We develop a modified exploration–exploitation algorithm which allocates a fixed resource (e.g., a fixed budget) to several units with the objective to attain maximum sales. This algorithm does not require knowledge of the form and the parameters of sales response functions and is able to cope with additive random disturbances. Note that additive random disturbances, as a rule, are a component of sales response functions estimated by econometric methods. We compare the developed algorithm to three rules of thumb which in practice are often used to solve this allocation problem. The comparison is based on a Monte Carlo simulation for 384 experimental constellations, which are obtained from four function types, four procedures (including our algorithm), similar/varied elasticities, similar/varied saturations, high/low budgets, and three disturbance levels. A statistical analysis of the simulation results shows that across a multi-period planning horizon the algorithm performs better than the rules of thumb considered with respect to two sales-related criteria.