Question

Inventory management. A computer store sells and maintains an inventory of fax machines (units). On average, one unit is sold per day, but the store experiences a burst of customers on some days. A marketing survey suggests that customer interarrival times are iid exponentially distributed with rate 1 per day.

When the inventory on hand drops down to 5 units, an order of 20 units is placed with the supplier, and the lead time is uniformly distributed between 5 and 10 days. Unsatisfied customers check back with the store and wait for the order to arrive (backordering case). Keep in mind that another order is placed immediately upon order backorder arrival, should the inventory level fall below the reorder level after satisfying all backorders.

Table 12.3 Simulation outputs for a replication of multiechelon supply chain Backorder Level Fill Rate (%) Backorder Level Fill Rate (%) Inventory Level Inventory Level Input Buffer Output Buffer DC Retailer 15.0203 23.6452 23.0257 8.5209 N/A 0.0003 0.0000 N/A 99.88 99.85 100.00 98.61 14.8334 22.9043 22.8343 8.3328 N/A 0.0013 0.0000 N/A 99.87 99.58 100.00 98.14 Inventory Backorder Level Fill Rate (%) Inventory Level Backorder Level Fill Rate (%) Input Buffer Output Buffer22.0530 DC Retailer Level 14.6480 22.6296 N/A 0.0052 0.0000 N/A 99.86 98.88 100.00 97.58 14.4680 21.0038 22.3842 7.9646 99.85 97.23 99.98 96.97 N/A 0.0199 0.0005 8.1465 Backorder Level Fill Rate (%) Inventory Level Backorder Level N/A 0.2507 0.0169 N/A Inventory Fill Rate (%) Input Buffer Output Buffer19.6205 DC Retailer Level 14.2924 22.0235 0.0731 0.0031 N/A 99.84 93.57 99.90 96.26 14.1222 17.6510 21.3356 7.5964 99.82 86.11 99.56 95.44 7.7828

What is the average stock on hand?
What is the average backorder level?
What percentage of the time does the store run out of stock? Note that this is the probability that a customer's order is not satisfied and is subsequently backordered.
What is the percentage of time that the stock on hand is above the reorder level?

Answer 1