately capture the value of flexibility. It is suggested that key elements of the optimization model are multiple points in time where investment decisions can be made as well as multiple scenarios representing possible energy price changes over time. The use of a systematic optimization methodology that incorporates these model features is illustrated by a case study, which includes opportunities for district heating cooperation as well as for lignin extraction and valorization. A quantitative valuation of flexibility is provided for this case study. The study also demonstrates how optimal investment decisions for a pulp mill today are influenced by expected future changes in the markets for energy and bioproducts