Optimization of Inventory and Distribution for Hip and Knee Joint Replacements via Multistage Stochastic Programming

  • Mohammad PirhooshyaranEmail author
  • Lawrence V. Snyder
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 279)


We introduce a multistage stochastic programming model to optimize the distribution–production network of medical devices; in particular, artificial hip and knee joints for orthopedic surgery. These devices are distributed to hospitals in kits that contain multiple sizes of the joint; the surgeon uses one device from the kit and then returns the rest of the kit to the distributor, which replaces the part that has been removed and distributes the kit anew. Therefore, the distribution problem for artificial joints has a shareability property and thus is related to closed-loop supply chains. We assume that demands for the devices follow a discrete probability distribution and therefore we use scenarios to model the random demands over time. We compare the results of our optimization model to an approximation of the simple distribution strategy that our industry partner currently uses. The proposed approach outperforms the present approach in terms of optimal cost. We also explore the sensitivity of the model’s computation time as the numbers of scenarios, hospitals, and time periods change. Finally, we extend the model to investigate the production of shareable items in sharing systems using a numerical example.


Hip and knee joint replacement logistics Sharing systems Production–distribution planning Multistage stochastic programming Healthcare systems 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Mohler Lab, Department of Industrial and Systems EngineeringLehigh UniversityBethlehemUSA

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