A joint model for cash and inventory management for a retailer under delay in payments

As retail companies continue to navigate through the economy downturn, it becomes critical to find innovative cost reduction methods. Cash management is a cost-intensive process for retailers, who are currently focusing on effective cash management, such as deciding on the maximum cash level to keep in their business accounts and how much to borrow to finance inventories and pay suppliers. In this paper, we consider the problem of finding the optimal operational (how much to order and when to pay the supplier) and financial decisions (maximum cash level and loan amount) by integrating the cash management and inventory lot sizing problems. We consider a supplier offering a retailer an interest-free credit period for settling the payment. Beyond this period, the supplier charges interest on the outstanding balance. Whenever the cash exceeds a certain limit, it will be invested in purchasing financial securities. At the time when the retailer pays the supplier for the received order, cash is withdrawn from the account, incuring various financial costs. If the cash level becomes zero or not sufficient, the retailer obtains an asset-based loan at interest. We model this problem as a nonlinear program and propose a solution procedure for finding the optimal solution. We perform a numerical study to analyze the impact of optimal cash management on the inventory decisions. The results indicate that the optimal order quantity decreases as the retailer’s return on cash increases. We compare our model to a model that ignores financial considerations of cash management, and show numerically that our model lowers the retailer’s cost. Also, we illustrate the effect of changing various model parameters on the optimal solution and obtain managerial insights.