**THE DANISH REJSEKORT** is an electronic payment system used in most danish public transportation systems like buses, trains and subways. Its an electronic card that comes in two variants: an anonymous edition where you manually deposit fare money by a kiosk system. The second edition is personalized and offers an online management system with option of association to a payment card (Dankort, VISA, Master card etc). This personal edition also offers a discount system which is intended to give the Rejsekort a price competitive incentive compared to single ticket purchases.

I commute a pretty long way to work. First i drive in my car about 25 km to the train station. There i take the train for an hour, switches train and ride another hour before i then walk the last 1.5 km to the office.

A discount system would be expected to benefit a person like me, which is riding public transportation for just about four hours a day. And it does, but not a much as one would expect (at first).

I jump on the first train 06:55 o’clock. This triggers the first discount system. Traveling outside the busiest hours gives a discount. My fare price is therefore

160 \,[kr] \rightarrow 128 \,[kr]This is however not true for my trip home. This gives a total daily travel cost of:

128 + 160 = 288 \,[kr]I only do the train ride three days a week (i take the car other days).

This makes my monthly cost:

288 \,[kr] * 3 \,[á/week] * 4 \, [week] = 3456 \,[kr]That is a pretty huge dent in the monthly budget. Fortunately a second parameter of the discount system is available. A level system is defined. It goes a this:

Customer/discount level | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|---|

Adult – Rejsekort personal | 0% | 10% | 10% | 25% | 25% | 25% | 40% | 40% |

The above discount system is not based on fare prices, distance, stops or zones but on the amount of rides alone.

The formula for the discount level is as follows:

discount\; point = (amount \; of \; travels * 10)(another formula translate discount points to discount level). With this system i reach discount level 3. This changes my monthly cost:

3456 \,[kr] - 25 \% = 2592 \,[kr]Okay. Now this is where the bonus system gets pretty weird – or perhaps just flawed. Remember how the discount system is not based on the price but amounts of travels alone? Increasing the amount of travels will bump you to a higher discount level, and at my monthly cost this can mean a significant saving. As the discount formula ignores ticket price, i can clime the discount latter by taking the cheapest possible ride. To reach next percentage level i need 10 more rides. Lets see where that brings me:

A public bus stops a few hundred meters away from my home. The next stop is an additional few hundred meters further way. As i am already at discount level 3, i got 25 % discount from get go. The ticket fare is 13.95 kr before this.

10 \,[ride] * (13.95 \,[kr/ride] - 25 \%) = 105 \,[kr]Having achieved a discount level that gives a 40% discount, my monthly travel cost to work will then reduce to:

3456 \,[kr] - 40 \% = 2074 \,[kr]Adding the extraneous trips, the total monthly travel cost will be:

2074 + 105 = 2179 \,[kr]Thus by traveling more, i save:

2592 - 2179 = 413 \,[kr]