The assignment model, Managerial Accounting

Assignment Help:

The assignment model

Consider the situation of assigning m jobs (or workers) to n machines. A job i(= 1,2,3 ...m) when assigned to machine j(= 1,2,3 ...n)  acquires a cost Cij. The objective is to assign the jobs to the machines (on job per machine) at the least total cost. The situation is known as the assignment problem.

The formulation of this problem may be regarded as a special case of the transportation model. These jobs represent "sources" and machines represent "destinations". The supply obtainable at each source is 1; which is  ai = 1 for all i. Likewise, the demand needed at each destination is 1, which is bj = 1 for all j. The cost of "transporting" (assigning) job i to machine j is Cij.  If a job cannot be assigned to a certain machine, the corresponding Cij is taken equal to M, a very high cost. We represent in the table the general ideal of the model.

1063_box1.jpg



Before the model can be solved by the transportation technique, it is necessary to balance the problem by adding fictitious jobs or machines, depending on whether m < n or m > n.  It will be assumed that
m = n without loss of generality.

The assignment model can be stated mathematically as shown below:

Let Xij  = 0 if the jth job is not assigned to the ith machine.
          = 1 if the jth job is allocated to the ith machine.

The model is thus specified by:

Minimize: 

1105_1.jpg

Subject to :

583_2.jpg

Xij = 0 or 1

1443_3.jpg

 


Related Discussions:- The assignment model

State the target pricing method, Rate of return or target pricing method ...

Rate of return or target pricing method Under this method of price determination first of all a rate of return desired by the enterprises on the amount of profit capital inves

Compute the operating cycle, Under this method, approximation is made of pa...

Under this method, approximation is made of payments and cash receipts in the ensuring period. The dissimilarity of these payments and receipts indicates deficiency or surplus of c

Concentration banking, When the customers of the company are spread over br...

When the customers of the company are spread over broad geographical areas then in place of a particular collection centre the company opens collection centres at the regional stag

Costs classification, identify and explain the many classification of costs...

identify and explain the many classification of costs for planning, control.performance evaluation and decision making.

What is ratio analysis, Ratio analysis A ratio is a simple arithmetical...

Ratio analysis A ratio is a simple arithmetical expression of the relationship of one number to another. It may be explained as the indicated quotient of two mathematical ex

Transition probabilities, Transition probabilities These are the probab...

Transition probabilities These are the probabilities of moving from one state to another in the next time period. Usually they are written in the form of a probability matrix.

Lease accounting, question:lease accounting implicit rate unknown,20%increm...

question:lease accounting implicit rate unknown,20%incremental rate leaseterm 4 years,find implicit rate using trial and error method.i know nothing about trial and error method in

What is liquidity ratios, Liquidity ratios Liquidity refers to the abil...

Liquidity ratios Liquidity refers to the ability of concern to meet its current obligations as and when these become due. The short term obligations are met by realizing amount

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd