LOGM 6111 – Analytical Methods in Supply Chain Analysis
Assignment 8
Answer the following questions. Provide answers in a .docx file and show screen captures if you used a software tool (such as Excel Solver, LPSolve or R Studio). Upload supporting files.
1. [30 points] A company produces window blinds at its Los Angeles, Atlanta, and New York facilities. Each month, the Los Angeles plant can produce up to 100,000 units of blinds. Atlanta can produce up to 120,000 units, and New York can produce up to 140,000 units. Each month, the company must ship to the four distribution regions of the United States—East, Midwest, South, and West—as shown in the table below. For example, the West region must receive at least 130,000 units each month. The cost of manufacturing a unit at each plant and shipping a unit to each region of the country is given in the table. The company wants to find how many units should be shipped from each plant to each region of the country to minimize the total production and transport costs.
Manufacturing and Transportation cost ($/unit)
Plant
East
Midwest
South
West
Capacity
Los Angeles
13.50
14.20
12.20
100,000
Atlanta
13.20
12.60
11.80
14.80
120,000
New York city
12.50
13.10
13.30
15.40
140,000
Demand
90,000
60,000
60,000
130,000
a. Develop a linear programming model (not just a spreadsheet or the LPSolve model) where you list every decision variable and what they represent as well as every parameter or input and what they mean.
b. Solve the model using LPSolve, Excel, or any other MILP Solver. What is the cheapest way ship blinds to get each region?
c. What is the total cost?
d. If the production and transportation cost at Los Angeles plant increases by $1 per unit, would it change the solution in (b)? Explain your answer.
2. [30 points] This problem seeks to determine the set of flows that minimizes the total cost of satisfying customer demand. The situation you can model in Exceland solve using Solver or LPSolve is depicted below where two plants can deliver to 3 distribution centers and directly to some retailers. The total cost associated with transporting and storing one unit along the arcs is given in the figure along with the capacity of each plant and the demand at each retailer. Notice that this is a balanced problem where total capacity equals total demand.
a. Write out the models using mathematical notation (not just a spreadsheet or the LPSolve model) where you list every decision variable and what they represent as well as every parameter or input and what they mean. Then write the model using mathematical notation.
b. Determine the flows along each arch that satisfy the design requirements at minimum cost. When you record your answer, include not only the flows along each arc but the total cost as well.
c. C. Assume that there is also a requirement on the maximum allowable flow through each DC’s that is given below:
Max flow
DC 1
400
DC 2
400
DC 3
350
Determine the flows along each arch that satisfy the design requirements at minimum cost. When you record your answer, include not only the flows along each arc but the total cost as well.
3. [30 points] Sunco Oil produces oil at two wells. Well 1 can produce as many as 150,000 barrels per day, and well 2 can produce as many as 200,000 barrels per day. It is possible to ship oil directly from the wells to Sunco’s customers in Los Angeles and New York. Alternatively, Sunco could transport oil to the ports of Mobile and Galveston and then ship it by tanker to New York or Los Angeles. Los Angeles requires 160,000 barrels per day, and New York requires 140,000 barrels per day. The costs of shipping 1,000 barrels between two points are shown in the following table:
To ($/barrel)
From
Well 1
Well 2
Mobile
Galveston
N.Y.
L.A
Well 1
0
–
10
13
25
28
Well 2
–
0
15
12
26
25
Mobile
–
–
0
6
16
17
Galveston
–
–
6
0
14
16
N.Y.
–
–
–
–
0
15
L.A.
–
–
–
–
15
0
a. Formulate a transshipment model (and equivalent transportation model) that could be used to minimize the transport costs in meeting the oil demands of Los Angeles and New York. What is the transportation plan that minimizes total cost? What is the cost?
b. Assume that before being shipped to Los Angeles or New York, all oil produced at the wells must be refined at either Galveston or Mobile. To refine 1,000 barrels of oil costs $12 at Mobile and $10 at Galveston. Assuming that both Mobile and Galveston have infinite refinery capacity, formulate a transshipment and balanced transportation model to minimize the daily cost of transporting and refining the oil requirements of Los Angeles and New York. What is the transportation plan? What is the total cost?
c. Assume that Galveston has a refinery capacity of 150,000 barrels per day and Mobile has one of 180,000 barrels per day. (Hint: Modify the method used to determine the supply and demand at each transshipment point to incorporate the refinery capacity restrictions, but make sure to keep the problem balanced.)
4. [20 points] A restaurant food supplier wants to deliver plan a route. All routes start with their distribution center (node 1). The (x,y) coordinates of the delivery nodes and the demand at each node is given in the attached file ‘demand_day_1.csv’. The vehicle capacity is 2500.
a. Assume that there is no maximum distance for vehicles. (Hint: For maxdistance, you can use Inf or a very large number when there is no maximum distance). Using the R scripts for nearest neighbor and/or Genetic Algorithm, find the routes to deliver the supplies to all nodes. What is the minimum distance in each method? How many vehicles are required?
b. Assume that a vehicle has a maximum distance of 250 (per route). Using the R scripts for nearest neighbor and/or Genetic Algorithm, find the routes to deliver the supplies to all nodes. What is the minimum distance in each method? How many vehicles are required?
