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

What does your analysis tell you about each firm, When the stock market is ...

When the stock market is going up over a long period of time, investors can become complacent about the risks of being a stockholder. After the significant decline of the stock mar

Temporary closure of factory or department, TEMPORARY CLOSURE OF FACTORY OR...

TEMPORARY CLOSURE OF FACTORY OR DEPARTMENT Here there is a similar situation to that of discontinuance of a product such as Model N40. A factory which is expected to earn some

Planning-role of management accountant , Planning Planning is the funda...

Planning Planning is the fundamental function of the management by means of which the managers decide: What goals are to be accomplished How they will be accomplished.

Explain term contribution - contribution margin analysis, Contribution marg...

Contribution margin Analysis Contribution Contribution is the  difference between sales and variable cost or marginal cost of sales . if may also be defined as the excess

150 to 200 words, solutions for (POS) slow printing of sales tickets and un...

solutions for (POS) slow printing of sales tickets and unpredictable action of cash drawers. when credit approvals delayed the checkout process or when the computer was down, thus

Planning, Planning A business must plan for its success. What do w...

Planning A business must plan for its success. What do we understand by business planning? It is about thinking in advance -- to decide on a course of the action to reach

What procedure are followed in kaizen costing, What Procedure are followed ...

What Procedure are followed in kaizen costing In brief kaizen costing involves setting a new cost reduction target every month. The difference between the target profits and th

Explain programmer budgeting according to burkhead, Explain Programmer budg...

Explain Programmer budgeting According to burkhead According to burkhead a program budget serves a different purpose than performance budget. A performance budget is useful fo

Implementation of the decisions, Implementation of the Decisions Once a...

Implementation of the Decisions Once alternative courses of action have been chosen, they must be implemented as part of the budgeting procedure. The budget is a financial plan

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