Optimal advertising/ordering policy and finance mode selection for a capital-constrained retailer with stochastic demand

Abstract

In this paper, we discuss how a capital-constrained retailer determines his optimal advertising/ordering policy and selects his financing mode when he faces the following modes: no financing service, bank financing, and supplier/mixed financing. For each mode, we construct an optimization model and present a method for how the retailer determines his corresponding optimal advertising and ordering policies in the terms of his initial capital level. Furthermore, we derive the conditions of retailer selecting the optimal financing mode based on both his initial capital level and the interest rates of the financing services. We show that when the retailer is relatively “poor,” he prefers bank financing mode if the bank interest rate is lower than the supplier, otherwise mixed financing mode; when he is moderately “rich,” he only selects supplier financing mode if the bank interest rate is greater than a threshold value and otherwise bank financing mode; however, when he is relatively “rich,” he always chooses bank financing mode even if the bank interest rate is higher than the supplier. We conduct numerical studies to illustrate the theoretical results and find adopting financing service significantly improves the retailer’s performance especially when he has relatively low initial capital level.