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Domain |
Components |
Comments |
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Planning / Operations Research |
- Linear programming
- Integer programming
- Transportation models
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Linear var. relations
Var. & constraints int.
Balance of Ss. = Dd.
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Linear programming |
- Formulate question with all required details
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Id. optimisation target
Collect operations details, cost rates, periods, capacities, constraints, manpower
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Id. design variables
Use 1 var. for each distinct category
Objective function, z (lowest cost, highest profit)
Non-negativity
Inequalities for constraints - equipment, men, utilities, Ss, Dd.
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- Solution & interpretation of outputs
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Software or hand solution
Interpret from optima
Whether new activity to be included
Whether old activity to be discarded
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Integer programming |
- Same as LP, but difference in integer entities only
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Use of integers present unique difficulties
Formulate IP in terms of mathematical expressions of integer var. to represent linguistic details
Often uses arbitrary variables - M, w, etc. to ensure certain criteria to be met
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Transportation model |
- Model assumes Ss =Dd.
- Deficiencies treated with dummies
- Initial solution:
- Northwest rule
- Least cost method
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Cij: cost rate from i to j
Minimise total cost
Ui + Vj = Cij for all
Cpq = Up + Vq - Cpq for unoccupied
Enter max. at the +ve highest Cpq
Loop
Repeat until all Cpq -ve
Optimal solution
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Ss deficiency: dummy plant
Dd. deficiency: dummy distribution centre
Dd. must be met: M Cij at dummy plant
Ss must be shipped: M Cij at distribution centre
Penalty: P Cij either at dummy plant
Storage cost: P Cij along row for plant P
Backorder penalty: along column for Ss centre
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