We examine when there is a commitment value to inventory in a dynamic game between two firms unde... more We examine when there is a commitment value to inventory in a dynamic game between two firms under stockout-based substitution. In our model, the firms face independent direct demand but some fraction of a firm's lost sales will switch to the other firm. This problem has been previously studied in both the single period and stationary infinite horizon (open loop) setting but not in a Markov perfect (closed loop) setting. We numerically show that, as seen in the economics literature, significantly different dynamics can occur in the closed loop setting and indeed there may be a commitment value to inventory in this setting. However, we give conditions under which the stationary infinite horizon equilibrium is also a Markov perfect equilibrium and provide a discussion on when the (simpler) stationary equilibrium may be sufficient for study. We provide a review of the types of equilibria typically found in operations management papers and provide some roadmaps on avenues for future research. *
We consider a congestible system serving multiple classes of customers who differ in their delay ... more We consider a congestible system serving multiple classes of customers who differ in their delay sensitivity and valuation of service (or product). Customers are endowed with convex-concave delay cost functions. A system manager offers a menu of lead times and corresponding prices to arriving customers, who then choose the lead-time-price pair that maximizes their net utility (value minus disutility of delay and price). We investigate how such menus should be chosen dynamically (depending on the system backlog) to maximize welfare. We formulate a novel fluid model of the problem and show that the cost-balancing policy (based on the convex hulls of the delay cost functions) is socially optimal if the system manager can tell customer types apart. If types are indistinguishable to the system manager, the cost-balancing policy is also incentive compatible under social optimization. Finally, we show through a simulation study that the cost-balancing policy does well in the context of the original (stochastic) problem by testing it against various natural benchmarks.
Line balancing has been an important technique for manufacturing system design, because a complet... more Line balancing has been an important technique for manufacturing system design, because a completely balanced system can provide maximum resource utilization at the designed capacity. However, even if a system is completely balanced, it still has capacity waste when the entire product life cycle is considered, because real production is often significantly less than capacity. Avoiding this mismatch requires scalable
A call center with both contract and non-contract customers was giving priority to the contract c... more A call center with both contract and non-contract customers was giving priority to the contract customers only in off-peak hours, precisely when having priority was least important. In this paper we investigate whether this is rational behavior on the part of the call center and what the implications are for customers. In particular, we show that under contracts on the percentile of delay, which are commonly used in the call-center industry, this is rational behavior, at least under the asymptotic regime considered in the paper. We then suggest other contracts that do not result in this type of undesirable behavior from a contract customer's perspective. We compare the performance of the different contracts in terms of mean, variance, and outer percentiles of delay for both customer types using both numerical and asymptotic heavy-traffic analyses. We argue that including terms reflecting the second moment of delay in a contract would be beneficial to contract customers and, in a sense, fairer.
ABSTRACT We provide a review of the types of equilibria typically found in operations management ... more ABSTRACT We provide a review of the types of equilibria typically found in operations management inventory papers and a discussion on when the commonly used stationary infinite-horizon (open-loop) equilibrium may be sufficient for study. We focus particularly on order-up-to and basestock equilibria in the context of inventory duopolies. We give conditions under which the stationary infinite-horizon equilibrium is also a Markov perfect (closed-loop) equilibrium. These conditions are then applied to three specific duopolies. The first application is one with stockout-based substitution, where the firms face independent direct demand but some fraction of a firm’s lost sales will switch to the other firm. The second application is one where shelf-space display stimulates primary demand and reduces demand for the other firm’s product. The final application is one where the state variables represent goodwill rather than inventory. These specific problems have been previously studied in both the single period and/or stationary infinite-horizon (open-loop) settings but not in Markov perfect (closed-loop) settings. Under the Markov perfect setting, a variety of interesting dynamics may occur, including that there may be a so-called commitment value to inventory.
This paper analyzes a finite buffer polling system with routing. Finite buffers are used to model... more This paper analyzes a finite buffer polling system with routing. Finite buffers are used to model the limited capacity of the system, and routing is used to represent the need for additional service. The most significant result of the analysis is the derivation of the generating function for queue length when buffer sizes are limited and a representation of the system workload. The queue lengths at polling instants are determined by solving a system of recursive equations, and an embedded Markov chain analysis and numerical inversion are used to derive the queue length distributions. This system may be used to represent production models with setups and lost sales or expediting.
