SCERT Maharashtra solutions for Mathematics and Statistics (Commerce) [English] 12 Standard HSC chapter 2.7 - Assignment Problem and Sequencing [Latest edition]

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The assignment problem is generally defined as a problem of ______

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Assignment Problem is special case of ______

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The assignment problem is solved by ______

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The cost matrix of an unbalanced assignment problem is not a ______

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When an assignment problem has more than one solution, then it is ______

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The assignment problem is said to be balanced if ______

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The optimal sequence for above data is

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In sequencing, an optimal path that minimizes ______

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If there are 3 machines A, B and C, conditions for reducing a 3 machine problem to a 2 machine problem with respect to minimum processing time is ______

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The objective of sequencing problem is ______

If there are n jobs and m machines, then there will be _______ sequence of doing jobs.

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In solving 2 machine and n jobs sequencing problem, the following assumption is wrong

If the given matrix is ______ matrix, the assignment problem is called balanced problem

An unbalanced assignment problems can be balanced by adding dummy rows or columns with ______ cost

A ______ assignment problem does not allow some worker(s) to be assign to some job(s)

In an assignment problem if number of rows is greater than number of columns, then dummy ______ is added

The Hungarian method is an ______ algorithm that solves an assignment problem

In assignment problem each worker or machine is ______ capable of handling any job

In sequencing problems one has to ______ the total processing time or cost

In sequencing problem the time which required to complete all the jobs i.e. entire task is called ______

______ time is the time when the machine is available but is waiting for a job to be processed

In sequencing problem the time required to transfer a job from one machine to another is ______

The optimum sequence for the above data is ______

In sequencing problem one has to determine the ______ in which jobs has to processed through the machines

State whether the following statement is True or False:

The objective of an assignment problem is to assign number of jobs to equal number of persons at maximum cost

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To convert the assignment problem into maximization problem, the smallest element in the matrix is to deducted from all other elements

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Optimal assignments are made in the Hungarian method to cells in the reduced matrix that contain a zero

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In assignment problem, if number of columns is greater than number of rows, then a dummy row is added

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The Hungarian method is used to assign n jobs on 2 machines to get the optimal sequence

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In assignment problem each worker or machine is assigned only one job

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One of the assumptions is made while sequencing n jobs on 2 machines is: two jobs must be loaded at a time on any machine

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The Total Elapsed is the time required to complete all the jobs i.e. entire task

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The idle time for a machine is the when machine is available but is not waiting for any job to be processed

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In sequencing problem the processing times are dependent of order of processing the jobs on machine

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In sequencing problem each job once started on any machine must be processed still its completion

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In sequencing problem each machine is of different type

Four new machines M₁, M₂, M₃ and M₄ are to be installed in a machine shop. There are five vacant places A, B, C, D and E available. Because of limited space, machine M₂ cannot be placed at C and M₃ cannot be placed at A. The cost matrix is given below.

Find the optimal assignment schedule

Solve the following problem :

Solve the following assignment problem to maximize sales:

Solve the following problem :

Consider the problem of assigning five operators to five machines. The assignment costs are given in following table.

Operator A cannot be assigned to machine 3 and operator C cannot be assigned to machine 4. Find the optimal assignment schedule.

Find the assignments of salesman to various district which will yield maximum profit

A dairy plant has five milk tankers, I, II, III, IV and V. Three milk tankers are to be used on five delivery routes A, B, C, D and E. The distances (in kms) between the dairy plant and the delivery routes are given in the following distance matrix.

How should the milk tankers be assigned to the chilling center so as to minimize the distance travelled?

Solve the following problem :

Find the sequence that minimizes the total elapsed time to complete the following jobs. Each job is processed in order AB.

Determine the sequence for the jobs so as to minimize the processing time. Find the total elapsed time and the idle times for both the machines.

Find the optimal sequence that minimizes total time required to complete the following jobs in the order ABC. The processing times are given in hours.

Solve the following problem :

Five jobs must pass through a lathe and a surface grinder, in that order. The processing times in hours are shown below. Determine the optimal sequence of the jobs. Also find the idle time of each machine.

A toy manufacturing company produces five types of toys. Each toy has to go through three machines A, B, C in the order ABC. The time required in hours for each process is given in the following table.

Solve the problem for minimizing the total elapsed time.

Find the sequence that minimizes total elapsed time to complete the following jobs in the order XY. Find the total elasped time and idle times for each machine.

For the following assignment problem minimize total man hours:

Subtract the `square` element of each `square` from every element of that `square`

Subtract the smallest element in each column from `square` of that column.

The lines covering all zeros is `square` to the order of matrix `square`

The assignment is made as follows:

Optimum solution is shown as follows:

A → `square, square` → III, C → `square, square` → IV

Minimum hours required is `square` hours

Solve the following problem of sequencing for minimizing the total elapsed time and idle time for both the machines.

The optimal sequence of the jobs as follows:

Total elasped time is obtained as follows:

Total elapsed time T = `square` minutes

Idle time for Machine A = T – `square` = `square` minutes

Idle time for Machine B = `square`