Question

Nestlé’s water bottling plant in rural Mecosta County, Michigan has ten production lines that each have a theoretical rated capacity of 1200 bottles per minute. A natural disaster has occurred in Flint Michigan and the plant is now being ran at full capacity 24/7. There are five processes that are involved in the bottling of water: Per line Process Bottles per minute Processing time minutes Molding 1200 0.19 Capping 2600 0.1506 Inspecting 6000 0.019 Labeling 3000 0.025 Printing 2500 0.032 On average during this time the plant is outputting 3.5 million bottles per day. The plant manager feels very good about this number and telling the press that his lines have never worked this hard before. Your boss has suspected that something might be amiss here and has asked that you do some investigation. Work-in-progress at the facility averages approximately 120 million bottles and is shared equally by each line at the facility. What is the critical WIP of the plant?

Answer 1

Process	Bottles per minute	Processing time minutes
Molding	1200	0.19
Capping	2600	0.1506
Inspecting	6000	0.019
Labeling	3000	0.025
Printing	2500	0.032
		0.4166

For single line

The bottle neck is the one with least capacity. Here it is molding.

Bottleneck rate = 1200 bottles per minute

T₀ =Row process time of the line= sum of average process time of each workstation in the line

= 8 hours

=0.4166

Critical WIP (W₀) of the line is the WIP level for which a line with given values of rb and T₀ achieves maximum throughput ( rb ) with minimum cycle time (which is in this case T₀ )

= rb x T₀

= 1200 x 0.4166

= 499.92

Critical WIP is the WIP level when a line without any congestion would achieve maximum throughput (i.e., rb) with minimum cycle time.

For 10 lines in the plant

Critical WIP =10* 499.92 =4999.2 bottles per minute

Critical WIP per day = 7,198,848 bottles per 24 hrs (24*60*4999.2) = 7.1 million bottles

Actual WIP= 120 million bottles