Casa Migliore is a production company that manufactures high quality furniture. The manager of Casa Migliore has realized the opportunity to increase the revenues by reducing the costs related to production and inventory levels. He now wants to optimize the production planning of three types of chairs, A, B, and C for the next 6 months. In Table 1, sales forecasts for each type of chair are given.
Table 1. Demand for each type of chair for the next 6 months.
March April May June July August
A 700 900 750 800 600 400
B 1500 1750 2500 2300 2200 1800
C 3200 3200 5200 6500 4700 4500
Due to the fluctuations in the prices, total material cost for each type of chair may vary each month and expected material costs are given in Table 2.
Table 2. Expected material cost for each type of chair for the next 6 months.
March April May June July August
A 20 20 20 40 40 40
B 16 22 22 26 26 26
C 11 11 8 8 16 16
For the production of the chairs type A, B, and C, 3, 2 and 1 worker hours are required, respectively.
There are currently 40 workers that produce these three types of chairs and each of them works 10 hours a day. The number of working days varies depending on the month and working days in each month are given in Table 3.
Table 3. Number of working days for the next 6 months.
March April May June July August
21 22 20 21 22 20
At the beginning of each month, new workers are hired at a cost of 250 TL and existing workers can be fired at a cost of 400 TL. Wages consist of the majority of the total cost and workers are paid 10 TL per day including insurance, meal and transportation. Monthly wages may change from one month to another month due to the number of working days. All demand must be satisfied on time. Assume that there is no backorders and lost sales. The inventory holding costs are 10, 5, 2 TL per item per month for products A, B and C, respectively. Note that initial inventory levels are 0.
In this project, you are required to develop an LP model to solve the production planning problem of Casa Migliore and answer the following questions.
Question 1)
A. Write an LP model to minimize total cost.
Define decision variables clearly
Write explanations for each constraint
B. Solve the proposed LP model using GAMS.
- In the output, display production and inventory levels for each month, numbers of hired
and fired workers for each month and the total cost.
Question 2)
Rewrite the above model according to the following instructions. You have to adjust or
update the constraints and/or the objective function. It may be necessary to add new variables.
A. Assume that employees will not be fired in April or May since May 1 is the International Worker’s
Day.
B. In Turkey, an employer should inform his/her employee one month before firing. Otherwise, a
penalty equal to the employee’s salary must be paid by the employer. In other words, if an employee
is fired, he/she leaves the workforce after one month.
Question 3)
A. Form excel file/files that include Tables 1 and 2 for the demand and expected material cost of each type of chair for the next 6 months. Modify your gams model that you have developed in Question 1 so that it reads Tables 1 and 2 from excel files.
B. Modify your gams model so that the optimal results you have obtained for question 1 are written in an excel file.
I had trouble constructing the linear programming model. I decided that my decision variables should be the number of hired-fired-current workers, production quantity and the inventory level. But I am not sure how I will write the constraint equations like how to hire or fire workers. Should I use some if-statements?