Assigned: Thu, 21 Oct (Groups of 2)
Due: 11:59p, Thu, 28 Oct
Group Members:
Please use the Code cells in this Jupyter notebook to answer each of the following questions. You can add additional cells for each question if that helps in organizing your solution. Please run all of the cells in your notebook and then submit it via Moodle. (There is a Run All Cells command under the Run menu.)
(1) Select the least cost combination of activities where the total cost is the product of the cost of each individual activity selected subject to the square root of the product of the cost of the selected activities exceeding six, where the cost of each activity is 6, 5, 1, 3, 4, 2, and 5, respectively. A BIP formulation of the problem is as follows:
$ \begin{eqnarray*} \quad \mbox{Minimize} \quad \prod_{i \in M} c_i x_i \\ \quad \mbox{subject to} \quad \sqrt{\prod_{i \in M} c_i x_i} &\gt& 6 \\ x_i &\in& \bigl\{ 0, 1 \bigr\}, &\quad i \in N \\ M &=& \bigl\{ i \in N : x_i = 1 \bigr\} \end{eqnarray*} $
(2) Products A, B, C, D, E, and F are to be produced using eight different machines, Machines 1–8. The routings are as follows:
$ \quad \begin{array}{lll} A: 3–6–5–8–6–4; & C: 8–4–2–6–5–3–1–7; & E: 5–8–2–6–5–3–1–7; \\ B: 5–3–4–1–7–5; & D: 6–1–4–7–3–5–8–2; & F: 7–6–4–6–4; \end{array} $
Assuming that 242, 472, 351, 82, 118, and 735 units of A, B, C, D, E, and F, respectively, are to be produced, determine a machine layout that minimizes the total cost for the following site locations:
(3) Recommend the best mix of construction and improvement procedures that should be used to schedule independent tasks on parallel identical resources without preemption to minimize makespan for the problem instance created using the following code:
n,m = 200,30
using Random
Random.seed!(543235)
t = rand(1:20,n)Describe your recommendation along with its justification in a short paragraph in the space below in this cell, where reference can be made to the results of experiments reported in the code cell below:
Recommendation:
Justification:
(4) Implement the MILP formulation of the scheduling independent tasks on parallel identical resources without preemption to minimize makespan problem provided in Comb Opt 3 and use it to solve the following extension of Ex 2 of Comb Opt 3:
A repair shop has four identical stations available. Today, 10, 7, 4, 2, 9, 8, 4, and 10 repairs will be performed for each of eight different types of repair, where each type takes, on average, 53, 20, 53, 15, 30, 55, 32, and 21 minutes, respectively. Determine the repairs that should be allocated to each station, assuming that it takes five minutes to switch between each repair at the station no matter the type of repair or the type of the preceding repair. Also, no more than 15 repairs per day should be made at any station.
(5) A hospital has three identical operating rooms available. Five different types of operations will be performed that each takes 50, 30, 150, 90, and 220 minutes, respectively, on average, and there are three, six, two, five, and one operation of each type, respectively, planned for tomorrow. Determine the operations that should be allocated to each room (your recommendation) along with a justification of your approach. Describe your recommendation along with its justification in a short paragraph in the space below in this cell, where reference can be made to computations reported in the code cell below:
Recommendation:
Justification: