Formulate the following problems as an LP and prepare the project deliverables that are listed at the end.
1- ABC company produces and sells wooden desks. The demand is forecasted for each month of the next year. The company currently has 20 employees and each employee can produce 30 desks in a month. The monthly salary of each employee is $110. Since raw material cost change at each month, the production costs are different for each month of the year. Excessive amount produced in a month can be stored in the inventory for use in the following months. However, the storage space has a capacity of 300 desks in total. The inventory holding costs are also different at each month. In order to satisfy excessive demand in a month, the company may use its inventories, may implement overtime working hours, or hire additional workers. The total overtime production for each worker at each month can be at most 10% of the regular time production. Also the overtime production cost is different than the regular time production cost. Furthermore, the maximum number of workers who can work in the company at the same time is 25. It is also possible to fire the workers but the workforce cannot be less than 15. Hiring and firing costs differ each month. All the necessary data of the problem will be provided as a separate MS Excel file. a. Formulate this problem as an LP. Type your model in MS Word or any other editor. Define your decision variables, explain the objective function, and all constraints. b. Implement the model in CPLEX OPL. Solve all the problems provided in the MS Excel file. In your implementation, the data should be read directly from the Excel file. Provide your solutions in your report and discuss your results.
2- There are currently 3 machines in a factory: P1, P2, and P3. Assume that this rectilinear shaped factory is located on the first quadrant of the coordinate system and one corner is at the origin (point (0,0)). The coordinates of the existing machines are as follows:
P1=(10,15), P2=(20,25) ve P3=(40,5)
To meet the increasing demand and respond to changing customer demands, the company decided to grow and acquired two new machines: N1 and N2. When these two machines are put into operation, they will exchange materials with each other and with the other three machines. 400 units of material will be transported between the
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two new machines in a week. Similarly, 400 units will be transported between N1 and P1, 0 between N1 and P2, and 500 units between N1 and P3. The transportation between N2 and P1, P2, and P3 are 200, 100, and 0, respectively.
Materials are transported with an overhead crane. This crane can move linearly in x and y coordinates and can move simultaneously in both directions. It moves at a speed of 0.8 m/sec on the x-axis, its movement on the y-axis occurs at a speed of 1 m/sec. While the crane moves from one point to another, it starts to move in both x and y directions at the same time. As soon as one of the coordinates reaches to the coordinate of the destination point, the movement in that direction is terminated. But its motion in the other direction continues until it reaches the coordinate point on that axis also.
You can check the provided links below to see how overhead cranes work. Crane movement consumes both time and energy. Therefore, minimizing the total movement time is the main goal.
The problem is to determine the coordinates of the new machines that will minimize the total movement time.
Vinçleri çalışırken görmek için:
a. Formulate the problem as an LP. Type your model in your report and explain the objective function and the constraints. If the resulting model is not linear, linearize it and explain how you linearized it. b. Implement the model in CPLEX OPL and solve it. Provide your solutions in your report and discuss your results.
PROJECT DELIVERABLES: 1. Project report typed in MS Word. The reports must contain the LP models of both problems, the explanations of the models, the results that you obtained, and a discussion of the results. All mathematical equations and notations must be written using equation format in Word. Upload your reports into the moodle system before the deadline. 2. CPLEX implementation of both models. Both models must be under the same project as different run configurations. Also prepare different run configurations for all the data given in the Excel files. Upload the CPLEX project directory into the moodle system after zipping. Name the zipped files with your name (i.e. if I am the student, my project file should be named HakanGultekin.zip or HakanGultekin.rar)
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