Mathematical Modeling for an Integrated Inventory System with Two-level Trade Credit and Random Defectiveness in Transport

Modern business environment focuses on improving the operational efficiency of supplier, retailer and customers through integrating their inventory. Although a smoothly running integrated inventory system is ideal, the reality is to deal with imperfectness in transportation. In actual production environments, inventory items are not perfect and defectiveness occurs in random process.  In this paper, we propose an integrated supplier–retailer inventory model in which both supplier and retailer have adopted trade credit policies, and the retailer receives an arriving lot which contains random defectiveness in quality of items. This paper proposes a mathematical model considering two situations such as (a) risk neutral and (b) risk-averse case and the solution procedures are described with computational algorithm. The optimization procedures are discussed for determining optimal cycle time and optimal number of shipments by minimizing the expected joint total cost in the integrated inventory system.  Numerical examples are provided to illustrate the theoretical results, and sensitivity analysis is made for major inventory parameters.