National Cranberry
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Question One: Process Analysis, Bottleneck, and Flow Diagram
We used barrels per hour (bbls/hr) as a common measure. Since no capacity information is provided for the receiving/testing or bulking/bagging steps, we assume that these steps are not bottlenecks. We estimated the average total input of cranberries into the system at 1,500 bbls/hr using data from Exhibit 1 and assuming that total deliveries in 1981 will be the same as 1980:
Average Wet Input = (.70)(1,500) = 1,050 bbls/hr
Average Dry Input = (.30)(1,500) = 450 bbls/hr
Our analysis (see table) indicates that the bottleneck for process fruit at Receiving Plant Number 1 (RP1) is the drying process for wet cranberries at 600 bbls/hr (see Exhibit A for flowchart).
Process Step
Notes
Total Available Capacity(bbls/hr)
Wet Capacity (bbls/hr)
Dry Capacity (bbls/hr)
Receiving/ Testing
No capacity information provided; nothing in the case indicates that this step could be a bottleneck
Dumping
(60 mins / 7.5 mins/truck) x 5 dumpers x 75 bbls/truck
3,000
Holding
Bins 17-24 are assumed to hold wet berries since they comprise 70% of total shipments
7,200
De-stoning (dry only)
Dry berries only (1500 bbls/hr x 3 units)
4,500
De-chaffing
2 dechaffers connected to wet process (1500 bbls/hr x 2 units); 1 to dry process (1500 bbls/hr x 1 unit)
4,500
Drying (wet only)
Wet berries only (200 bbls/hr x 3 units)
Separation
400 bbls/hr/line x 3 lines (priority given to wet berries since they are majority of product, take the longest to process and can not be stored over night)
1,200
Bulking/ Bagging
No capacity information provided; nothing in the case indicates that this step could be a bottleneck
Question Two: Peak Day Analysis
Total berry input for the day will be 20,000 bbls. Over a 12 hour period, trucks will deliver berries at a rate of 1667 bbls/hr (20,000 bbls / 12 hrs) starting at 7:00 am. Since trucks are delivering wet berries 70% of the time, 1,167 bbls/hr of wet berries are being delivered. But because of the dryer bottleneck, the flow rate for wet berries is only 600 bbls/hr. The wet holding bins are therefore filling up at a rate of 567 bbls/hour (1,167 bbls/hr – 600 bbls/hr). With a total capacity of 3,200 bbls, the wet bins will become completely full after 5.65 hours (3,200 bbls / 567 bbls/hr). Trucks will now start to back up.
Once the wet bins are full, trucks can only deliver wet berries at a rate of 600 bbls/hr since this is the batch size that can be processed per hour. Since wet berries make up 70% of all deliveries, a new delivery rate of 857 bbls/hr will yield 600 bbls/hr of wet berries (600 bbls/hr / .70). Delivery of 9,419 bbls will have occurred when the wet bins are first filled up (1,667 bbls/hr x 5.65 hrs). This means that 10,581 bbls (20,000-9,419) are yet to be delivered. Since trucks will deliver berries 857 bbls/hr after 5.65 hours, it will be another 12.35 hours (10,581 bbls / 857 bbls/hr) before all berries are delivered for the day. Therefore, the last truck will unload at 1:00 am the next morning – 18 hours after the first one unloaded at 7:00 am the day before (5.65 hrs + 12.35 hrs).
Trucks start to back up after having delivered 9,419 bbls (5.65 hrs after the beginning of the day). This means that inventory of 10,581 bbls is still waiting to be delivered. We established that the rate of delivery when trucks are waiting is 857 bbls/hr. Using Littles Law, we have r = 857 bbls/hr, and average inventory L = 10,581 bbls / 2 = 5,290.5 bbls. Therefore we find that the average waiting time for trucks that do have to wait (W) is 5,290.5 bbls / 857 bbls/hr = 6.17 hrs.
Once the last truck has unloaded, there will be 3,200 bbls of inventory in the wet bins waiting to be processed. This inventory will decrease at a rate of 600 bbls/hr, which means the bins will finally be empty at 6:20 am, or 5.33 hours after the last truck unloads (3,200 bbls / 600 bbls/hr). Flow time for the wet berries through the process is 1 hour 42 mins ((600 bbls / 3,000 bbls/hr) * 60 mins = 12 minutes at the dechaffer; (600 bbls / 600 bbls/hr) * 60 mins = 60 minutes