Optimal cash management with uncertain, interrelated and bounded demands

•The online algorithm BCSID for the cash management problem with interrelated demands.•The proof of competitive ratio and optimality of BCSID.•A heuristic online algorithm aBBCSID for the cash management problem with interrelated and bounded demands.•A numerical testing to compare the performance of BCSID and aBBCSID to other online algorithms. We consider the cash management problem with uncertain demands. These demands may be interrelated and globally bounded. Most research done in this field assumes a given information about a probability distribution of demands. In practice, however, it is difficult to correctly estimate this distribution. Here, we report on an optimal online algorithm called balanced cash supply for interrelated demands (BCSID) which is free of any distribution assumption. BCSID has information about the minimal and maximal ratio of two consecutive demands. The new algorithm has the smallest relative difference in relation to the optimal result when demands are adverse. Hence, our algorithm is particularly relevant for risk averse cash managers. Furthermore, we provide a heuristic algorithm called approximated balanced bounded cash supply for interrelated demands (aBBCSID). This algorithm has the same information as does BCSID; it also has information about the global bounds of the demands. In addition, we carry out extensive numerical testing and compare these two algorithms to simple benchmarks and the solution of Liu and Xin (2008). The testing proves the practical relevance of BCSID and aBBCSID.