Problem 1: Process Analysis
You manage an assembly line consisting of 6 work stations (referred to as Work Station 1, Work Station 2, ... , Work Station 6) in series, each manned by a single worker (Alex, Barbara, Chuck, Donna, Ed, and Fran). Each unit of product is processed first at Work Station 1, then at Work Station 2, and onward through the six work stations in numerical order. For reasons not completely understood, the amount of time required to complete the work at each work station depends on which worker is assigned to that station. The following table gives the number of minutes each worker requires to complete the tasks associated with each work station.
|
Workers
|
Work Stations
|
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Alex
|
10
|
35
|
41
|
45
|
15
|
23
|
|
Barbara
|
33
|
40
|
24
|
19
|
49
|
13
|
|
Chuck
|
16
|
20
|
39
|
32
|
18
|
48
|
|
Donna
|
47
|
12
|
14
|
26
|
44
|
33
|
|
Ed
|
25
|
43
|
37
|
31
|
27
|
21
|
|
Fran
|
50
|
28
|
22
|
11
|
38
|
42
|
Therefore, if Alex is assigned to Work Station 1, he will require a total of 10 minutes to complete the tasks at that work station for every unit of product. In contrast, he will require 45 minutes if assigned to Work Station 4. Similarly, Donna will require 47 minutes if assigned to Work Station 1, but only 12 minutes if assigned to Work Station 2. Clearly, one worker must be assigned to each work station, and these assignments are considered permanent for the foreseeable future.
Assume that the system is always busy (i.e., there is always demand for this product), and there is no transient state (so, e.g., workers can stop work on a unit of product at the end of a shift and resume work at precisely the same point the next day). Also assume that no inventory is allowed between work stations; instead, workers who complete their tasks faster than the bottleneck work station accumulate idle time.
a. To which work station should each worker be assigned in order to minimize the flow time of the assembly line? What is the associated flow time?
Alex _10____ Barbara 19_ Chuck 18_ Donna 12_ Ed _21 Fran _22
Flow Time (minutes) _81