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18
Optimal Leadtime Differentiation via Diffusion Approximations
, 2004
"... This study illustrates how a manufacturer can use leadtime differentiation—selling the same product to different customers at different prices based on delivery leadtime—to simultaneously increase revenue and reduce capacity requirements. The manufacturer’s production facility is modeled as an expon ..."
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Cited by 24 (5 self)
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This study illustrates how a manufacturer can use leadtime differentiation—selling the same product to different customers at different prices based on delivery leadtime—to simultaneously increase revenue and reduce capacity requirements. The manufacturer’s production facility is modeled as an exponential singleserver queue with two classes of customers that differ in price sensitivity and delay sensitivity. The manufacturer chooses the service rate and a static price for each class of customer, and then dynamically quotes leadtimes to potential customers and decides the order in which customers are processed. The arrival rate for each class decreases linearly with price and leadtime. The manufacturer’s objective is to maximize profit, subject to the constraint that each customer must be processed within the promised leadtime. Assuming that some customers will tolerate a long delivery leadtime, we show that this problem has a simple nearoptimal solution. Under our proposed policy, capacity utilization is near 100%. Impatient customers pay a premium for immediate delivery and receive priority in scheduling, whereas patient customers are quoted a leadtime proportional to the current queue length. Queue length and leadtime can be closely approximated by a reflected OrnsteinUhlenbeck diffusion process. Hence, we have a closed form expression for profit, and choose prices and capacity to optimize this. In case customers may choose either the class 1 deal or the class 2 deal, the proposed policy is made incentive compatible by quoting a leadtime for the class 2 (patient) customers that is longer than the actual queueing delay.
Dynamic product assembly and inventory control for maximum profit. ArXiv
, 2010
"... Abstract — We consider a manufacturing plant that purchases raw materials for product assembly and then sells the final products to customers. There are M types of raw materials and K types of products, and each product uses a certain subset of raw materials for assembly. The plant operates in slott ..."
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Cited by 8 (7 self)
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Abstract — We consider a manufacturing plant that purchases raw materials for product assembly and then sells the final products to customers. There are M types of raw materials and K types of products, and each product uses a certain subset of raw materials for assembly. The plant operates in slotted time, and every slot it makes decisions about restocking materials and pricing the existing products in reaction to (possibly timevarying) material costs and consumer demands. We develop a dynamic purchasing and pricing policy that yields time average profit within of optimality, for any given > 0, with a worst case storage buffer requirement that is O(1/). The policy can be implemented easily for large M, K, yields fast convergence times, and is robust to nonergodic system dynamics. Index Terms — Queueing analysis, pricing, optimization I.
A Separation Principle for a Class of AssembletoOrder Systems with Expediting Operations Research 55(3
 603–609, © 2007 INFORMS 609
, 1996
"... informs ® doi 10.1287/opre.1060.0372 ..."
Sensitivity of optimal capacity to customer impatience in an unobservable M/M/S queue (Why you shouldn't shout at the DMV)
, 2009
"... ..."
The value of component commonality in a dynamic inventory system with lead times
 Manufacturing and Service Operations Management
, 2007
"... Component commonality has been widely recognized as a key factor in achieving product variety at low cost. Yet, the theory on the value of component commonality is rather limited in the inventory literature. The existing results were built primarily on singleperiod models or periodicreview models ..."
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Cited by 5 (1 self)
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Component commonality has been widely recognized as a key factor in achieving product variety at low cost. Yet, the theory on the value of component commonality is rather limited in the inventory literature. The existing results were built primarily on singleperiod models or periodicreview models with zero lead times. In this paper, we consider a continuousreview system with positive lead times. We find that while component commonality is in general beneficial, its value depends strongly on component costs, lead times and dynamic allocation rules. Under certain conditions, several previous findings based on static models do not hold here. In particular, component commonality does not always generate inventory benefits under certain commonly used allocation rules. We provide insight on when component commonality generates inventory benefits and when it may not. We further establish some asymptotic properties that connect component lead times and costs to the impact of component commonality. Through numerical studies, we demonstrate the value of commonality and its sensitivity to various system parameters in between the asymptotic limits. In addition, we show how to evaluate the system under a new allocation rule, a modified version of the standard FIFO rule.
Noholdback allocation rules for continuoustime assembletoorder systems
 Operations Research
"... This paper analyzes a class of commoncomponent allocation rules, termed noholdback (NHB) rules, in continuousreview assembletoorder (ATO) systems with positive lead times. The inventory of each component is replenished following an independent basestock policy. In contrast to the usually assu ..."
