Vendor-buyer inventory problem revisited: modeling random yield and trade credit

Abstract

This paper revisits the vendor-buyer inventory problem considering random yield and trade credit. The problem deals with a single vendor, single buyer setting with deterministic demand and stochastic supply due to the random nature of yield associated with the vendor’s production process. Since a trade credit agreement is in place, the buyer is not required to make a payment to the vendor at the time of delivery of the order. The full payment must be delivered at the end of the trade credit period dictated by the agreement. The problem of interest was originally studied by Chen and Kang (Int J Prod Econ 123(1):52–61, 2010) who treat the delivery frequency, i.e., buyer’s order cycle length, as a decision variable. The current paper demonstrates that the buyer’s order cycle length is in fact a random variable due to the random nature of yield, and there is no guarantee that the trade credit period will be longer or shorter than the buyer’s order cycle length. As a result, the modeling and solution approach presented by Chen and Kang (2010) is flawed. The approach is remedied here by formal application of renewal theory. The exact cost expressions for the vendor-buyer system are redeveloped rigorously. The newly developed expressions are utilized to investigate the optimal decisions under decentralized control. Furthermore, the results are generalized to consider a general distribution of random yield associated with the vendor’s production process. Operational and financial consequences these new and more general results are demonstrated via numerical examples.

Keywords:

• vendor-buyer inventory model
• trade credit
• random yield
• decentralized model

Electronic supplementary material

The online version of this article (doi:10.1057/s41274-016-0110-6) contains supplementary material, which is available to authorized users.

Electronic supplementary material

The online version of this article (doi:10.1057/s41274-016-0110-6) contains supplementary material, which is available to authorized users.

Acknowledgments

This research was supported in part by the National Science Foundation (USA) under Grant No. 1131756 and 1530965. The authors thank the Associate Editor and referees for their constructive feedback.

Notes

1 Note that (B.v) and (B.vi) are given by (1515 )–(1818 ) depending on the value of Q.

2 There is no harm in including the boundaries and here due to continuity of in (1919 ) by Property 1.1.

3 Here, needs to be computed using a search algorithm over .

4 Here, due to convexity of , is the solution of over .