The JRP with Multiple Replenishment Sources and Fill Rates

The JRP with Multiple Replenishment Sources and Fill Rates


  • Serge M . Karalli
  • A D . Flowers


California Journal of Operations Management, 2 ed., vol. 9, pp. 1-19, September 2011




This paper extends the Joint Replenishment Problem (JRP) to a stochastic demand environment where the demand service is measured by fill rates. This paper also considers replenishment from multiple locations. The relevant costs include family order costs, item order costs, and inventory holding costs for both cycle and safety stocks. Safety stock costs are explicitly considered in the formulation, as their holding costs vary nontrivially with the model’s decision variables. An efficient solution procedure is developed for this model. Properties of the non-convex feasible space are identified and used in the solution approach. The solution to the mathematical model is comprised of the basic period length, the family multipliers, and the item multipliers that give the lowest total cost of placing orders and carrying inventory. The family multipliers and items multipliers are restricted to integer-powers-of-two.