Production Line Cookies 1 2 3 4 5 Chocolate mint 30 18 26 17 15 Peanut butter 23
ID: 436186 • Letter: P
Question
Production Line
Cookies
1
2
3
4
5
Chocolate mint
30
18
26
17
15
Peanut butter
23
22
32
25
30
Shortbread
17
31
24
22
29
Fudge delight
28
19
13
18
23
Macaroons
23
14
16
20
27
Sunshine house received a contract this year as a supplier of girl scout cookies. Sunshine currently has five production lines, each of which will be dedicated to a particular line of cookies. The production lines differ by sophistication of the machines, site, and experience of personnel. Given the following estimates of processing times in hours, assign cookies to lines to minimize the sum of completion hours.
Production Line
Cookies
1
2
3
4
5
Chocolate mint
30
18
26
17
15
Peanut butter
23
22
32
25
30
Shortbread
17
31
24
22
29
Fudge delight
28
19
13
18
23
Macaroons
23
14
16
20
27
Explanation / Answer
Let I be the set of Cookies, I ={CM,P,S,F,M}
Let C be the set of productionLine, C= {1,2,3,4,5}
Let xij = 1 if cookie i is assigned production line j, where i belongs to I and j belongs to C
= 0 otherwise
Let tij be the time spent by cookie i on chore j and the data is given in the question
Our objective is to minimize the total completion time on processing
Minimize total completion time i,j (xij * tij)
subject to
Constraint 1: Each cookie i should be assigned only to one production line j
jxij == 1 for each cookie i belongs to I
Constraint 2: Each production line j should be assigned to only one cookie i
ixij == 1 for each production line j belongs to J
Constraint 3: Binary constraint xij belongs to {0,1}
Solving the above optimization problem will give an assignment problem, we get
Chocolate mint -PL 5
Peanut butter - PL 4
Shortbread - PL 1
Fudge delight - PL 3
Macaroons - PL 2
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