Optimization of Inventory and Capacity in Large-Scale Assembly Systems Using Extreme-Value Theory

High-tech systems are typically produced in two stages: (1) production of components using specialized equipment and staff and (2) system assembly/integration. Component production capacity is subject to fluctuations, causing a high risk of shortages of at least one component, which results in costly delays. Companies hedge this risk by strategic investments in excess production capacity and in buffer inventories of components. To optimize these, it is crucial to characterize the relation between component shortage risk and capacity and inventory investments. We suppose that component production capacity and produce demand are normally distributed over finite time intervals, and we accordingly model the production system as a symmetric fork-join queueing network with N statistically identical queues with a common arrival process and independent service processes. Assuming a symmetric cost structure, we subsequently apply extreme value theory to gain analytic insights into this optimization problem. We derive several new results for this queueing network, notably that the scaled maximum of N steady-state queue lengths converges in distribution to a Gaussian random variable. These results translate into asymptotically optimal methods to dimension the system. Tests on a range of problems reveal that these methods typically work well for systems of moderate size

Essays in Operations Management: Applications in Health Care and the Operations-Finance Interface

I present three essays pertaining to the management of supply chain risks in this dissertation. The first essay and the second essay analyze supply chain risks from a financial perspective, while the third essay analyzes supply chain risk with the objective of maximizing societal benefits in health care. In my first essay, I consider a firm facing inventory decisions under the influence of the financial market. With stochastic analytical methods, the purpose of this essay is to examine the optimal inventory decisions under a variety of conditions. I have identified the relevant factors impacting such decisions and the firm's value. Moreover, I have studied the benefits brought by efforts to improve the random capacity of the firm. I conclude that the financial market can significantly impact both a firm's inventory decisions and process improvement incentives. In my second essay, I model a stylized supply chain managed by a base-stock inventory policy where the decision maker holds concerns about the down-side risk of the supply chain cost. With stochastic analytical methods, the purpose of this essay is to obtain solutions of the problem of minimizing Conditional Value-at-Risk under various supply chain scenarios. I find that various supply chain parameters may influence the optimal solution and the optimality of a stock-less operation. I conclude that operating characteristics of a supply chain can shape its inventory policy when down-side risks are taken into account. For my third essay, the purpose of this essay is to investigate the operational decisions of a medical center specializing in bone marrow transplants. Using the queuing system method, I formulate the medical center as a queuing system with random patient arrivals and departures. I find optimal decisions and efficient frontiers regarding waiting room size and the number of transplant rooms with the objective of maximizing patient health benefits. I conclude that the design of a health care delivery system is crucial for health care institutions to sustain and improve their social impacts. In each of the three essays, I use analytical and numerical approaches to optimize managers' decisions with respect to various sources of risk

On Production and Subcontracting Strategies for Manufacturers with Limited Capacity and Backlog-Dependent Demand

We study a manufacturing firm that builds a product to stock to meet a random demand. If there is a positive surplus of finished goods, the customers make their purchases without delay and leave. If there is a backlog, the customers are sensitive to the quoted lead time and some choose not to order if they feel that the lead time is excessive. A set of subcontractors, who have different costs and capacities, are available to supplement the firm's own production capacity. We derive a feedback policy that determines the production rate and the rate at which the subcontractors are requested to deliver products. The performance of the system when it is managed according to this policy is evaluated. The subcontractors represent a set of capacity options, and we calculate the values of these options

Serial production line performance under random variation:Dealing with the ‘Law of Variability’

Many Queueing Theory and Production Management studies have investigated specific effects of variability on the performance of serial lines since variability has a significant impact on performance. To date, there has been no single summary source of the most relevant research results concerned with variability, particularly as they relate to the need to better understand the ‘Law of Variability’. This paper fills this gap and provides readers the foundational knowledge needed to develop intuition and insights on the complexities of stochastic simple serial lines, and serves as a guide to better understand and manage the effects of variability and design factors related to improving serial production line performance, i.e. throughput, inter-departure time and flow time, under random variation

