Subunit Results with no Shortages

Given the lot size, one can compute a variety of results associated with the policy. We call these the instance results.

Lot Size (q): This is the fixed quantity received at each inventory replenishment. The instance results depend directly on this quantity. (units)

Total Profit (): This is the product revenue less the product cost less the cost the cost of running the inventory. In some cases, the optimum inventory policy does not depend on product cost and revenue, so we often set these factors to zero. Then the profit will be simply the negative of the inventory cost.($/time)
Inventory Cost () This is the cost associated with having an inventory. It includes the ordering cost and the holding cost. Traditionally we select a policy to minimize the inventory cost.($/time).
Mean Inventory Level: This is the average level of inventory over time. (units)
Maximum Inventory Level: We do not show the minimum since it is always 0 for the deterministic system with no loses. (units)
Reorder Point (r): This is the inventory level that signals that an order for replenishment should be made. For this system, it is the inventory level for a time L before the inventory reaches 0. (units)
Cycle Time (): The time between successive orders. For this case it is q/D. (time)
Mean Residence Time: This is average time a unit spends in the inventory. By Little's law it is: (mean inventory level)/D. (time)

Optimum Lot Size (q*): This the lot size that minimizes inventory cost and maximizes inventory profit. The results above can be computed for the optimum lot size. We append a (*) to the notation to indicate that the result is for the optimum policy. (units)


Operations Management / Industrial Engineering
by Paul A. Jensen
Copyright 2004 - All rights reserved