Non-Preemptive Shunting in M/M/1 and Dynamic Service Queueing Systems

We provide a study of two queueing systems, namely, an M/M/1 queueing system in which an incoming customer shunts, or skips line, and a dynamic server in an infinite capacity system moving among service nodes. In the former, we explore various aspects of the system, including waiting time, and the relationships between shunting and position in queue and rate of service. Through use of global balance equations, we find the probability that an arriving non-priority customer, finding customers waiting in the system, will shunt to a position other than behind the queue. In the latter, we explore a system in which a server with infinite capacity moves among indexed linear service nodes, receives customers at various nodes, and transports the customers to other indexed nodes in the hierarchy. We determine the expected waiting times at the nodes, expected service times, expected number of customers at a given node, expected number in the system, and expected number in service. The probabilities that an arrival finds n customers at a particular node, and in the entire system are obtained

Optimal and Heuristic Resource Allocation Policies in Serial Production Systems

We have studied the optimal server allocation policies for a tandem queueing system under different system settings. Motivated by an industry project, we have studied a two stage tandem queueing system with arrival to the system and having two flexible servers capable of working at either of the stations. In our research, we studied the system under two different circumstances: modeling the system to maximize throughput without cost considerations, modeling the system to include switching and holding costs along with revenue for finished goods. In the maximizing throughput scenario, we considered two different types of server allocations: collaborative and non-collaborative. For the collaborative case, we identified the optimal server allocation policies for the servers and have proved the structure of the optimal server allocation policy using mathematical iteration techniques. Moreover, we found that, it is optimal to allocate both the servers together all the time to get maximum throughput. In the non-collaborative case, we have identified the optimal server allocation policies and found that it is not always optimal to allocate both the servers together. With the inclusion of costs, we studied the system under two different scenarios: system with switching costs only and system having both switching and holding costs. In both the cases, we have studied the optimal server allocation policies for the servers. Due to the complicated structure of the optimal server allocation policy, we have studied three different heuristics to approximate the results of the optimal policy. We found that the performance of one of the heuristics is very close to the optimal policy values

Design and control of agile automated CONWIP production lines

In this article, we study the design and control of manufacturing cells with a mix of manual and automated equipment, operating under a CONWIP pull protocol, and staffed by a single agile (cross-trained) worker. For a three-station line with one automated station, we fully characterize the structure of the optimal control policy for the worker and show that it is a static priority policy. Using analytical models and extensive simulation experiments, we also evaluate the effectiveness of practical heuristic control policies and provide managerial insights on automation configuration design of the line. This characterization of the worker control policy enables us to develop managerial insights into the design issues of how best to locate and concentrate automation in the line. Finally, we show that, in addition to ease of control and greater design flexibility, the CONWIP protocol also offers higher efficiency and robustness than does the push protocol. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/61525/1/20325_ftp.pd

On the Introduction of an Agile, Temporary Workforce into a Tandem Queueing System

We consider a two-station tandem queueing system where customers arrive according to a Poisson process and must receive service at both stations before leaving the system. Neither queue is equipped with dedicated servers. Instead, we consider three scenarios for the fluctuations of workforce level. In the first, a decision-maker can increase and decrease the capacity as is deemed appropriate; the unrestricted case. In the other two cases, workers arrive randomly and can be rejected or allocated to either station. In one case the number of workers can then be reduced (the controlled capacity reduction case). In the other they leave randomly (the uncontrolled capacity reduction case). All servers are capable of working collaboratively on a single job and can work at either station as long as they remain in the system. We show in each scenario that all workers should be allocated to one queue or the other (never split between queues) and that they should serve exhaustively at one of the queues depending on the direction of an inequality. This extends previous studies on flexible systems to the case where the capacity varies over time. We then show in the unrestricted case that the optimal number of workers to have in the system is non-decreasing in the number of customers in either queue.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47647/1/11134_2005_Article_2441.pd

Online Learning Algorithms for Stochastic Inventory and Queueing Systems

The management of inventory and queueing systems lies in the heart of operations research and plays a vital role in many business enterprises. To this date, the majority of work in the literature has been done under complete distributional information about the uncertainties inherent in the system. However, in practice, the decision maker may not know the exact distributions of these uncertainties (such as demand, capacity, lead time) at the beginning of the planning horizon, but can only rely on realized observations collected over time. This thesis focuses on the interplay between learning and optimization of three canonical inventory and queueing systems and proposes a series of first online learning algorithms. The first system studied in Chapter II is the periodic-review multiproduct inventory system with a warehouse-capacity constraint. The second system studied in Chapter III is the periodic-review inventory system with random capacities. The third system studied in Chapter IV is the continuous-review make-to-stock M/G/1 queueing system. We take a nonparametric approach that directly works with data and needs not to specify any (parametric) form of the uncertainties. The proposed online learning algorithms are stochastic gradient descent type, leveraging the (sometimes non-obvious) convexity properties in the objective functions. The performance measure used is the notion of cumulative regret or simply regret, which is defined as the cost difference between the proposed learning algorithm and the clairvoyant optimal algorithm (had all the distributional information about uncertainties been given). Our main theoretical results are to establish the square-root regret rate for each proposed algorithm, which is known to be tight. Our numerical results also confirm the efficacy of the proposed learning algorithms. The major challenges in designing effective learning algorithms for such systems and analyzing them are as follows. First, in most retail settings, customers typically walk away in the face of stock-out, and therefore the system is unable to keep track of these lost-sales. Thus, the observable demand data is, in fact, the sales data, which is also known as the censored demand data. Second, the inventory decisions may impact the cost function over extended periods, due to complex state transitions in the underlying stochastic inventory system. Third, the stochastic inventory system has hard physical constraints, e.g., positive inventory carry-over, warehouse capacity constraint, ordering/production capacity constraint, and these constraints limit the search space in a dynamic way. We believe this line of research is well aligned with the important opportunity that now exists to advance data-driven algorithmic decision-making under uncertainty. Moreover, it adds an important dimension to the general theory of online learning and reinforcement learning, since firms often face a realistic stochastic supply chain system where system dynamics are complex, constraints are abundant, and information about uncertainties in the system is typically censored. It is, therefore, important to analyze the structure of the underlying system more closely and devise an efficient and effective learning algorithm that can generate better data, which is then feedback to the algorithm to make better decisions. This forms a virtuous cycle.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/149894/1/aschenwd_1.pd