Controlling lead times and minor ordering costs in the joint replenishment problem with stochastic demands under the class of cyclic policies

2018 ◽  
Vol 28 (1) ◽  
pp. 376-400 ◽  
Author(s):  
Marcello Braglia ◽  
Davide Castellano ◽  
Liberatina Santillo ◽  
Dongping Song
Keyword(s):  
Lead Times ◽  
Joint Replenishment ◽  
Joint Replenishment Problem ◽  
Stochastic Demands

scholarly journals Determining the Optimum Ordering Policy in Multi-Item Joint Replenishment Problem Using a Novel Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wen-Tsung Ho
Keyword(s):  
Cycle Time ◽  
Heuristic Algorithms ◽  
Optimal Solution ◽  
Lead Times ◽  
Joint Replenishment ◽  
Joint Replenishment Problem ◽  
Ordering Policy ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Time Division

This work investigates the joint replenishment problem (JRP) involving multiple items where economies exist for replenishing several items simultaneously. The demand rate for each item is known and constant. Shortages are not permitted and lead times are negligible. Many heuristic algorithms have been proposed to find quality solutions for the JRP. In this paper, cycle time division and recursive tightening methods are developed to calculate an efficient and optimal replenishment policy for JRP. Two theorems are demonstrated to guarantee that an optimal solution to the problem can be derived using cycle time division and recursive tightening methods. Restated, cycle time division and recursive tightening methods theoretically yield the optimal solution in 100% of instances. The complexity of cycle time division and recursive tightening methods is justO(NlogN), whereNrepresents the number of items involved in the problem. Numerical examples are included to demonstrate the algorithmic procedures.

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