Spatila-box-Software system for replenishment quantities of many commodities under simultaneous restrictions on space and capital, and with quantity discount options

This paper presents a radically new solution to a well known problem: how to determine economic replenishment quantities of many goods passing through restrictions on space or capital in stocks, and other problems, to which no solution has been suggested: Space and capital constraints. Quantity discount options. It is also an illustration of how an assumption thought to be so obvious that it need not be stated, can avoid being revealed as false and prevent for a long time the search for a better solution. Further it is an illustration of how electronics can open for solutions which otherwise would be excluded from practical application due to the quantity of calculations it would require. The traditional ‘Lagrangian’ method of determining order sizes for multi item inventory under space constraint secure optimality only under the tacit and quite arbitrary assumption that all replenishments of one item must be equal. This implies that of the supposedly scarce space available to accommodate replenishments on the average 50% is exploited. Newer theoretical models improve this by methods of staggering orders that are still of constant size over time. But they are not practically implementable.