Exact Analysis of Divergent Inventory Systems with Time-Based Shipment Consolidation and Compound Poisson Demand

Olof Stenius (), Ayşe Gönül Karaarslan (), Johan Marklund () and A. G. de Kok ()
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Olof Stenius: Department of Industrial Management and Logistics, Lund University, 22100 Lund, Sweden
Ayşe Gönül Karaarslan: Department of Econometrics, Erasmus University Rotterdam, 3000DR Rotterdam, Netherlands
Johan Marklund: Department of Industrial Management and Logistics, Lund University, 22100 Lund, Sweden
A. G. de Kok: Department of Industrial Engineering and Innovation Sciences, Eindhoven University of Technology, 5600MB Eindhoven, Netherlands

Operations Research, 2016, vol. 64, issue 4, 906-921

Abstract: Sustainable and efficient management of a distribution system requires coordination between transportation planning and inventory control decisions. In this context, we consider a one warehouse multi-retailer inventory system with a time-based shipment consolidation policy at the warehouse. This means that there are fixed costs associated with each shipment, and retailer orders are consolidated and shipped periodically to groups of retailers sharing the same delivery routes. Customer demand is compound Poisson distributed and unsatisfied demand at each stock point is backordered and allocated on a first-come first-served basis. The system is centralized and inventory levels are reviewed continuously. The warehouse has access to real-time inventory information from the retailers, and uses a ( R , nQ ) policy to replenish from an outside supplier/manufacturer. We derive the exact probability distributions for the inventory levels at the retailers, and use these to obtain exact expressions for the system’s expected shipment, holding and backorder costs, its average inventory levels, and fill rates. Based on the analytical properties of the objective function, we construct an optimization procedure by deriving bounds on the optimal reorder levels and shipment intervals both for single-item and multi-item systems.

Keywords: inventory; multiechelon; multi-item; stochastic; shipment consolidation; continuous review; compound Poisson demand (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (16)

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