Question

International Cranberry Uncooperative (ICU) is a competitor to the National Cranberry Cooperative (NCC). At ICU, barrels of cranberries arrive on trucks at a rate of 150 barrels per hour and are processed continuously at a rate of 100 barrels per hour. Trucks arrive at a uniform rate over eight hours, from 6:00 a.m. until 2:00 p.m. Assume the trucks are sufficiently small so that the delivery of cranberries can be treated as a continuous inflow. The first truck arrives at 6:00 a.m. The bins at ICU can hold up to 250barrels of cranberries before overflowing. If a truck arrives and the bins are full, the truck must wait until there is room in the bins.

ICU is considering using seasonal workers in addition to their regular workforce to help with the processing of cranberries. When the seasonal workers are working, the processing rate increases to 125 barrels per hour. The seasonal workers would start working when trucks start to waitand finish working when the truck inventory reaches its peak level. At what time would ICU finish processing the cranberries using these seasonal workers?

Answer 1

The difference in arrival rate and normal service rate is 150 - 100 = 50 barrels per hour. So, in one hour, 50 barrels of inventory will be accumulated.

So, to get inventory level at 250 barrels, 250 / 50 = 5 hours will be spent (i.e. from 6:00 to 11:00 hours). After that, the seasonal workers will start working.

For the next 3 hours (i.e. up to 2:00 pm), input material received will be 150 x 3 = 450 barrels. 250 barrels of inventory was lying already. So, the seasonal workers need to clear 450+250 = 700 barrels in total.

The processing rate for the seasonal workers is 125 barrels per hour. So, the time required will be 700 / 125 = 5.6 hours or 5 hours and 36 minutes. Recall that the temporary workers have started working at 11:00 hours. So, they will complete at 16:36 hours.