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November 25th, 2016, 06:07 AM   #1
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linear optimization (Linear programming )

Dears ,

I am looking to find a mathematical relation to find optimal number of bus for the below scenario. I will be grateful if you can help me.

there is a bus which circulate between four stations but because its a single bus the passenger are waiting for long time so for decreasing the passenger frustration more bus added to pick up passenger but by increasing number of bus waiting time is decrease however, cost is increasing.

my question is: how to find a relation to trad off between cost and waiting time.

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November 25th, 2016, 07:07 AM   #2
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As you have stated the problem, there is NO answer.

You need a function that relates cost and customer frustration. In essence, you need an index that quantitatively measures in a common unit cost and frustration for one and two buses. Then you pick the number of buses that minimizes the cost/frustration index. In other words, the difficulty is not mathematical, but conceptual.

One conceptual way to address it is to ask passengers how much higher a fare they would be willing to pay to reduce waiting time by different amounts. You could then compare extra revenue against extra cost. This is related to a Pareto optimum and suffers from the difficulties associated to Pareto optima. Another conceptual way is to see whether those passengers who are willing to pay a higher fare would cover the cost of a bus or van that would be available only to those willing to pay the higher fare. This price discrimination is common in transportation systems, where costs are discontinuous and different people have different structures of preference.

The fundamental point is that, whoever is going to bear the cost, the cost-bearer must find the reduction in frustration worth the increased cost. Ultimately, this is a question of psychology and the distribution of income.

Last edited by JeffM1; November 25th, 2016 at 07:12 AM.
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