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

Operating cycle concepts, Operating cycle considers to the average time lap...

Operating cycle considers to the average time lapse among the acquisition of raw material and the final cash realization. This notion is used to determine the needs of cash working

Capital budgeting – planning investments, The management of Popular Stores ...

The management of Popular Stores Sdn. Bhd. are in the process of exploring the company’s investment opportunities.

Determine the value of equipment at the current date, A company is preparin...

A company is preparing a value in use calculation for a factory building and the equipment used to make a particular product. It has prepared cash flows for the next five years fro

Explain the mark up pricing, Full cost or mark up pricing or cost plus pric...

Full cost or mark up pricing or cost plus pricing method: In this method the marketer estimates the total cost of producing or manufacturing the product and then adds it a mar

Extra cost decision, Discuss arguably how management accountants should dec...

Discuss arguably how management accountants should decide when are faced with the extra shift decision

Distinguish between advertising and public relation, Question 1: a. Dis...

Question 1: a. Distinguish between Advertising and Public Relation? b. Discuss the methods adopted by a Public Relation company in promoting the image of a destination in th

State direct material cost standard, State Direct material cost standard ...

State Direct material cost standard The determination of direct material cost standard would involve: a) Determination of quantity standards and b) Determination of pric

Explain phases of life cycle of a product, Q. Explain Phases of life cycle ...

Q. Explain Phases of life cycle of a product? Every product move through a life cycle having five phases as shown in figure and they are 1) Pricing during introduction 2)

Willco Inc. manufactures electronic parts, Willco Inc. manufactures electro...

Willco Inc. manufactures electronic parts. They are analyzing their monthly maintenance costs to determine the best way to budget these costs in the future. They have collected the

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