Stochastic joint replenishment problem with quantity discounts and minimum order constraints

Ji Seong Noh, Jong Soo Kim, Biswajit Sarkar

Research output: Contribution to journalArticlepeer-review

31 Citations (Scopus)


This paper analyzes a logistics system involving a supplier who produces and delivers multiple types of items and a buyer who receives and sells to end customers. The buyer controls the inventory of each item by ordering at a preset time interval, which is an integer multiple of a base cycle, to meet the stochastic demands of the end customers. The supplier makes contracts with the buyer that specify that the ordered amount is delivered at the start of each period at a unit price determined by a quantity discount schedule. The contract also specifies that a buyer’s order should exceed a minimum order quantity. To analyze the system, a mathematical model describing activities for replenishing a single type of item is developed from the buyer’s perspective. An efficient method to determine the base cycle length and safety factor that minimizes the buyer’s total cost is then proposed. The single item model is extended to a multiple items joint replenishment model, and algorithms for finding a cost-minimizing base cycle, order interval multipliers, and safety factors are proposed. The result of computational experiments shows that the algorithms can find near-optimal solutions to the problem.

Original languageEnglish
Pages (from-to)151-178
Number of pages28
JournalOperational Research
Issue number1
Publication statusPublished - 2019 Mar 12

Bibliographical note

Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation
  • Strategy and Management
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research
  • Computational Theory and Mathematics
  • Management of Technology and Innovation


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