Effect of Supply Chain Finance Solutions on Production Planning Under Yield and Lead Time Uncertainty

For capital constrained suppliers, use of supply chain finance requires consideration of interplay between production and finance decisions. We solve the optimal input procurement problem for a capital constrained make to order manufacturer subject to yield and lead time uncertainty and compare use of supply chain finance methods (Advance Payment Discount (APD), Bank Loan (BL), Reverse Factoring with initial bank loan (RF), and Buyer Backed Purchase Order Finance (BPOF)). Our model applies to manufacturing from raw material such as mechanical and electronics and service processes such as cold chain transportation with individual cooling units, e.g. for vaccine distribution. We model our problem via stochastic optimization with binomial production yield and discrete random lead time. We prove the convexity of the objective functions for APD, BL, and RF; and we show that the objective function for BPOF can be expressed as difference of two convex functions and employ Difference of Convex Functions programming to find the optimal production input amount. We see that, as frequently applied in practice, payment terms longer than 90 days may make the supplier give up on the order due to no expectation for any profit. Optimal profit is more sensitive than procurement amounts to the joint effect of interest rates and yield probability as well as fluctuations in lead time. For suppliers with higher yield rates BPOF brings the most advantage when interest rates are the same for all methods, and APD brings the most advantage when flexibility on interest rates it provides is employed for suppliers with lower yield rates. Methodologically, we develop an analytical make-to-order model under yield and lead time uncertainty and solve the resulting optimization problems using expected profit maximization, including DC programming for the BPOF scheme.