Question

Consider the assignment problem with the following cost table Assignment 4 65 84 50 45 34 69 24 61 57 64 92 Assignee 49 23 34 45 50 18 59 30 Use the branch-and-bound technique to find the set of assignments that minimizes total cost. Use the best bound rule. Please Show the entire branch-and-bound tree; Highlight the optimal solution

Answer 1

Solution Giuen that 3ed Cost- ng minim banch andoundtchnaue Assignment 31 6s 69 66 ST Assignee sc9 3y go. Зу 18- Assigoment Setor Asse 1 39 Job os Ascignmint fos Ascignee 2,

Assignee Ament foY ASsignee 3, 2 3 Assignee 7453 Assinmen ASS ignment Or SSnee2 3 SO 61 31 3 30 3u 18 2 3 YS ASanee 391 22 ASS gomentS

fos Assignee 3 2 3 8 45 23. Assrgnee 3 4 ST 33) fo ASSrgnee , set 3 Assigne St s 34 30 2 5 Assnee. 39 223 45 assgnment fox nssignee S, the left is 30 fos Sob 3 of Asrgnment 3 3 31 3 "Thus,the minim/3ed-total cost forn br and bound -techniaue s men m breanch

Bearch and Pound daom root A1 A-I A1-12 A-{-13 Coct -160 Cost Is Cose 13 Optimal 代29y optimal Cost-tㅋ 5 A:412 Ceuel y A-S 2 optima) Colutfon

Path folloced ic yoob Ascrgnee Assignment Asstgnee 3-7 Assigoment y Assigneey Assiyment2 AS SigneeAss