The paper evaluates and compares classes of multi-item inventory problems, where joint order of several items may save a part of the setup cost. A cost ratio and simple decision rule are determined for joint versus individual orders in specified cases. The comparisons call for the necessity of a new policy for reorder point-triggered random output multi-item systems. This policy, the "random joint order policy," operates through the determination of a reorder range within which several items can be ordered. The existence of an optimum reorder range is proved, and a computational technique is demonstrated with the help of a machine-interference type queueing model. Under favorable conditions the results exhibited on the diagram of optimum reorder ranges are generally applicable. The random joint order policy model is especially suitable for computer controlled inventory systems.

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A multistage multiple choice programming system was developed to reduce the food cost of institutional feeding programs by computer assisted menu planning and data control. Food management objectives were formulated as finding combinations of menu items for a sequence of days which satisfy desired nutritional, structural, compatibility and variety constraints at least cost, problems routinely faced by all volume feeding organizations and individuals. Solution was achieved by sequential solution of large integer programs with a specially developed truncated block enumeration algorithm. Programmed dialog made on-line postoptimal adjustments possible. A complete computerized food management information subsystem was also developed to support the matrix generator and provide a uniform file organization and data coding system applicable to any institution. System documentation, called S/360 CAMP, is available through the IBM Contributed Program Library. After initial implementation in four hospitals proved that mathematical optimization had indeed reduced the food service cost by 10–15 percent while maintaining prescribed nutritional and acceptability levels, two companies were formed to serve institutions in the application of CAMP and its derivatives. Published reports indicate successful applications in numerous hospitals, colleges, schools, and mental and penal institutions, realizing 5–34 percent cost savings. The number of applications in the United States and abroad has been increasing over the years with beneficial impact on food management and nutritional health. The results motivated a new approach to food price index theory since the applications provide a practical mechanism to optimally readjust food consumption in the face of price fluctuation.