About

Vidyadhar Kulkarni is a professor in the Department of Statistics and Operations Research at the University of North Carolina at Chapel Hill. He holds a Ph.D. in Operations Research from Cornell University, earned in 1980, along with a Master's degree in Operations Research from Cornell (1978) and a B.Tech. in Mechanical Engineering from IIT Bombay (1976). His research interests include stochastic modeling and analysis of manufacturing and service systems, as well as the optimal control of stochastic systems. Professor Kulkarni has authored both undergraduate and graduate texts on stochastic systems, including 'Introduction to Modeling and Analysis of Stochastic Systems' (Second Edition, Springer, 2010) and 'Modeling and Analysis of Stochastic Systems' (Second Edition, CRC Press, 2011). He has developed software tools such as MAXIM, a MATLAB program to accompany his undergraduate text, and MAXIMGUI, a graphical user interface for accessing MAXIM. His teaching portfolio includes courses on decision sciences, probability, and stochastic models in operations research, with special topics courses in market microstructure, healthcare, and telecommunications.

Research topics

• Computer Science
• Artificial Intelligence
• Machine Learning
• Mathematics
• Applied mathematics
• Economics
• Mathematical optimization
• Computer network
• Mathematical analysis
• Algorithm
• Microeconomics
• Econometrics

Selected publications

• Optimal control of a single server in a finite-population queueing network

  UNC Libraries · 2026-04-03

  articleOpen accessSenior author
  PublisherDOI

• Optimal Allocation of Limited Inventory Among Multiclass Customers with Finite Populations

  Operations Research · 2025-08-20

  article

  New Analytical Insights on Inventory Allocation How should a limited inventory of a single resource be allocated across multiple customer groups with distinct rewards and arrival rates, especially when each group has a finite population? In their paper “Optimal allocation of limited inventory among multiclass customers with finite populations” in Operations Research, the authors develop a stochastic framework and formulate the problem as a Markov decision process. By analyzing the structure of the optimal value function, they reveal a new insight; rather than gradually expanding access to lower-priority groups over time, it is in fact optimal to progressively restrict access to these groups. The paper also introduces a fluid model with an explicit solution, which provides a good approximation when the system size is large. These findings offer both theoretical and practical contributions to inventory allocation problems, with potential applications in healthcare and humanitarian resource management as well as commercial product sales.

  PublisherDOI

• Random variables

  Elsevier eBooks · 2025-06-02

  book-chapter1st authorCorresponding
  PublisherDOI

• Asymptotically Optimal Appointment Scheduling in the Presence of Patient Unpunctuality

  arXiv (Cornell University) · 2024-12-24

  preprintOpen accessSenior author

  We consider the optimal appointment scheduling problem that incorporates patients' unpunctual behavior, where the unpunctuality is assumed to be time dependent, but additive. Our goal is to develop an optimal scheduling method for a large patient system to maximize expected net revenue. Methods for deriving optimal appointment schedules for large-scale systems often run into computational bottlenecks due to mixed-integer programming or robust optimization formulations and computationally complex search methods. In this work, we model the system as a single-server queueing system, where patients arrive unpunctually and follow the FIFO service discipline to see the doctor (i.e., get into service). Using the heavy traffic fluid approximation, we develop a deterministic control problem, referred to as the fluid control problem (FCP), which serves as an asymptotic upper bound for the original queueing control problem (QCP). Using the optimal solution of the FCP, we establish an asymptotically optimal scheduling policy on a fluid scale. We further investigate the convergence rate of the QCP under the proposed policy. The FCP, due to the incorporation of unpunctuality, is difficult to solve analytically. We thus propose a time-discretized numerical scheme to approximately solve the FCP. The discretized FCP takes the form of a quadratic program with linear constraints. We examine the behavior of these schedules under different unpunctuality assumptions and test the performance of the schedules on real data in a simulation study. Interestingly, the optimal schedules can involve block booking of patients, even if the unpunctuality distributions are continuous.

