Reference no: EM133131401
IE 505 Production Planning and Scheduling
Term Project Assignment
Objective
This term project assignment focuses on:
• developing a mixed integer programming model to solve a production planning problem,
• practicing optimization software package GAMS, and
• communicating the results of a study in written form.
Formation of Term Project Study Teams
• In doing the term project assignment, students should exactly work in teams of two or three. Thus, there will be two teams with 2 students and one team with 3 students since the number of students taking the course is 7.
• It is the student's responsibility to find his/her team members.
• Each study team should fill out a single copy of the Info Form of the Term Project Study Team, which can be downloaded from the course's webonline site, on which the student number, name and surname, cellular phone number and e-mail of the team members appear.
• Incomplete forms are not accepted.
• One member of a study team should complete their Info Form and share it with other team members.
Report Preparation
• Term Project Reports should be typed in Microsoft Word and be prepared in accordance with the technical report writing specifications.
• There is no limitation on the number of pages but the report should be brief, concise, and to the point.
• A member of the team should write the following HONOR CODE with his/her own handwriting on the cover page of the term project report, and each member of the team should sign underneath.
PRODUCTION PLANNING PROBLEM IN THE FCC COMPANY
FCC Company that manufactures 3 different products is considering the preparation of an aggregate production plan for the next 6 months ahead. The products are manufactured in a plant that has 4 manufacturing lines where the production capacity of each line is represented in terms of dedicated number of workers to that line. Line 1 and Line 2 can be used for products 1 and 2, Line 3 only for product 3. Line 4 can be used to manufacture all three products. The monthly production capacity of a worker in terms of units is changing from one product to another in each line as tabulated below:
|
Line 1
|
Line 2
|
Line 3
|
Line 4
|
|
Product 1
|
Product 2
|
Product 1
|
Product 2
|
Product 3
|
Product 1
|
Product 2
|
Product 3
|
|
2
|
1
|
1
|
2
|
2
|
4
|
3
|
3
|
In each manufacturing line, the plant currently (beginning of month 1) maintains an employment level of 20 workers, each of whom works on an 8 hour/day and 20 days/month basis and earns $20 per day. At the beginning of each month, additional workers may be hired and trained at a cost of $400 per worker, or current ones may be laid off at a cost of $300 per worker. But, no more than 25 % of the workforce can be laid off in any month. The newly hired workers are subject to a training program, which lasts one month, during which the workers are not employed in the production. Minimum and maximum number of workers required to operate each of the manufacturing line in any month is 10 and 30, respectively. Moreover, overtime for each worker is allowed at a rate which is 50% more than the regular time payment in each month, but is limited to 20% of the regular time hours.
At the beginning of month 1, the inventory levels for products 1, 2, and 3 are 35, 50, and 45 units, respectively. The demand for a product in a month is uniform throughout the month, and can be supplied by production in that month or from the inventory received from the previous month. The company has a warehouse restriction that permits the storage of maximum 200 units of all products left to the next month. The inventory holding costs are $2, $4, and $3 for products 1, 2, and 3, respectively, for carrying one unit for one month. The production of product 1 features economies of scale (a concave cost structure) while the other products have fixed unit production costs.
The demand and unit production cost (excluding labor cost) are given below.
|
Month
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Product
|
1
|
2
|
3
|
1
|
2
|
3
|
1
|
2
|
3
|
1
|
2
|
3
|
1
|
2
|
3
|
1
|
2
|
3
|
|
Demand (units)
|
100
|
200
|
150
|
110
|
200
|
160
|
120
|
200
|
155
|
130
|
200
|
160
|
140
|
200
|
155
|
150
|
200
|
160
|
|
Unit Production Cost (excluding labor cost)
($/unit)
|
*
|
40
|
30
|
*
|
40
|
30
|
*
|
40
|
30
|
*
|
40
|
30
|
*
|
40
|
30
|
*
|
40
|
30
|
(*) 20 $/unit if the production amount is less than 100 units; otherwise (100 units or more), 18 $/unit.
Since the market in which the company exists is very competitive, no shortages are allowed for the products. However, products can be supplied from subcontractors provided that a subcontracting setup cost is incurred to each of the product subcontracted and the amount subcontracted does not exceed a certain proportion of the production amount of the corresponding product in any month as shown in the following tableau.
|
Product
|
1
|
2
|
3
|
|
Subcontracting setup cost ($/unit)
|
200
|
300
|
100
|
|
Purchasing cost ($/unit)
|
100
|
150
|
125
|
|
Maximum allowable percentage of
subcontracted products (%)
|
50
|
50
|
80
|
Task 1: Formulate a mixed integer programming model to obtain a production plan of the company for the next 6 months.
Task 2: Solve your model using GAMS.
Task 3: Present and discuss your results on production and subcontracting quantities, inventory levels, workforce levels, etc.
Task 4: Based on the results you obtained, determine the minimum average selling price for each product.
Attachment:- Production Planning and Scheduling.rar