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

Objectives of receivables management, After going through this section, you...

After going through this section, you must be capable to: Know the need for establishing sound credit policy; Identify the different credit policy variables; Know the cred

Collection policy, Exact management of receivables acquires a suitable coll...

Exact management of receivables acquires a suitable collection policy that outlines the collection procedures. Collection policy consider as the procedure adopted through a firm to

Value analysis-material control, Value analysis Is a formalized techniq...

Value analysis Is a formalized technique involving a rigorous analysis of products at the design stage or at any time during the saleable lives, to determine their value charac

Explain budgetary control according to CIMA, Budgetary control Accordin...

Budgetary control According to CIMA the establishment of budgets relating the responsibilities of executive to the requirement of a policy and the continuous comparison of achi

Calculate transfer price - management control system, Calculate Transfer Pr...

Calculate Transfer Price - Management Control System? Question: Compute the Transfer Price for Product X and Y and the Standard Cost of Product Z as the intra company pricing r

Accounting for pension plans, how do i calculate the actuarial gains or los...

how do i calculate the actuarial gains or losses on the present value of plan obligations?

Implied interest rate, Suppose the spot price of gold is $1700 per ounce. T...

Suppose the spot price of gold is $1700 per ounce. The futures price for delivery in six months is $1712, while the futures price for delivery in one year is $1720. The interest ra

Financial perspective, Financial Perspective How do we produce value fo...

Financial Perspective How do we produce value for our shareholders? This perspective covers traditional measures e.g. growth, liability, shareholder value. But these are set on

Types of games, Types of games Four basic ways in which competitive sit...

Types of games Four basic ways in which competitive situations (or games) can be classified are: (a) Number of Competitors: In game theory a competitor is characteriz

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