ABSTRACT Hospital emergency departments (EDs) typically rely on central laboratories to analyze p... more ABSTRACT Hospital emergency departments (EDs) typically rely on central laboratories to analyze patient samples for the purposes of diagnosing and treating patients. Point-of-care testing (POCT) is a process redesign that shifts the analysis of samples from the central lab to the ED. Using a queueing model, we generate hypotheses about how POCT impacts operational performance and then test those hypotheses empirically using data collected from a large, urban, tertiary, academic hospital. Specifically, we analyze how the adoption of POCT impacts service time, defined as the time between patient bed assignment and disposition, and waiting time, defined as the time between patient intake and bed assignment, as well as the quality of care provided to patients, defined by the 72 hour bounceback rate. We find POCT to be associated with statistically significant improvements in nearly all measures of operational performance. Specifically, we find the adoption of POCT to be associated with a 21.6% reduction in service time among test patients during peak hours and a 35.5% reduction in waiting time among all low priority patients presenting during peak hours. Moreover, we find the adoption of POCT to be associated with improved service quality as patients’ predicted probability of bounceback decreased by 0.6% during its usage. We also find system wide spillover effects for patients who do not receive POCT (no-test patients). In other words, the adoption of POCT is associated with a service time reduction among these no-test patients of 4.73% and the observed changes in waiting time are statistically similar across test and no-test patients. By examining the impact of POCT among both the population of patients receiving the test and the population that does not, this research is unique in identifying the system-wide benefits that can be attained through ED process redesign.
This paper studies a queuing model where two customer classes compete for a given resource and ea... more This paper studies a queuing model where two customer classes compete for a given resource and each customer is dynamically quoted a menu of price and leadtime pairs upon arrival. Customers select their preferred pairs from the menu and the server is obligated to meet the quoted leadtime. Customers have convexconcave delay costs. The firm does not have information on a given customer's type, so the offered menus must be incentive compatible. A menu quotation policy is given and proven to be asymptotically optimal under traditional large-capacity heavy-traffic scaling.
Page 1. CONTROL OF A SINGLE-SERVER TANDEM QUEUEING SYSTEM WITH SETUPS IZAK DUENYAS, DIWAKAR GUPTA... more Page 1. CONTROL OF A SINGLE-SERVER TANDEM QUEUEING SYSTEM WITH SETUPS IZAK DUENYAS, DIWAKAR GUPTA, and TAVA LENNON OLSEN University of Michigan, Ann Arbor, Michigan (Received November ...
We examine when there is a commitment value to inventory in a dynamic game between two firms unde... more We examine when there is a commitment value to inventory in a dynamic game between two firms under stockout-based substitution. In our model, the firms face independent direct demand but some fraction of a firm's lost sales will switch to the other firm. This problem has been previously studied in both the single period and stationary infinite horizon (open loop) setting but not in a Markov perfect (closed loop) setting. We numerically show that, as seen in the economics literature, significantly different dynamics can occur in the closed loop setting and indeed there may be a commitment value to inventory in this setting. However, we give conditions under which the stationary infinite horizon equilibrium is also a Markov perfect equilibrium and provide a discussion on when the (simpler) stationary equilibrium may be sufficient for study. We provide a review of the types of equilibria typically found in operations management papers and provide some roadmaps on avenues for future research. *
We consider a congestible system serving multiple classes of customers who differ in their delay ... more We consider a congestible system serving multiple classes of customers who differ in their delay sensitivity and valuation of service (or product). Customers are endowed with convex-concave delay cost functions. A system manager offers a menu of lead times and corresponding prices to arriving customers, who then choose the lead-time-price pair that maximizes their net utility (value minus disutility of delay and price). We investigate how such menus should be chosen dynamically (depending on the system backlog) to maximize welfare. We formulate a novel fluid model of the problem and show that the cost-balancing policy (based on the convex hulls of the delay cost functions) is socially optimal if the system manager can tell customer types apart. If types are indistinguishable to the system manager, the cost-balancing policy is also incentive compatible under social optimization. Finally, we show through a simulation study that the cost-balancing policy does well in the context of the original (stochastic) problem by testing it against various natural benchmarks.
Line balancing has been an important technique for manufacturing system design, because a complet... more Line balancing has been an important technique for manufacturing system design, because a completely balanced system can provide maximum resource utilization at the designed capacity. However, even if a system is completely balanced, it still has capacity waste when the entire product life cycle is considered, because real production is often significantly less than capacity. Avoiding this mismatch requires scalable
A call center with both contract and non-contract customers was giving priority to the contract c... more A call center with both contract and non-contract customers was giving priority to the contract customers only in off-peak hours, precisely when having priority was least important. In this paper we investigate whether this is rational behavior on the part of the call center and what the implications are for customers. In particular, we show that under contracts on the percentile of delay, which are commonly used in the call-center industry, this is rational behavior, at least under the asymptotic regime considered in the paper. We then suggest other contracts that do not result in this type of undesirable behavior from a contract customer's perspective. We compare the performance of the different contracts in terms of mean, variance, and outer percentiles of delay for both customer types using both numerical and asymptotic heavy-traffic analyses. We argue that including terms reflecting the second moment of delay in a contract would be beneficial to contract customers and, in a sense, fairer.