Optimizing the Performance of Robotic Mobile Fulfillment Systems

A robotic mobile fulfillment system is a novel type of automated part-to-picker material handling system. In this type of system, robots transport mobile shelves, called pods, containing items between the storage area and the workstations. It is well suited to e-commerce, due to its modularity and it's ability to adapt to changing orders patterns. Robots can nearly instantaneously switch between inbound and outbound tasks, pods can be continually repositioned to allow for automatic sorting of the inventory, pods can contain many different types of items, and unloaded robots can drive underneath pods, allowing them to use completely different routes than loaded robots. This thesis studies the performance of robotic mobile fulfillment systems by solving decision problems related to warehouse design, inventory and resource allocation, and real-time operations. For warehouse design, a new queueing network is developed that incorporates realistic robot movement, storage zones, and multi-line orders. For inventory allocation, we develop a new type of queueing network, the cross-class matching multi-class semi-open queueing network, which can be applied to other systems as well. Resource (re)allocation is modeled by combining queueing networks with Markov decision processes while including time-varying demand. This model compares benchmark policies from practice wit

Service Co-Production, Customer Efficiency and Market Competition

Customers’ participation in service co-production processes has been increasing with the rapid development of self-service technologies and business models that rely on self-service as the main service delivery channel. However, little is known about how the level of participation of customers in service delivery processes influences the competition among service providers. In this paper, a game-theoretic model is developed to study the competition among service providers when selfservice is an option. The analysis of the equilibria from this model shows that, given a certain level of customer efficiency, the proportion of the service task outsourced to the customer is a decisive factor in the resulting competitive equilibria. In the long run, two extreme formats of service delivery are expected to prevail rather than any mixture of both: either complete employee service or complete self-service. In the two-firm queuing game, we find that both firms are better off when they both deliver their service through self-service. It is also shown that full-service providers dominate the market if firms providing service products featuring self-service fail to have enough market demand at a profitable price. Meanwhile, the limited ranges of customer efficiency and the price for the self-service-only product are shown to be essential conditions for the coexistence of the different types of service providers.

Throughput and Yield Improvement for a Continuous Discrete-Product Manufacturing System

A seam-welded steel pipe manufacturing process has mainly four distinct major design and/or operational problems dealing with buffer inventory, cutting tools, pipe sizing and inspection-rework facility. The general objective of this research is to optimally solve these four important problems to improve the throughput and yield of the system at a minimum cost. The first problem of this research finds the optimal buffer capacity of steel strip coils to minimize the maintenance and downtime related costs. The total cost function for this coil feeding system is formulated as a constrained non-linear programming (NLP) problem which is solved with a search algorithm. The second problem aims at finding the optimal tool magazine reload timing, magazine size and the order quantity for the cutting tools. This tool magazine system is formulated as a mixed-integer NLP problem which is solved for minimizing the total cost. The third problem deals with different type of manufacturing defects. The profit function of this problem forms a binary integer NLP problem which involves multiple integrals with several exponential and discrete functions. An exhaustive search method is employed to find the optimum strategy for dealing with the defects and pipe sizing. The fourth problem pertains to the number of servers and floor space allocations for the off-line inspection-rework facility. The total cost function forms an integer NLP structure, which is minimized with a customized search algorithm. In order to judge the impact of the above-mentioned problems, an overall equipment effectiveness (OEE) measure, coined as monetary loss based regression (MLBR) method, is also developed as the fifth problem to assess the performance of the entire manufacturing system. Finally, a numerical simulation of the entire process is conducted to illustrate the applications of the optimum parameters setting and to evaluate the overall effectiveness of the simulated system. The successful improvement of the simulated system supports this research to be implemented in a real manufacturing setup. Different pathways shown here for improving the throughput and yield of industrial systems reflect not only to the improvement of methodologies and techniques but also to the advancement of new technology and national economy