Results when Shortages are Allowed

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) Fill Rate (v): This is the proportion of demand filled immediately from inventory. 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, holding cost and costs related to shortages. Traditionally we select a policy to minimize the inventory cost.(\$/time). Mean Inventory Level: This is the average level of inventory over time. (units) Mean Backorder Level: This is the average level of backorders over time. (units) Maximum Backorder Level: This is the total number of shortages during a cycle. This result is presented only when shortages are backordered. (units) Lost Sales Rate: This is the rate of lost sales. It is only used for models with lost sales. (units/time) 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 the minimum inventory position. (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) Mean Backorder Time: This is average time a unit spends in the backorder. By Little's law it is: (mean backorder level)/D. (time) Optimum Lot Size (q*): This the lot size that minimizes inventory cost when the optimum fill rate is used. (time) Optimum Fill Rate (v*): This is the fill rate that minimizes inventory cost. (no dimension)

Operations Management / Industrial Engineering
Internet
by Paul A. Jensen