Analytical framework for the multi-item, economic order quantity model with permissible delay in payments and a budget constraint. A note

In a previous work (Chandrashekar, A., and Gopalakrishnan, M., Purchase cards and inventory control - an analytical framework. Prod. Plan. Cont., 2005, 16(5), 437-443) we developed a framework for comparing the use of 'purchase cards' (P-cards) to order merchandise directly from a supplier versus obtaining direct credit from the supplier. We illustrated for the single-item case, that there exists a critical ordering cost such that the P-card can be used if and only if the actual cost of ordering using P-card is less than this critical value. In this paper we extend this framework for determining the optimal replenishment quantity for multi-item ordering under the conditions of permissible delay in payment, a budget constraint, and permissible partial payment at a penalty. The analysis indicates that it is more economical for the purchaser to make entire payments even when the interest earned is greater than the interest charged. This note reflects reality more accurately.