An accelerative enumeration algorithm for the bottle combination problem and the menu planning problem

In the clinical practice, there are a number of instances in which the request tailored to each patient must be satisfied with a combination of ready-made medical supplies. For example, in intravenous infusion and feeding, an appropriate combination of commercially available bottles must be chosen such that fluid, electrolyte, and nutritional requirements can be satisfied for the individual patient. Menu planning also has the same feature. However, the problem of the optimal combination of medical supplies is difficult to solve exactly and quickly even with the aid of the computer, because of the combinatorial nature of this problem. We formulate the combinatorial problem of medical supplies as a nonlinear all-integer programming problem and present a fast exact algorithm to solve the problem. The proposed algorithm is proved to find an optimal combination in an acceptable calculation time for medical problems of the usual size.