Volume 54, Number 4, July-Août 2020
|Page(s)||961 - 979|
|Published online||28 April 2020|
A vendor–buyer inventory model with lot-size and production rate dependent lead time under time value of money
Department of Mathematics, Jadavpur University, Kolkata, India
* Corresponding author: firstname.lastname@example.org
Accepted: 6 March 2019
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.
Mathematics Subject Classification: 90B05 / 90B06
Key words: Supply chain / variable production rate / NPV method / lead time reduction / backordering / demand uncertainty
© EDP Sciences, ROADEF, SMAI 2020
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