Problem 4. (10 PTS) WIDGETCO IS MAKING A PROTOTYPE OF A NEW PRODUCTCONSISTS OF TWO SUBASSEMBLIES. BEFORE BUILDING EITHER SUBASSEMBLY, THE FIRM MUST PURCHASERAW MATERIALS AND TRAIN WORKERS. BEFORE THE SUBASSEMBLIES CAN BE COMBINED, SUBASSEMBLY2 MUST BE INSPECTED. THE FOLLOWING TABLE DESCRIBES THE PROJECT:THE PRODUCTActivityDescriptionTrain workersPurchase materialsMake subassembly 1Make subassembly 2Inspect subassembly 2Combine subassembliesSubassembly 2 safety reportDuration (Days)RequiresA6B9CA,B8DA,B7D10FC, E12G6How QUICKLY CAN WIDGETCO COMPLETE THIS PROJECT?(A) DEFINE DECISION VARIABLES.(B) WRITE A SUITABLE LP PROBLEM FORMULATION.2%

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Asked Oct 29, 2019

Define Decision Variables and write LP problem formulation. Please see picture attached for problem.

Problem 4. (10 PTS) WIDGETCO IS MAKING A PROTOTYPE OF A NEW PRODUCT
CONSISTS OF TWO SUBASSEMBLIES. BEFORE BUILDING EITHER SUBASSEMBLY, THE FIRM MUST PURCHASE
RAW MATERIALS AND TRAIN WORKERS. BEFORE THE SUBASSEMBLIES CAN BE COMBINED, SUBASSEMBLY
2 MUST BE INSPECTED. THE FOLLOWING TABLE DESCRIBES THE PROJECT:
THE PRODUCT
Activity
Description
Train workers
Purchase materials
Make subassembly 1
Make subassembly 2
Inspect subassembly 2
Combine subassemblies
Subassembly 2 safety report
Duration (Days)
Requires
A
6
B
9
C
A,B
8
D
A,B
7
D
10
F
C, E
12
G
6
How QUICKLY CAN WIDGETCO COMPLETE THIS PROJECT?
(A) DEFINE DECISION VARIABLES.
(B) WRITE A SUITABLE LP PROBLEM FORMULATION.
2%
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Problem 4. (10 PTS) WIDGETCO IS MAKING A PROTOTYPE OF A NEW PRODUCT CONSISTS OF TWO SUBASSEMBLIES. BEFORE BUILDING EITHER SUBASSEMBLY, THE FIRM MUST PURCHASE RAW MATERIALS AND TRAIN WORKERS. BEFORE THE SUBASSEMBLIES CAN BE COMBINED, SUBASSEMBLY 2 MUST BE INSPECTED. THE FOLLOWING TABLE DESCRIBES THE PROJECT: THE PRODUCT Activity Description Train workers Purchase materials Make subassembly 1 Make subassembly 2 Inspect subassembly 2 Combine subassemblies Subassembly 2 safety report Duration (Days) Requires A 6 B 9 C A,B 8 D A,B 7 D 10 F C, E 12 G 6 How QUICKLY CAN WIDGETCO COMPLETE THIS PROJECT? (A) DEFINE DECISION VARIABLES. (B) WRITE A SUITABLE LP PROBLEM FORMULATION. 2%

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check_circleExpert Solution
Step 1

The project network can be represented as an LP problem using the idea that if a node depends upon its completion on multiple incoming arcs then it can be represented as a series of constraints so that the earliest finish time of the dependent node (activity) is more than equal to the activity times of all the incoming arcs (activities).

The decision variables are the earliest finish times of each of the 7 activities which are denoted as A, B, C, D, E, F and G in the model. The objective is to minimize the total time of the project hence the objective function is

min Z = A + B + C + D + E + F + G

Step 2

The constraints are:

  1. A >= 6
  2. B >= 9
  3. C >= A + 8
  4. C >= B +8
  5. D >= A + 7
  6. D >= B + 7
  7. E >= D + 10
  8. G >= E + 6
  9. F >= C + 12
  10. F >= E + 12

 

along with the non-negativity constraints.

Step 3

Representing the model i...

A
B
C
D
E
F
G
K
M
н
1
A
B
C
D
E
F
G
DV
2
6
17
16
26
38
32
C
1
1
0
0
0
0
0
0
6
6
9
2
0
1
0
0
0
0
0
9
3
-1
0
1
0
0
0
0
11 >
6
S
0
0
0
0
0
8>
8
-1
1
5
0
0
0
10
7
-1
0
1
0
7
8
7
6
0
1
0
1
0
0
0
10
9
7
0
0
0
-1
1
0
0
10
10
8
0
0
0
0
-1
0
6
б
11
N
9
0
0
-1
0
0
0
21
12
12
12
TS
10
0
0
0
0
-1
0
12
13
14
OF
1
1
1
1
1
1
1
1
144
0
I
OOO
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Image Transcriptionclose

A B C D E F G K M н 1 A B C D E F G DV 2 6 17 16 26 38 32 C 1 1 0 0 0 0 0 0 6 6 9 2 0 1 0 0 0 0 0 9 3 -1 0 1 0 0 0 0 11 > 6 S 0 0 0 0 0 8> 8 -1 1 5 0 0 0 10 7 -1 0 1 0 7 8 7 6 0 1 0 1 0 0 0 10 9 7 0 0 0 -1 1 0 0 10 10 8 0 0 0 0 -1 0 6 б 11 N 9 0 0 -1 0 0 0 21 12 12 12 TS 10 0 0 0 0 -1 0 12 13 14 OF 1 1 1 1 1 1 1 1 144 0 I OOO

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