Clark Equipment distributes the Clanton Model 406 bread slicer used in bakeries. The slicers cost $250 each, and Clark sells them to net $310 after marketing and related expenses. The company estimates that the annual demand for this product is 450 units. The policy at Clark has been never to allow stockouts intentionally, and the company has carried a safety stock of 30 units in order to protect against such occurrences. Because of mounting fiscal pressure, however, Clark is considering eliminating the safety stock for the bread slicers and adopting a policy that allows for stockouts.
Clark estimates that it will suffer a customer goodwill loss of $25 per week for each week a customer must wait for a back ordered bread slicer. Clark also believes that there is an administrative cost of $30 in handling a backorder and that adopting such a policy would result in a 4% decrease in annual sales of the bread slicer. Clark uses a 15% annual inventory holding cost rate, and the cost of ordering slicers from Clanton is $180. Delivery lead time is 10 working days, and Clark is open 250 days a year.
a. Determine the optimal order quantity, re-order point, and annual profit under the current policy of not intentionally allowing backorders.
b. Determine the optimal order quantity, reorder point, and annual profit if Clark intentionally allows for backorders.
c. What is your recommendation to management as to whether Clark should intentionally allow for backorders? Justify this recommendation.