Trips Logistics, a third-party logistics firm that provides warehousing and other logistics services, is facing a decision regarding the amount of space to lease for the upcoming three-year period. 1,000 square feet of warehouse space is required for every 1,000 units of demand, and the current demand at Trips Logistics is for 100,000 units per year. The manager forecasts that from one year to the next, demand may go up 20 percent with a probability of 0.6 or go down by 20 percent by a probability of 0.4. The probabilities of the two outcomes are independent.
The manager can sign a three year lease at a price of 1 dollar per square feet per year or obtain the warehouse space from sport market with 1.2 dollar per square feet per year. From the current year to the next year, spot prices for warehouse space may go up by 12% with probability 0.45 or go down by 12% with probability 0.55. The probabilities of the two outcomes are independent.
The manager believes that the process of warehouse space and demand for the product fluctuate independently. Each unit Trip Logistics handles results in revenue of 1.8 dollar. Trips Logistics uses a discount rate of k=0.06 for each of the three years.
Question:
[1] Please evaluate the spot market option, i.e., calculate the overall profit obtained with not signing a lease and obtaining all warehouse space from the spot market.
[2] Please evaluate a flexible lease option: the company has the flexibility of using between 85,000 sq ft and 105,00 sq.ft at 1 dollar per sq. ft. This means The company must pay for the first 85,000 sq. ft and can the use up tp another 20,000 sq.ft at 1 dollar