Profit management of car rental companies

A car rental company consists of a fleet of available rentable vehicles (waiting to be rented and being rented). We model the company as a family of Birth-Death Processes (BDPs) in equilibrium with finite size, indexed by the company utilization parameter. This metric is the ratio of the primary birth and death rates in these BDPs. Relying on the basic concepts of company information and company entropy (i.e., mean information), we promote a procedure for profit management of car rental companies. The company entropy represents the company uncertainty (i.e., risk); moreover, finding optimal values of company utilization and fleet size leads to a unique management of that uncertainty. Introducing the coefficient of proportionality of a company, as ratio of the renting revenue per vehicle per day and costs per vehicle per day, we obtain an expression for the mean profit per day of a company (i.e., profit attained per day from the average number of simultaneously rented vehicles) as a function of company utilization, fleet size and coefficient. Thus, the profit management procedure reduces to finding optimal values of these three metrics, as the key profit drivers of the rental business. Moreover, an expression for the minimal value of the coefficient is introduced (as a function of the other two metrics), determining the zero mean profit per day. Thereby, the efficiency of the company's fleet is determined as a reciprocal of this minimal value. The developed procedure is illustrated on a company which is represented by the Erlang loss system.