Assignment Problems

Prof. Vinay Pandit ASSIGNMENT PROBLEMS 1) A company has five jobs A, B, C, and D & E to be done by five workers 1, 2, 3, 4&5. Each worker is assigned one and only one job. The no. of hours each worker would take to complete each job is given by the following table. Jobs Worker A B C D E 1 28 27 24 35 38 2 26 24 23 32 39 3 18 20 22 30 32 4 27 30 25 24 27 5 29 31 40 40 36 Find the assignment of jobs to workers in such a way that the total time taken to perform 5 jobs is minimum. 2) ABC limited is engaged in manufacturing 5 brands of packed snacks. It is having 5 manufacturing setups, each capable of manufacturing any of its brand one at a time. The costs of making a brand on these setups vary accordingly. B1 B2 B3 B4 B5

S1 4 7 8 9 7

S2 6 3 5 12 5

S3 7 6 4 7 9

S4 5 9 6 11 8

S5 11 5 9 10 11

Assuming 5 setups are S1, S2, S3, S4, S5 and 5 brands are B1, B2, B3, B4, and B5. Find the optimum assignment on these setups resulting in the minimum cost 3) The MBI manufacturing company plans to manufacturer 4 types of new minicomputers. Each of the plant has manufacturing capacity for one product only. The unit manufacturing cost for producing the different minicomputers at the four plants are shown in table below. a) How should the products be allocated for the lowest total manufacturing cost? b) What is the lowest total manufacturing cost? PLANT 1 2 3 4

1 24 28 26 22

MINICOMPUTERS TYPE 2 18 20 28 32

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3 22 16 20 24

4 28 24 24 22

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Prof. Vinay Pandit 4) A company has five manufacturing plants P1, P2, P3, P4, P5; it now wants to introduce three products A, B, C, but not more than one in a plant. The unit production cost and distribution cost is given below Product A B C Product A B C

P1 20 12 21

Unit production cost P2 24 28 17

P3 21 40 30

P1 12 14 17

Unit distribution cost P2 6 6 8

P3 13 8 12

P4 35 25 22

P5 28 20 16 P4 3 10 18

The estimates sales and prices of the three products Products Sales(no. of units) A 800 B 1000 C 400

P5 6 12 16 Selling price 50 50 70

Using this information state which product should be assignment to which plant so as to maximize the aggregate profits? 5) Airfreight has five aircrafts which he uses to carry bulk freight for single customer. These crafts are presently located at different sites A, B, C, D and E. on a particular day; he has received orders from four factories for goods transport. These factories are located at P, Q, R & S the carrier will assign an air craft to a factory, fly unloaded from the present location to the factory location. Then after loaded, fly loaded from factory location to destination of the goods. Data on the cost of transportation, distances to be flown etc. are shown From A B C D E To destination from factory

DISTANCE MATRIX (UNITS) To P Q 25 28 33 35 22 28 17 19 21 29 26 25

Cost of flying unloaded: 20 mu/unit

R 32 26 23 25 34 30

S 20 27 34 36 20 22

Cost of flying loaded: 35 mu/unit

Determine the optimal assignment of air crafts to the factories and the overall cost. Which aircraft will remain unused?

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Prof. Vinay Pandit 6) A manufacturer of complex electronic equipment has just received a sizable contract and plans to subcontract part of job. He has solicited bids for 6 subcontracts from 4 firms. Each job is sufficiently large that any one firm can take on only one job. The table below shows the bids and the cost estimates (in Rs. 10000) for doing the jobs internally. Note that not more than 2 jobs can be done internally JOB FIRM 1 2 3 4 5 6 1 48 72 36 52 50 65 2 44 67 41 53 48 64 3 46 69 40 55 45 68 4 43 73 37 51 44 62 INTERNAL 50 65 35 50 46 63 Q1) How do you complete this table so that problem con be solved by HUNGARIAN method Q2) solve the problem by the Hungarian method, minimizing total cost 7) A departmental store agency runs five stores located at different pars of greater Bombay. Each store is administered by the manager appointed by the agency. The manager resides in the different parts of the city. The agency reimburses the car travel expenses incurred by the managers in commuting of the work from their residence to he stores to which they are assigned. The basis of reimbursements is A fixed sum of Rs. 300/- PER month for repair and maintenance. A variable amount at the rate of Rs. 1.60 per Km. of travel incurred during the month. All stores work for 25 days in a month. The distance in kilometers from a manager’s residence to stores is displayed in the following table. Find the optimal assignment of managers to stores so that the monthly expenditure to be incurred by the agency on car travel of managers is minimum. After having operated optimal assignment for some time, manager A request the agency to assign him store S1, which is he closest to his residence, as he has been advised not to take long journeys. If the agency agrees to this request, how should the present assignment be changed and how much extra will it cost to the agency? Managers A B C D E

S1 4 7 8 11 9

STORES (DISTANCE in Km.) S2 S3 10 12 16 16 6 9 12 15 14 19

S4 18 22 19 12 18

S5 17 18 21 13 14

8) Well-done company has taken the third floor of a multi-storeyed building for rent with a view to locate one of the zonal offices. There are five main rooms in this to be assigned to five managers. Some have

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Prof. Vinay Pandit windows, some are closer to wash rooms or to canteen or secretarial pool. The rooms are all of different sizes and shapes. Each of the 5 managers were asked to rank their room preferences among the rooms 301, 302,303,304,305.their preferences were recorded in a table as indicated below M1 302 303 304 -

M2 302 304 305 301 -

MANAGERS M3 303 301 304 305 302

M4 302 305 304 303 -

M5 301 302 304 -

Most of the managers did not list all the 5 rooms since they were not satisfied with some of the rooms and they had left these from the list. Assuming that their preferences can be quantified by numbers, find out as to which managers should be assigned to which room so as that their total preference ranking is a minimum 9) A firm produces four products. There are four operators who are capable of producing any of these four products. The firm records 8 hours a day and allows 30 min for lunch. The processing time in minutes and the profit for each of the products are given below. Operators 1 2 3 4 Profit(Rs.) per unit

A 15 10 25 15 8

B 9 6 15 9 6

C 10 9 15 10 5

D 6 6 9 10 4

Find the assignment schedule of products to operators to maximize the profits.

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Prof. Vinay Pandit 10) ABC airline operating 7 days a week has given the following time table. Crews must have a minimum layover time of 5 hrs. Between flights. Obtain the paring flight that minimizes layover time away from home. For any given pairing the crew will be based at the city that results the smallest layover Hyderabad – Delhi FLIGHT DEPARTURE ARRIVAL NO. A1 6AM 8 AM A2 8 AM 10 AM A3 2 PM 4 PM A4 8 PM 10 PM Delhi – Hyderabad FLIGHT DEPARTURE ARRIVAL NO. B1 8 AM 10AM B2 9 AM 11 AM B3 2PM 4 PM B4 7 PM 9 PM 11) The marketing research team of the look forward company requires some house hold data from four different cities. The team has to perform this job in two days- next Saturday and Sunday. It plans to spend half a day in each of the city. The relevant data are given Day and time Sat morning Sat evening Sun morning Sun evening No. of household expected to interview

Probability of a house holds contact City1 City2 0.32 0.85 0.60 0.56 0.70 0.35 0.10 0.72 150 100

City3 0.16 0.96 0.40 0.64 200

City4 0.64 0.80 0.62 0.90 200

How should the team plan its visit to the four cities so as that the expected response may be maximized? State this expected response.

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