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

Capital investment decision, Your company is considering investing in its o...

Your company is considering investing in its own transport fleet. The presentposition is that carriage is contracted to an outside organization. The life of thetransport fleet woul

Explain zero base budgeting, Introduction of zero base budgeting Steps ...

Introduction of zero base budgeting Steps involved in the introduction of zero base budgeting 1) Corporate objectives should be established and laid down in detail 2) Dec

Explain the ratio analysis according to kosher, Explain the Ratio analysis ...

Explain the Ratio analysis according to kosher A ratio is the relation of the amount a to another b expressed as the ratio of a to b; a: b (a is to b) or a as simple fraction i

Selective inventory management, Selective Inventory Management The inve...

Selective Inventory Management The inventory of an industrial firm generally comprises thousands of items with diverse prices, usage and lead time, as well as procurement and/o

State the steps for standard costing system, State the steps for Standard c...

State the steps for Standard costing system standard costing system involves the following steps 1) Setting-up of standards for each element of cost: standards should be s

Explain the objectives of management accounting, Explain the Objectives of ...

Explain the Objectives of management accounting? 1. Planning and policy formulation: the object of management accounting is to supply necessary data to the management for fo

Job-order costing, #quesXERCISE 3-15 Departmental Overhead Rates [LO1, LO2,...

#quesXERCISE 3-15 Departmental Overhead Rates [LO1, LO2, LO3] Diewold Company has two departments, Milling and Assembly. The company uses a job-order costing system and computes a

Accounting Ratios, Explain TWO limitations of using accounting ratios to as...

Explain TWO limitations of using accounting ratios to assess the performance of a firm and suggest how each limitation may be improved

Revolving credit, The revolving credit facility will be specified by the ba...

The revolving credit facility will be specified by the banker to the customer through providing specific amount of credit facility for a continuous basis. The borrower will not be

Homework, costs/per unit labor ... $ 4 materials ...5 fixed cost... $ 12 ...

costs/per unit labor ... $ 4 materials ...5 fixed cost... $ 12 determine the break even point in units if the seeling price is $ 19 determine the break even point in sales at

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