A textile manufacturer is interested in optimally determining a production policy for the cutting operation in men’s product line. The production manager would like to establish the optimal reorder point and production quantity for each item in the line. Elvis 605 jean, atypical product, is demanded uniformly throughout the year; total demand is 14,000 items. The production rate is 2,000 items/months. Sewing, the operation following cutting, is staffed to meet annual demand exactly. Set up costs for cutting are $240 and the cost of carrying one item for one year is $0.5. The unit variable production cost is estimated at $10.
a) Determine the optimal production policy for Elvis 605 jean (production lot size, cycle time, and production time).
b) Repeat the first question, when the production manager is willing to allow for some shortages. The unit shortage cost per unit time is $2.
Please show detailed solution using optimal order quantity derivation.