A vendor–buyer inventory model with lot-size and production rate dependent lead time under time value of money

Sumon Sarkar · Bibhas Chandra Giri · Ashis Kumar Sarkar

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Supply Chain and Inventory Management Sustainable Supply Chain Management Operations Management Techniques

Abstract

The paper studies an integrated vendor–buyer model with shortages under stochastic lead time which is assumed to be variable but depends on the buyer’s order size and the vendor’s production rate. The replenishment lead time and the market demand uncertainty are assumed to be reduced by changing the regular production rate of the vendor at the risk of paying additional cost. Shortages are partially backlogged and the backlogging rate depends on the length of the buyer’s replenishment lead time. The proposed model is formulated to obtain the net present value (NPV) of the expected total cost of the integrated system through optimization of (i) the buyer’s order quantity, (2) the buyer’s safety factor, and (3) the vendor’s production rate. Theoretical results are derived to demonstrate the existence and uniqueness of the optimal solution. Through extensive numerical study, some valuable managerial insights are obtained.

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References

1999Inventory management and production planning and scheduling 1982Principles of inventory and materials management 1996Optimal Pricing and Lot-Sizing Under Conditions of Perishability and Partial Backordering 1991An Analytical Determination of Lead Time with Normal Demand 2003Integrated single vendor single buyer model with stochastic demand and variable lead time 2001Optimal price and order size for a reseller under partial backordering 1995An EOQ Model for Deteriorating Items with Linear Time-dependent Demand Rate and Shortages under Inflation and Time Discounting 2002A study of an integrated inventory with controllable lead time

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