A single-period inventory and payment model with partial trade credit

We model a capital-constrained retailer who is offered partial trade credit.We show the retailer's optimal policy under given fraction of immediate payment.We extend the model to the situation of deciding fraction of immediate payment.Partial trade credit may hurt the retailer in many cases.Suppliers can design a suitable interest rate to elicit retailer's cash status. In this paper, we consider the ordering and payment issues for a retailer facing stochastic demand. We assume that the retailer can enjoy the partial trade credit from his supplier and borrow money from bank as well if needed, and he can also earn return by investing his superfluous on-hand cash (if any). The retailer's objective is to maximize the expected cash level at the end of the selling period. We formulate the model of this problem by taking initial inventory and capital levels as the two-dimensional state. First, given the exogenous fraction of immediate payment, we show that unlike the critical fractile solution the retailer's optimal ordering strategy is a two-threshold policy, which is independent of the retailer's initial inventory level and capital level. Second, we consider an extensive model where the fraction of immediate payment is decided by the retailer. We employ the sequential optimization procedure to solve the extensive problem, and present the structure of the retailer's optimal policies under different partial-trade-credit penalty rates. Numerical experiments show that if the fraction of immediate payment is exogenous, both partial trade credit and loan opportunity are detrimental to the capital-constrained retailer in many cases, although they can stimulate the retailer to order more.

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