Assigned: Tue, 12 Oct (Groups of 2)
Due: 11:59p, Tue, 19 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) Continuing with Question 2 from HW 3, just before purchasing the items, you found out that, in addition to the 30-pound weight and three-cubic-foot cube limits, the items can only be purchased in unit-sized packages. The table below lists the weight (lb) and cube (in3) of each unit along with maximum and minimum order size (units) and the sale and purchase prices (\$/unit). Either zero units or at least the minimum order size of each item must be purchased. Also, due to cross-contamination of odors, ginger and tea cannot both be purchased.
│ Item UnitWt UnitCube MaxOrder MinOrder SalePrice PurPrice
─────┼────────────────────────────────────────────────────────────────────
1 │ Coffee 4 216 5 1 24 8
2 │ Peppers 3 648 2 1 45 18
3 │ Ginger 1 58 5 2 8 1
4 │ Tea 1 864 6 2 35 5
5 │ Candy 2 173 4 3 12 2(1a) How many units of each item should be purchased?
(1b) What is the impact on profit of the ginger and tea restriction?
(2) Weekend staffing needs to be determined at a clinic, and six employees are available. In order to operate, the clinic must have at least one staff member working that is certified in each of twelve different skills. Employee A is certified in skills 1, 4, and 11; employee B in 1, 3, 6, 7, 8, and 10; C in 2, 5, 8, 9, 10, 11, and 12; D in 6, 7, 10, and 11; E in 2, 4, 5, 8, 9, and 12; and employee F in skills 3, 4, 7, 8, 10, and 12. Each employee selected works for the entire time the clinic is open on the weekend, and the fully burdened cost of employees A to F is \$25, 70, 40, 30, 50, and 40 per hour, respectively. Determine which employees should staff the clinic.
(3) There are 100 cities located throughout a region of a state, and public service radio transmitters can be located in any of the cities. The signal from a transmitter can only reach other cities that are within 30 units of distance because of signal attenuation. The coordinates of the cities can be generated by running the following code:
using Random, Statistics
Random.seed!(62738462)
P = 200*rand(100,2)(3a) Determine the cities where transmitters should be located.
(3b) Due to interference, the signals from transmitters that are within 60 units of distance from each other should use different frequencies. Determine the minimum number of different frequencies needed for the transmitters.
(4) A single product is produced in a single-stage production process. A 13-week rolling horizon is used for planning production. The process has a capacity of 60 tons per week. The forecasted demand (ton) over the horizon is provided in HW5-Data-forecasted_demand.csv. Production data for the past year is provided in HW5-Data-historical_prod_cost.csv, where production (ton/wk) and cost (\$000/wk) are listed for the weeks in which the process was operating. The inventory carrying rate is estimated as 0.125 per week. Currently, there are 13 tons of finished product in storage, and this same amount should be in inventory at the end of the planning period. There is enough space to store up to 120 tons of finished product. Determine the best production plan over the planning horizon.
(5) A plant can use a three-stage process to produce three products. A 13-week rolling horizon is used for planning production. The products’ forecasted demand (ton) over the horizon is provided in HW5-Data-forecasted_demand_2.csv.The plant can produce up to 600, 550, and 500; 500, 450, and 350; and 400, 350, and 300 tons per week for each stage of each product, respectively; has production costs of \$12, 75, and 35; 20, 130, and 60; and 16, 100, and 50 per ton for each stage of each product, respectively; and has costs of \$4000, 900, and 500; 6000, 1100, and 600; and 5000, 1000, and 600 per set up for each stage of each product, respectively. The annual inventory carrying rate is 0.3. The plant is currently set up to produce each stage of the first product, and the first three weeks of demand for the other two products are being held as inventory at each stage. The final inventory for all stages of all products is zero. Determine the amount of each product that should be produced in order to for the total costs over the planning horizon to be within 1% of the optimal value.