Question: Inventory system-A large discount store is planning to install a system to control the inventory of a particular video game system. The time between demands for a video game system is exponentially distributed with a mean time of 0.2 weeks. In the case where customers demand the system when it is not in stock, 80% will go to another nearby discount store to find it, thereby representing lost sales; the other 20% will back-order the video system and wait for the arrival of the next shipment. The store employs a periodic review-reorder point system whereby the inventory status is reviewed every 4 weeks to decide whether an order should be placed. The company policy is to order up to the stock control level of 72 video systems whenever the inventory position, consisting of the systems in stock plus the systems on order minus the ones on back order, is found to be less than or equal to the reorder point of 18 systems. The procurement lead time (the time from the placement of an order to its receipt) is constant and requires 3 weeks. Develop an ExtendSim model to simulate the inventory policies for a period of 6 years (312 weeks) to obtain statistics on

(a) the number of video systems in stock,

(b) the inventory position,

(c) the safety stock (the number of video systems in stock at the time of receiving a new order), and

(d) the number of lost sales.

Investigate improvements on this inventory policy by changing the reorder point, the stock control level, and the time between reviews.