Determination of the optimal procurement policy under integrating working capital.

INTRODUCTION

In view of the interrelationships among inventory, procurement, cash discounts, accounts payable and accounts receivable policies, both academicians and practitioners appear to have recognized the need to integrate them. Until now, there have been few studies on integrating working

capital decisions. Some exceptions include joint credit/inventory models, cash discounts/credit period models and inventory/accounts payable interactions that have been considered and studied by Kim and Chung [4], Sartories and Hill [5], Chapman, Ward, Cooper and Page [2] and their references, respectively.

Recently, Arcelus and Srinivasan [1] considered the problem of integrating the main components of working capital decisions within a discounted cash flow framework to study the interrelationships among inventory procurement, cash discounts, accounts payable and accounts receivable policies. This paper discusses the same model as that of Arcelus and Srinivasan [1]. The purpose of this paper is threefold: first, this paper will prove the discounted infinite horizon present value function is concave with respect to the cycle time; second, bounds for the optimal cycle time will be derived; third, a simple algorithm to locate the optimal cycle time will be developed. Finally, numerical examples are given to illustrate the algorithm.

THE MODEL

The following notation will be used. Let

U = demand rate per unit time;

T = cycle time;

[T.sup.*] = optimal cycle time;

P = sales price per unit;

C = purchasing costs;

h = holding cost per unit per unit time;

k = discount rate per unit time;

d = cash discount (percent of P) offered by wholesaler for early payment;

[Mathematical Expression Omitted] = cash discount (percent of C) offered to wholesaler for early payment;

M = cash discount period offered by wholesaler for early payment;

[Mathematical Expression Omitted] = cash discount period offered to wholesaler for early payment;

L = net credit period offered by wholesaler for full payment;

[Mathematical Expression Omitted] = net credit period offered to wholesaler for full payment;

r = average percent of sales with cash discount

= probability of paying within cash discount date, M;