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This paper analyzes a class of commoncomponent allocation rules, termed noholdback (NHB) rules, in continuousreview assembletoorder (ATO) systems with positive lead times. The inventory of each component is replenished following an independent basestock policy. In contrast to the usually assumed firstcomefirstserved (FCFS) component allocation rule in the literature, an NHB rule allocates a component to a product demand only if it will yield immediate fulfillment of that demand. We identify metrics as well as cost and product structures under which NHB rules outperform all other component allocation rules. For systems with certain product structures, we obtain key performance expressions and compare them to those under FCFS. For general product structures, we present performance bounds and approximations. Finally, we discuss the applicability of these results to more general ATO systems. Subject classifications: stochastic multiitem inventory system; assembletoorder; basestock policy; commoncomponent allocation rule; nonFCFS; samplepath analysis.
Exploiting market size in service systems
 Manufacturing Service Oper. Management
, 2010
"... W e study a profitmaximizing firm providing a service to price and delay sensitive customers. We are interested in analyzing the scale economies inherent in such a system. In particular, we study how the firm's pricing and capacity decisions change as the scale, measured by the potential mark ..."
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Cited by 4 (2 self)
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W e study a profitmaximizing firm providing a service to price and delay sensitive customers. We are interested in analyzing the scale economies inherent in such a system. In particular, we study how the firm's pricing and capacity decisions change as the scale, measured by the potential market for the service, increases. These decisions turn out to depend intricately on the form of the delay costs seen by the customers; we characterize these decisions up to the dominant order in the scale for both convex and concave delay costs. We show that when serving customers on a firstcome, firstserved basis, if the customers' delay costs are strictly convex, the firm can increase its utilization and extract profits beyond what it can do when customers' delay costs are linear. However, with concave delay costs, the firm is forced to decrease its utilization and makes less profit than in the linear case. While studying concave delay costs, we demonstrate that these decisions depend on the scheduling policy employed as well. We show that employing the lastcome, firstserved rule in the concave case results in utilization and profit similar to the linear case, regardless of the actual form of the delay costs.
Convexity Properties and Comparative Statics for an M/M/S Queue with Impatient Customers: Why You Shouldn’t Shout at the DMV
"... We use sample path arguments to derive convexity properties of an M/M/S queue with impatient customers that balk and renege. First, assuming that the balking probability and reneging rate are increasing and concave in the total number of customers in the system (headcount), we prove that the expect ..."
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Cited by 2 (1 self)
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We use sample path arguments to derive convexity properties of an M/M/S queue with impatient customers that balk and renege. First, assuming that the balking probability and reneging rate are increasing and concave in the total number of customers in the system (headcount), we prove that the expected headcount is convex decreasing in the capacity (service rate). Second, with linear reneging and balking, we show that the expected lost sales rate is convex decreasing in the capacity. Finally, we employ a samplepath submodularity approach to comparative statics. That is, we employ sample path arguments to show how the optimal capacity changes as we vary the parameters of customer demand and impatience. We find that the optimal capacity increases in the demand rate and decreases with the balking probability, but is not monotone in the reneging rate. This means, surprisingly, that failure to account for customers ’ reneging may result in overinvestment in capacity. Finally, we show that a seemingly minor change in system structure, customer commitment during service, produces qualitatively different convexity properties and comparative statics. 1.
CongestionBased Leadtime Quotation and Pricing for Revenue Maximization with Heterogeneous Customers
, 2008
"... We consider a maketoorder …rm that has the ability to dynamically o¤er menus of prices and production (or service) leadtimes to its customers. Customers seeking a particular product (or service) will choose from the o¤ered menu the pair of prices and leadtimes that maximizes their value for the pr ..."
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Cited by 1 (0 self)
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We consider a maketoorder …rm that has the ability to dynamically o¤er menus of prices and production (or service) leadtimes to its customers. Customers seeking a particular product (or service) will choose from the o¤ered menu the pair of prices and leadtimes that maximizes their value for the product minus their delay cost and the price for that leadtime. Dynamic control allows the retailer to tune leadtimes and prices to the current backlog. We consider two classes of customers who have the same valuation for the product but di¤er in their level of patience (a concept made precise in the paper). We investigate how such dynamic menus should be chosen in the context of a large capacity asymptotic regime and propose policies when customers’leadtime costs are convexconcave. We consider both the full information case and the (more realistic) case where the …rm, being unaware of customer type, must o¤er incentivecompatible menus. We propose readilyimplementable policies and test them numerically against a number of natural benchmarks. 1
MODEL OF PRODUCTION CONTROL IN JUSTINTIME DELIVERY SYSTEM CONDITONS
"... S u m m a r y The article presents the mathematical model of production control in the Justintime delivery system’s conditions for a planning fixed horizon. The aim of the control model is to determine the demand for means of production (materials, labour force) at the right moment of time. The st ..."
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S u m m a r y The article presents the mathematical model of production control in the Justintime delivery system’s conditions for a planning fixed horizon. The aim of the control model is to determine the demand for means of production (materials, labour force) at the right moment of time. The stochastic model of appearing the fault products was taking into account. Minimization both the costs of manufacturing and possible penalties connected with the incomplete execution of the order was taken as a criterion of optimization process.