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

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.