Article: Analytical solution and optimisation of serial supply chains with multiple nodes, lost sales, continuous review replenishment policies, stochastic lead times and external demand Journal: International Journal of Industrial and Systems Engineering (IJISE) 2022 Vol.41 No.4 pp.519 - 550 Abstract: This work analyses a serial supply chain with an arbitrary number of nodes (retailer, wholesaler, manufacturer, supplier, etc.). Every node faces supply uncertainty in both replenishment lead time and quantity delivered (except for the most upstream node, assumed saturated). The most downstream node (retailer) faces external Poisson demand with rate λ. Each node follows a continuous review (si, Si), i = 1, 2, …, K - 1 replenishment policy. If a node is insufficiently stocked, then the order is only partially satisfied. The system parameters that influence the performance of the supply chain are the number of nodes, the upper level of inventories, the reorder levels, the replenishment times, and the demand rate. The supply network is modelled as a continuous time Markov process with discrete states. We explore the structure of the transition matrices and develop a computational algorithm to generate the stationary probability distributions for any combination of the system parameters. We also use the proposed algorithm as a design and optimisation tool to determine the optimal inventory policies (i.e., reorder level and order-up-to-level) to maximise the fill rate (FR) or minimise the work-in-process (WIP) for multi-echelon serial supply chains. Inderscience Publishers - linking academia, business and industry through research

Title: Analytical solution and optimisation of serial supply chains with multiple nodes, lost sales, continuous review replenishment policies, stochastic lead times and external demand

Authors: M. Geranios; M.I. Vidalis; S.I. Koukoumialos; A.C. Diamantidis

Addresses: Department of Business Administration, University of the Aegean, Chios Island, Greece ' Department of Business Administration, University of the Aegean, Chios Island, Greece ' Department of Business Administration, University of Thessaly, Larissa, Greece ' Department of Economics, Aristotle University of Thessaloniki, Thessaloniki, Greece

Abstract: This work analyses a serial supply chain with an arbitrary number of nodes (retailer, wholesaler, manufacturer, supplier, etc.). Every node faces supply uncertainty in both replenishment lead time and quantity delivered (except for the most upstream node, assumed saturated). The most downstream node (retailer) faces external Poisson demand with rate λ. Each node follows a continuous review (s_i, S_i), i = 1, 2, …, K - 1 replenishment policy. If a node is insufficiently stocked, then the order is only partially satisfied. The system parameters that influence the performance of the supply chain are the number of nodes, the upper level of inventories, the reorder levels, the replenishment times, and the demand rate. The supply network is modelled as a continuous time Markov process with discrete states. We explore the structure of the transition matrices and develop a computational algorithm to generate the stationary probability distributions for any combination of the system parameters. We also use the proposed algorithm as a design and optimisation tool to determine the optimal inventory policies (i.e., reorder level and order-up-to-level) to maximise the fill rate (FR) or minimise the work-in-process (WIP) for multi-echelon serial supply chains.

Keywords: supply chain management; SCM; inventory control; lost demand; continuous review policy; performance evaluation.

DOI: 10.1504/IJISE.2022.125004

International Journal of Industrial and Systems Engineering, 2022 Vol.41 No.4, pp.519 - 550

Received: 24 Jul 2020
Accepted: 09 Nov 2020
Published online: 22 Aug 2022 *

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Title: Analytical solution and optimisation of serial supply chains with multiple nodes, lost sales, continuous review replenishment policies, stochastic lead times and external demand

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