modelinglogistics

modeling

Problem 02 (ABET A, 35pts ). The operations manager of a company that provides logistics services to manufacturing companies in the region (warehousing, transportation, import and export services) wants to determine how many positions in the main warehouse he should reserve to offer to customers who demand storage positions urgently at the last minute. The main warehouse is huge and has a total of 40,000 positions. The regular storage rental price for customers who book well in advance is $30 per position per week. This price is so competitive that the company could rent all 40,000 positions at that rate, however, the number of customers who demand positions on a weekly basis on an urgent basis (at the last minute and without notice) represents a source of increased revenue that could be tapped, as they are willing to pay $70 per position per week because of their urgency. It has been estimated that the demand for positions by last minute clients follows a normal distribution with a mean of 5,000 positions per week and a deviation of 1,700 . On the other hand, for transportation operations, the manager must also decide how many vehicles the company should own. It has been estimated that a company-owned vehicle costs $80 per day, however, if additional vehicles are required, the company can easily rent vehicles at $130 per day (per rented vehicle). According to statistics, daily vehicle demand in transport operations follows a Poisson distribution with an average of 10 vehicles per day. Questions: (1) Determine the optimal number of positions that should be reserved in the main warehouse for last minute customers in order to maximize total revenue. ( 5 pts) (2) Determine what would be the maximum expected revenue in the warehousing line of business according to your answer to question \#1 (10 pts). (3) Determine the optimal number of own vehicles that the company should own for transportation operations, in order to minimize costs. (10 pts) (4) Determine the expected daily cost associated with the use of owned and leased vehicles in the transportation line of business based on your answer to question \#3