Shshs

Matching Supply with Demand: An Introduction to Operations Management

Solutions to End-of-Chapter Problems

(last revised February 25, 2008; make sure to visit www.cachon-terwiesch.net for the latest updates, excel files, ppt files and other information)

Chapter 3

Q3.3. Cranberry

Cranberries arrive at a rate of 150 barrels per hour. They get processed at a rate of 100 barrels per hour. Thus, inventory accumulates at a rate of 150-100=50 barrels per hour. This happens while trucks arrive, i.e. from 6am to 2pm. The highest inventory level thereby is 8h*50 barrels per hour=400 barrels. From these 400 barrels, 200 barrels are in the bins, the other 200 barrels are in trucks.

(a) 200 barrels

(b) From 2pm onwards, no additional cranberries are received. Inventory gets depleted at a rate of 100 barrels per hour. Thus, it will take 2h until the inventory level has dropped to 200 barrels, at which time all waiting cranberries can be stored in the bins (no more truck waiting)

(c) It will take another 2 hours until all the bins are empty

(d) Since the seasonal workers only start at 10:00am, the first 4 hours of the day we accumulate 4hours * 50barrels per hour=200 barrels. For the remaining time that we receive incoming cranberries, our processing rate is higher (125 barrels per hour). Thus, inventory only accumulates at a rate of 25 (150-125 barrels per hour). Given that this happens over 4 hours, we get another 100 barrels in inventory. At 2pm, we thereby have 300 barrels in inventory. After 2pm, we receive no further cranberries, yet we initially process cranberries at a rate of 125 barrels per hour. Thus, it only takes 100 barrels / 125 barrels/hour=0.8 hours=48 minutes until all bins are empty. From then, we need another 2h until the bins are empty.

Q3.4. Western Pennsylvania Milk

We start the day with 25,000 gallons of milk in inventory. From 8am onwards, we produce 5,000 gallons, yet we ship 10,000 gallons. Thus inventory is depleted at a rate of 5000 gallons...