Marketing Spending and Customer Lifetime Value for Firms with Limited Capacity

The concept of customer lifetime value (CLV) is widely used by marketing practitioners and academics in making decisions about customer acquisition and retention spending. The traditional view of CLV, however, assumes that the firm has the unlimited capacity to serve all its acquired and retained customers. In this paper we consider a firm with limited capacity and determine the role that CLV plays in its acquisition and retention spending decisions. We find that the optimal spending for the firm with limited capacity increases in capacity and decreases in the number of customers. This stands in contrast to the firm with unlimited capacity that spends the CLV-maximizing amount regardless of the number of other customers. Surprisingly, however, the firm with limited capacity may spend more than the CLV-maximizing amount, which happens when the time value of money is large. When the time value of money is small, the two spending levels are nearly identical when the firm is well under capacity, but as the firm grows and approaches its capacity limit, optimal acquisition and retention spending decrease to substantially lower, but still non-zero levels. We characterize optimal spending for the firm at capacity in closed form and discuss the role CLV plays in optimizing customer mix. We also examine customer selection decisions. We again find that CLV alone does not determine those decisions. In particular, we show the firm with limited capacity may prefer a customer with a lower CLV. Lastly, we consider capacity expansion. We show that the expansion decision is of the threshold type: intuitively, the firm should expand when it becomes large enough. Interestingly, however, the value of expansion is largest when the firm still has significant unutilized capacity. CLV again offers little guidance in determining this value – per unit value of expanded capacity is much larger than the CLV of the customer who will occupy it. We also observe an interesting behavior of spending during the timelag between the decision to expand and the period when the additional capacity becomes operational: in that timelag the firm drastically reduces spending on the low-value customers, while increasing the spending on the high-value ones in order to rebalance its customer mix in anticipation of additional capacity.