Flexible resource allocation for service and production systems - WANG, Peng (Institutional Knowledge at Singapore Management University, 2021)
Resource flexibility hedges against uncertainty in service and production systems. However, flexibility also brings complexity and difficulty in allocating resources. The thesis mainly studies managing flexible resources in two scenarios. The first scenario is a type of coordination of workers in a production or assembly line – bucket brigade. Specifically, the study shows how to manage a stochastic bucket brigade with discrete work stations. The second scenario is a service system with flexible service resources. The study proposes a distributive decision rule for the allocation of resources under both supply and demand uncertainty. Chapter 2 studies a J-station, I-worker bucket brigade with preemptible work content. The time duration for each worker to serve a job at a station is exponentially distributed with a rate that depends on the station’s work content and the worker’s work speed. We analytically derive the throughput and the coefficient of variation (CV) of the inter-completion time. We study the system under three cases. (i) If the work speeds depend only on the workers, the throughput gap between the stochastic and the deterministic systems can be up to 47% when the number of stations is small. (ii) If the work speeds depend on the workers and the stations such that the workers may not dominate each other at every station, the asymptotic throughput can be expressed as a function of two factors. (iii) The work speeds depend on the workers, the stations, and the jobs. There is a trade-off between the intensification of the learning experience and the diversification of the skills. Chapter 3 further studies a J-station, I-worker bucket brigade with non-preemptible work content. If the work content is non-preemptible, the work on each station can not be preempted and has to be processed by the same worker. We properly denote the waiting workers, re-analyze the state of the system, and the transition probability matrix of the reset vectors. Finally, we derive the average throughput. In the numerical experiments, we first verify the theoretical results by simulations. Then we compare the throughput difference between a non-preemptible line and a preemptible line. If the workers are sequenced slowest-to-fastest, the preemptible line dominates the non-preemptible line. However, if the workers are sequenced fastest-to-slowest, the non-preemptible line can possibly dominate the preemptible line. As such, the management needs to consider the actual setting to enhance the performance. Chapter 4 studies a resource allocation problem, where the planner needs to decide simultaneously on both the supply and the allocation policy to fulfill the uncertain demand over a multi-period horizon. We introduce a distributive decision rule, which decides on the proportion of jobs awaiting dispatch to each of the possible resource supply pools. Our model has a convex reformulation that can be solved efficiently. Through simulations, we illustrate that the optimal solution evolves with changes in service distribution, initial conditions, temporal fluctuations in demand, and resource availability. At last, we benchmark our model against the static rule and a fluid model. In doing so, we justify the adaptivity of the proposed distributive decision rule and show the robustness of our model to different settings.