  PublisherOA PDFDOI

• Nonparametric Adaptive Age-Replacement with Censored Data: A Multi-Armed Bandit Framework

  SSRN Electronic Journal · 2024-01-01

  preprintOpen accessSenior author
  PublisherDOI

• Optimal Allocation of Limited Inventory among Multi-class Customers with Finite Populations

  SSRN Electronic Journal · 2024-01-01

  articleOpen access
  PublisherDOI

• Admission Control in Multi-server Systems Under Binary Reward Structure

  Production and Operations Management · 2024-05-03

  articleSenior author

  We study a multi-server queueing system where a customer is satisfied (and generates a unit revenue) if their queueing time is at most a given constant. If the queueing time of the admitted customer exceeds this constant, the customer gets served, but is unsatisfied and generates no revenue. Such queueing systems arise in the context of modeling service systems where excessive delays are of concern. A key challenge is how to design an admission control policy to maximize the number of satisfied customers per unit time in the long run, assuming that we can observe the number of customers in the system at any time. We call this the binary reward structure system and show that a threshold-type admission policy is optimal. The optimal threshold policy has to be computed numerically. Hence we propose a square-root admission policy to approximate the optimal admission control policy, and compare the performance of these two policies. We derive an analytical upper bound on the performance of optimal admission control policy by deriving an optimal admission policy assuming we have full information over the queueing time of the admitted customers. This is equivalent to a queueing system where customers abandon the queue (i.e., leave without service) if their queueing time exceeds the given constant. We demonstrate that the optimal policy that includes customer abandonment, or alternatively, the optimal policy under full information, the optimal threshold policy, and the square-root admission policy, all exhibit identical performance in the asymptotic regions of the parameter space. Our numerical results indicate that the worst optimality gap of the square-root admission policy is within 3.9% of the optimal revenue, and implementing the square-root admission policy in the observable queueing system leads to a revenue loss that is at most 5.6% of the maximum possible revenue rate in the full information system. We also compare the binary reward structure with the more common linear reward structure where the system incurs holding cost per unit queueing time per customer. In addition, we also show that the analysis based on queueing time is applicable to the system time as well.

  PublisherDOI

• Obituary Narahari Umanath (‘Uma’) Prabhu (April 25th, 1924–October 14th, 2022)

  Queueing Systems · 2023-06-13

  articleOpen access1st author
  PublisherOA PDFDOI

• Parking game

  Queueing Systems · 2022-03-30

  articleOpen accessSenior author
  PublisherOA PDFDOI

• Periodic review inventory models with multiclass demands and fixed order costs

  Stochastic Models · 2022-11-21

  article1st author

  We consider a periodic review inventory system with multiclass demands and fixed setup cost. Demand arrivals of each class are assumed to be a Poisson process, and a lost-sales setting is adopted. The demand classes are classified by the cost of their unsatisfied demands. We consider two cases: the leftover inventory at the end of a restocking interval is entirely discarded or entirely carried over to the next period. We obtain the optimal rationing policy, the optimal ordering policy and the optimal duration of the periodic review interval that minimize the average cost per unit time. We derive the differential equations satisfied by the value function characterized by the on-hand inventory level and the residual restocking time. This value function does not have the traditional modularity and convexity properties. Hence, the optimal policy is derived directly based on the ordinary differential equations satisfied by the value function. Moreover, some structural properties of the optimal policy such as the monotone property of the optimal rationing policy are obtained.

  PublisherDOI

Frequent coauthors

• I.J.B.F. Adan

  Eindhoven University of Technology

  13 shared

• Qi Gong

  University of North Carolina at Chapel Hill

  8 shared

• Srinagesh Gavirneni

  6 shared

• Xin Liu

  Clemson University

  6 shared

• Kishor S. Trivedi

  Duke University

  5 shared

• Michelle Opp

  4 shared

• Rajeeva L. Karandikar

  Chennai Mathematical Institute

  4 shared

• K. D. Glazebrook

  Lancaster University

  4 shared