KG International produces T-shirts. KG International must decide how many T-shirts to produce each month. The company has decided to use a six-month planning horizon. The forecasted monthly demands for the next three months are 20,000, 32,000, and 30,000. KG International wants to meet these demands on time, knowing that it currently has 5,000 T-shirts in inventory.
During each month, there is enough production capacity to produce up to 30,000 T-shirts, and there is enough storage capacity to store up to 10,000 T-shirts after demand has occurred. (For simplicity, we assume that production occurs during the month, and demand occurs at the end of the month.)
The forecasted production costs per T-shirt for the next three months are $20, $17, and $22, respectively. The holding cost incurred per T-shirt held in inventory at the end of any month is 10% of the production cost for that month. KG International wants to determine the production schedule that minimizes the total production and holding costs.
Formulate a mathematical model for KG International.