15.066 Systems Optimization and Analysis Optimization Project Labor Planning for a Manufacturing Line Team 1 The Tek Team Lane Ballard Christine Cheung Justin Ging Omur Kaya David Jackson Alyson NaughtonIntroduction The objective of this project was to create an LP model which could allocate labor on a manufacturing line. The line manufactures precision thermostats for the aerospace industry (see Exhibits 1 and 2). Current monthly demand for the product ranges from 25 thousand and 45 thousand units with an average of 35 thousand units per month. Parts are processed continuously through the line so there is no need to complete all operations on all parts during the month (or day) and parts are shipped on a daily basis. There are three main manufacturing areas: an open area and two clean rooms. Machine operators are paid on an hourly basis depending on their job grade and the area they are working. Job grades range from one to five – grade fives perform the highest skilled work and are paid the highest. A grade five worker is able to perform all jobs from one to five, but a grade one worker can only perform grade one jobs. There are 2nd and 3rd shift hourly premiums as well as clean room hourly premiums paid to workers. For safety reasons, there is also a minimum requirement of at least five people per shift if the shift is to be run. A single worker can only work a single machine at any given time. The hourly pay rates for each job grade can be seen in Exhibit 3 and the minimum grade required to perform each job can be seen in Exhibit 4. The LP model minimizes the total labor cost per month and allows supervision to schedule daily work. Analysis of the output of the model shows the effect of demand fluctuations on labor cost and machine utilization. This optimization tool can be used to determine the size and skill level of the workforce required to meet product demand as well as aid the supervisor to direct each shift to the operations needed to be done. Note that the LP model is not intended for the scheduling of individual workers to a specific task per hour. Description of the LP Model: The LP model is built to analyze the number of work hours needed from each grade level worker for different operations on different shifts. The model gives the plant information for deciding how many workers are needed to meet the demand in a given month. Decision Variables Work hours required: This is the number of work hours required for each operation at each grade level by shift. Shifts: This decision variable is a binary variable. It indicates which shift has to run depending on the demand. It is equal to 1 if shift has to be run, 0 otherwise. Constants and Inputs Number of days per month: This is an input of the work days in a given month. This number can be changed based upon holidays and the plant schedule for each month. This is used later in the constraints section of the LP model.Demand: Demand is the number of units that the plant needs to produce in a given month. It can be changed by changing the demand cell in the LP model. Fraction Fraction is a constant that is percentage of the products that goes through a given operation. Thus, there is a fraction for every operation. If all of the products have to go through an operation the fraction is equal to one. If 50% of the products have to go through an operation, the fraction is equal to 0.5. Current work force: In some of the LP runs the current work forces is entered as an input to the model. All of the hours of the current workforce must be used before additional workers can be added. Number of work stations: The number of available machines for each operation was entered as an input to the model. (See Exhibit 4) Number of units produced per hour: This is the number of parts that can be processed per hour by each machine for a given operation. (See Exhibit 4) Second and third shift penalty: For 2nd and 3rd shifts, there is a fixed cost of starting up the additional shift. This represents the additional electricity consumption, additional security and so on. This fixed cost is the same for both shifts and it is estimated at $5000 per month. Constraints Labor demand per day: We assume that there is level demand for the month and that production is continuous. We calculate the number of required production hours for an operation by using the demand per month, number of work days per month, the fraction of the demand that goes through the operation and the number of products produced per hour for the operation. Therefore, for a given operation: The required production hours per day= Monthly demand*fraction / (number of work days per month*number products produced per hour) For each operation, the actual hours have to be at least the required production hours. Machine capacity per shift: There are a limited number of machines for each operation and these machines can be run only for 8 hours per shift with the exception of laser weld which can be run for 7 hours (this machine is shared part-time with another production line). This capacity is the number of hours that the machine can be worked in a shift. The number of labor work hours spent on each operation must be less than the machine capacity. The machine capacities are calculated by multiplying the number of machines with 8 since every shift lasts for 8 hours, except for laser weld.Number of workers for each shift: The number of workers for each shift has to be more than 5. Therefore for each shift the total number of labor hours is forced to be greater than 40 hrs, which is the total number of labor hours that can be contributed by 5 workers on each shift. Work hours by each grade vs. the available number of work hours at each grade level: This constraint is applied by making the works hours at each grade level to be greater than or equal to the available work hours. This constraint causes each current worker to work to his/her maximum capacity, before additional workers are hired. Non-negativity constraints for decision variables: applied when running the solver by using the check box toggle. Objective Function The objective function of the model is to minimize the overall daily cost of production. The cost is calculated by adding up the cost of labor on each operation per shift. See Exhibit 3 for a listing of all the labor costs. There is a $0.25 per hour premium paid on a