ABSTRACT We provide a review of the types of equilibria typically found in operations management ... more ABSTRACT We provide a review of the types of equilibria typically found in operations management inventory papers and a discussion on when the commonly used stationary infinite-horizon (open-loop) equilibrium may be sufficient for study. We focus particularly on order-up-to and basestock equilibria in the context of inventory duopolies. We give conditions under which the stationary infinite-horizon equilibrium is also a Markov perfect (closed-loop) equilibrium. These conditions are then applied to three specific duopolies. The first application is one with stockout-based substitution, where the firms face independent direct demand but some fraction of a firm’s lost sales will switch to the other firm. The second application is one where shelf-space display stimulates primary demand and reduces demand for the other firm’s product. The final application is one where the state variables represent goodwill rather than inventory. These specific problems have been previously studied in both the single period and/or stationary infinite-horizon (open-loop) settings but not in Markov perfect (closed-loop) settings. Under the Markov perfect setting, a variety of interesting dynamics may occur, including that there may be a so-called commitment value to inventory.
This paper analyzes a finite buffer polling system with routing. Finite buffers are used to model... more This paper analyzes a finite buffer polling system with routing. Finite buffers are used to model the limited capacity of the system, and routing is used to represent the need for additional service. The most significant result of the analysis is the derivation of the generating function for queue length when buffer sizes are limited and a representation of the system workload. The queue lengths at polling instants are determined by solving a system of recursive equations, and an embedded Markov chain analysis and numerical inversion are used to derive the queue length distributions. This system may be used to represent production models with setups and lost sales or expediting.
ABSTRACT Hospital emergency departments (EDs) typically rely on central laboratories to analyze p... more ABSTRACT Hospital emergency departments (EDs) typically rely on central laboratories to analyze patient samples for the purposes of diagnosing and treating patients. Point-of-care testing (POCT) is a process redesign that shifts the analysis of samples from the central lab to the ED. Using a queueing model, we generate hypotheses about how POCT impacts operational performance and then test those hypotheses empirically using data collected from a large, urban, tertiary, academic hospital. Specifically, we analyze how the adoption of POCT impacts service time, defined as the time between patient bed assignment and disposition, and waiting time, defined as the time between patient intake and bed assignment, as well as the quality of care provided to patients, defined by the 72 hour bounceback rate. We find POCT to be associated with statistically significant improvements in nearly all measures of operational performance. Specifically, we find the adoption of POCT to be associated with a 21.6% reduction in service time among test patients during peak hours and a 35.5% reduction in waiting time among all low priority patients presenting during peak hours. Moreover, we find the adoption of POCT to be associated with improved service quality as patients’ predicted probability of bounceback decreased by 0.6% during its usage. We also find system wide spillover effects for patients who do not receive POCT (no-test patients). In other words, the adoption of POCT is associated with a service time reduction among these no-test patients of 4.73% and the observed changes in waiting time are statistically similar across test and no-test patients. By examining the impact of POCT among both the population of patients receiving the test and the population that does not, this research is unique in identifying the system-wide benefits that can be attained through ED process redesign.
This paper studies a queuing model where two customer classes compete for a given resource and ea... more This paper studies a queuing model where two customer classes compete for a given resource and each customer is dynamically quoted a menu of price and leadtime pairs upon arrival. Customers select their preferred pairs from the menu and the server is obligated to meet the quoted leadtime. Customers have convexconcave delay costs. The firm does not have information on a given customer's type, so the offered menus must be incentive compatible. A menu quotation policy is given and proven to be asymptotically optimal under traditional large-capacity heavy-traffic scaling.
Page 1. CONTROL OF A SINGLE-SERVER TANDEM QUEUEING SYSTEM WITH SETUPS IZAK DUENYAS, DIWAKAR GUPTA... more Page 1. CONTROL OF A SINGLE-SERVER TANDEM QUEUEING SYSTEM WITH SETUPS IZAK DUENYAS, DIWAKAR GUPTA, and TAVA LENNON OLSEN University of Michigan, Ann Arbor, Michigan (Received November ...
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