international journal of production economics ELSEVIER Int. J. Production Economics 45 (1996) 65-75 Financing constraints and reordering rules Abstract Constraints on external finance modify a simple inventory investment decision. Optimal policy is no action when cash holdings are less than threshold levels (the control boundaries) which are functions of the current level of inventories. On the control boundaries additional cash is used for inventory replenishment, when inventory holdings are below the level which would be held in the absence of financing constraints, and for dividend payment, when inventory holdings are equal to or exceed this level. A fixed boundary at all inventory levels is used as an approximation to the fully optimal control allowing computation of the behaviour of aggregate inventory and cash holdings for a population of financially constrained firms. There is a pronounced and extended dynamic response from inventory investment following aggregate disturbances to cash holdings, to prices, and to the standard error of the diffusion process for cash holdings. This contrasts with the unconstrained case where such shocks have no effect on either inventory holdings or inventory investment. Keywor-ds: Inventory dynamics; Financial constraints 1. Introduction and assumptions This paper considers the effect of financing con- straints on a simple inventory holding decision. The analysis follows that of Greenwald and Stiglitz [l] and Milne and Robertson [2], who impose exogenous financing constraints and consider the implications this has for the valuation of the firm, the level of output and (in the latter paper) fixed capital investment. In the present analysis firms have two decisions: they replenish inventory and (as in [2]) pay out dividends with the objective of maximising the expected present discounted level of current and future dividends. In the absence of financing constraints this would be a standard deterministic inventory prob- lem. There is a fixed rate of sales out of inventory with both the sales price and the per-unit cost of replenishment constant. Inventory holding costs are a convex function of the level of inventory. Orders to replenish inventory are non-negative and filled instantaneously. There are no fixed costs of making an order. Thus in the absence of financing constraints optimal policy is of the “one-bin” class: when inventory is below the desired level immedi- ately replenish up to this level and take no action when inventory exceeds this level. The introduction of three additional assump- tions leads to a marked change of re-ordering pol- icy: these assumptions are that the firm holds cash which follow a stochastic process (specifically a dif- fusion process); that the firm is liquidated with no OY25-5273/96/$15.00 Copyright \((: 1996 Elsevier Science B.V. All rights reserved SSDI 0925-5273(96)00013-8