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A complete algebraic solution to the optimal dynamic rationing policy in the stock-rationing queue with two demand

Quan-Lin Li1, Yi-Meng Li2, Jing-Yu Ma3

  • 1School of Economics and Management, Beijing University of Technology, Beijing, 100124 China.

Journal of Combinatorial Optimization
|March 27, 2023
PubMed
Summary

This study introduces an optimal dynamic rationing policy for stock-rationing queues with two demand classes. The research reveals that this policy is of a transformational threshold type, offering insights into inventory management.

Keywords:
Inventory rationingMarkov decision processOptimal dynamic rationing policySensitivity-based optimizationStock-rationing queue

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Area of Science:

  • Operations Research
  • Queueing Theory
  • Inventory Management

Background:

  • Stock-rationing queues are critical in managing limited inventory across multiple demand classes.
  • Determining optimal dynamic rationing policies is essential for maximizing system profitability and efficiency.

Purpose of the Study:

  • To develop a complete algebraic solution for the optimal dynamic rationing policy in a two-demand-class stock-rationing queue.
  • To identify the structural properties of this optimal policy.

Main Methods:

  • Sensitivity-based optimization techniques were employed.
  • The performance difference equation was utilized to analyze monotonicity and optimality.
  • Numerical experiments were conducted to validate theoretical findings.

Main Results:

  • The optimal dynamic rationing policy was proven to be of a transformational threshold type.
  • Three sufficient conditions were refined under which the policy exhibits a threshold type (critical rationing level).
  • New structural properties of the optimal dynamic rationing policy were established.

Conclusions:

  • The developed methodology provides a comprehensive algebraic solution for optimal dynamic rationing policies.
  • The findings offer significant insights into stock-rationing queue management and suggest avenues for future research.