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Prepared by: Dayani Jathunge061011V Dissanayake G.P. 061016P Fernando C.I. 061020X

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This is a special type of transportation problem in which each source should have the capacity to fulfill the demand of any of the destinations. In other words any operator would be able perform any job regardless of his skills, although the cost( or the time taken) will be more if the job does not match with operators skill. 2

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The objective might be, minimize the total time to complete a set of tasks maximize skill ratings minimize the cost of the assignments 3

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Job Operato rs 12…j…m 1 t 11 t 12 t 1j t 1m 2. i t i1 t ij t im. m t m1 t m2 t mj t mm 4 General format of assignment problem

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5 Transportation ProblemAssignment Problem No equal number of sources & destination Equal number of sources & destination Source supply & destination have a fix demand for units Source supply & destination demand is equal to 1 Quantity allocated or assigned must be a fix quantity Quantity allocated or assigned must be 0 or 1

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A network model is one which can be represented by a set of nodes, a set of arcs, and functions associated with the arcs and/or nodes. e.g. costs, supplies, demands, etc. AP is an example of a network problem.

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AP can be formulated as an LP and solved by general purpose LP codes. However, there are many computer packages, which contain separate computer codes for these models which take advantage of the problem network structure.

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Network Representation WORKERS JOBS 2 3 1 2 3 1 c 11 c 12 c 13 c 21 c 22 c 23 c 31 c 32 c 33

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This method can solve a special form of LP problem, including the classical assignment problem, with these typical characteristics: is a special case of a transportation problem the right-hand sides of constraints are all 1 the signs of the constraints are = rather than the value of all decision variables is either 0 or 1

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As in transportation problems assignment problems also can be balanced ( with equal number of rows and columns) or unbalanced. When it is unbalanced the necessary number of row/s or column/s are added to balance it. That is to make a square matrix. The values of the cell entries of the dummy rows or columns will be made equal to zero. 10

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Applications of assignment problem 11 Raw entity Column entity Cell entity operatorsjobsOperating cost programmerprogramProcessing time operatorsMachineOperating cost DriversRoutesTravel time Teachers SubjectsStudents pass percentage

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Operator Operator job job123451101215128 2716141411 31314799 41210111310 5813151115 12

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Applications of assignment problem 13 Raw entity Column entity Cell entity operatorsjobsOperating cost programmerprogramProcessing time operatorsMachineOperating cost DriversRoutesTravel time Teachers SubjectsStudents pass percentage

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Sales region Sales region Sales person 1234110221214 216182210 324201218 416142420 14

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Applications of assignment problem 15 Raw entity Column entity Cell entity operatorsjobsOperating cost programmerprogramProcessing time operatorsMachineOperating cost DriversRoutesTravel time Teachers SubjectsStudents pass percentage

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1 1 Slide © 2006 Thomson South-Western. All Rights Reserved. Slides prepared by JOHN LOUCKS St. Edward’s University.

1 1 Slide © 2006 Thomson South-Western. All Rights Reserved. Slides prepared by JOHN LOUCKS St. Edward’s University.

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