Abstract:
A lot sizing and scheduling problem in this research is a daily production planning
problem for an automobile body part pressing machine. Production volumes of the body parts are
determined to meet the customer demand during next 14 working shifts and then a production
schedule for each shift is created with a delivery restriction that the parts must be finished 6 hours
before shipping at the end of the shift. This research proposed four steps for lot sizing
determination. First, a mixed integer linear programming model for minimizing the maximum
tardiness was used to discover if a production plan is capable of meeting the delivery restriction.
Second, a mixed integer linear programming model for minimizing the total weighted tardiness
was used to determine the upper limit of the tardiness for each shift where the first four shifts are
more important than others. Third, an integer linear programming model for maximizing the
average earliness was used to determine the lower limit of the average of part completion time
before delivery in its production shift.Final, an integer linear programming model for minimizing
the total cost of holding cost and setup cost was used for lot sizing determination. Next, the
decision variables corresponding to the part delivery of the final model were utilized to build the
production schedules. The performance of the proposed method was evaluated by comparing with
the real production plan of 21 days with the average demand per shift equal to 3600 pieces of 29
parts. The results revealed that the optimal solutions were found for all models of all problems.
The total cost was reduced 0.49% and the average completion times of parts produced in their
shipping period before delivery were met the delivery restriction. The number of shifts from all
14 shifts and first two shifts per the dailyproduction plan that fail to meet the delivery restriction
was reduced 5.7% and 11.9%, respectively. The average computational time for creating the daily
production plan was less than one minute comparing to 109 minutes of previous method