A company wants to plan its fleet size for the next 5 months. At the moment, they do not own any trucks, however they will need to lease multiple ones for each of the following months. Their demands are as follows: The leasing company they work with offers only two plans: - leasing a truck for 2 months at a cost of $1,500; - leasing a truck for 3 months at a cost of $2,000. Answer the following questions: (a) Formulate the problem of minimizing the cost of the lease while satisfying every period demand. (b) Using the formulation of part (a), create a minimum cost flow problem and draw its corresponding network. (c) Right now the company plans to do the following: 1. Lease 15 trucks for 3 months at month 1 . 2. Lease 15 trucks for 2 months at month 1 . 3. Lease 15 trucks for 3 months at month 3 . 4. Lease 10-trucks for 2 months at month 3 . 5. Lease 10 trucks for 2 months at month 5. Verify that this is indeed a feasible solution to your original planning problem formulation of part (a) and to the minimum cost flow problem of part (b). (d) The leasing company imposes that no lease can be made for more than 15 vehicles at a time. Moreover, the company board has indicated that they will not allow any solution where more than 20 trucks are leased but not used from month to month. With this new information (capacity constraints!), and starting from the previous solution, perform one iteration of bounded network Simplex on the network you have identified in part (b). A company wants to plan its fleet size for the next 5 months. At the moment, they do not own any trucks, however they will need to lease multiple ones for each of the following months. Their demands are as follows: The leasing company they work with offers only two plans: - leasing a truck for 2 months at a cost of $1,500; - leasing a truck for 3 months at a cost of $2,000. Answer the following questions: (a) Formulate the problem of minimizing the cost of the lease while satisfying every period demand. (b) Using the formulation of part (a), create a minimum cost flow problem and draw its corresponding network. (c) Right now the company plans to do the following: 1. Lease 15 trucks for 3 months at month 1 . 2. Lease 15 trucks for 2 months at month 1 . 3. Lease 15 trucks for 3 months at month 3 . 4. Lease 10-trucks for 2 months at month 3 . 5. Lease 10 trucks for 2 months at month 5. Verify that this is indeed a feasible solution to your original planning problem formulation of part (a) and to the minimum cost flow problem of part (b). (d) The leasing company imposes that no lease can be made for more than 15 vehicles at a time. Moreover, the company board has indicated that they will not allow any solution where more than 20 trucks are leased but not used from month to month. With this new information (capacity constraints!), and starting from the previous solution, perform one iteration of bounded network Simplex on the network you have identified in part (b)
