Dynamic resource allocation in manufacturing and service industries
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In this thesis, we study three applications of dynamic resource allocation: the first two consider dynamic lead-time quotation in make-to-order (MTO) systems with substitutable products and order cancellations, respectively; and the third application is a manpower allocation problem with job-teaming constraints. Matching supply and demand for manufacturing and service industries has been a fundamental focus of operations management literature, which concentrated on optimizing or improving supply-side decisions since demand has generally been assumed to be exogenously determined. However, recent business trends and advances in consumer behavior modeling have shown that demand for goods and services can clearly be shaped by various decisions that a firm makes, such as price and lead-time. In fact, competition between companies is no longer mainly based on price or product features; lead-time is one of the strategic measures to evaluate suppliers. In MTO manufacturing or service environments that aim to satisfy the customers' unique needs, lead-time quotation impacts the actual demand of the products and the overall profitability of the firm. In the first two parts of the thesis, we study the dynamic lead-time quotation problem in pure MTO (or service) systems characterized by lead-time sensitive Poisson demand and exponentially distributed service times. We formulate the problem as an infinite horizon Markov decision process (MDP) with the objective of maximizing the long-run expected average profit per unit time, where profits are defined to specifically account for delays in delivery of the customer orders. We study dynamic lead-time quotation problem in two particular settings; one setting with the possibility of demand substitution and another setting with order cancellations. The fundamental trade-off in lead-time quotation is between quoting short lead-times and attaining them. In case of demand substitution, i.e., in presence of substitutable products and multiple customer classes with different requirements and margins, this trade-off also includes capacity allocation and order acceptance decisions. In particular, one needs to decide whether to allocate capacity to a low-margin order now, or whether to reserve capacity for potential future arrivals of high-margin orders by considering customer preferences, the current workload in the system, and the future arrivals. In the case of order cancellations, one needs to take into account the probability of cancellation of orders currently in the system and quote lead-times accordingly; otherwise quotation of a longer lead-time may result in the loss of customer order, lower utilization of resources, and, in turn, reduced in profits. In Chapter 2, we study a dynamic lead-time quotation problem in a MTO system with two (partially) substitutable products and two classes of customers. Customers decide to place an order on one of the products or not to place an order, based on the quoted lead-times. We analyze the optimal profit and the structure of the optimal lead-time policy. We also compare the lead-time quotes and profits for different quotation strategies (static vs. dynamic) with or without substitution. Numerical results show that substitution and dynamic quotation have synergetic effects, and higher benefits can be obtained by dynamic quotation and/or substitution when difference in product revenues or arrival rates, or total traffic intensity are higher. In Chapter 3, we study a dynamic lead-time quotation problem in a MTO system with single product considering the order cancellations. The order cancellations can take place during the period that the order is being processed (either waiting or undergoing processing), or after the processing is completed, at the delivery to the customer. We analyze the behavior of optimal profit in terms of cancellation parameters. We show that the optimal profit does not necessarily decrease as cancellation rate increases through a numerical study. When the profit from a cancelled order, arrival rate of customers, or lead-time sensitivity of customers are high, there is a higher probability that optimal profit increases as cancellation rate increases. We also compare the cancellation scenarios with the corresponding no-cancellation scenarios, and show that there exists a cancellation scenario that is at least as good in terms of profit than a no-cancellation scenario for most of the parameter settings. In Chapter 4, we study the Manpower Allocation Problem with Job-Teaming Constraints with the objective of minimizing the total completion time of all tasks. The problem arises in various contexts where tasks require cooperation between workers: a team of individuals with varied expertise required in different locations in a business environment, surgeries requiring different composition of doctors and nurses in a hospital, a combination of technicians with individual skills needed in a service company. A set of tasks at random locations require a set of capabilities to be accomplished, and workers have unique capabilities that are required by several tasks. Tasks require synchronization of workers to be accomplished, hence workers arriving early at a task have to wait for other required workers to arrive in order to start processing. We present a mixed integer programming formulation, strengthen it by adding cuts and propose heuristic approaches. Experimental results are reported for low and high coordination levels, i.e., number of workers that are required to work simultaneously on a given task.