# What-if scenarios with time-space networks

Route planning over time, where there is fluctuating demand, is a prime example of the application of what-if scenarios: what if the demand were drastically reduced? What if it increased? What if it became irregular?

Would I then have enough trucks in my fleet to make the deliveries? Would it be more favorable to enlarge the fleet or increase the stock capacity in the warehouse? These are all questions which can be answered with the help of mathematical optimization.

## What-if as a standard tool

Using comparative calculations to evaluate strategic action alternatives is a standard tool of any strategic planner. Underpinned by mathematical optimization, the tool becomes a multitool because generating alternative scenarios comes with two benefits:

• One exchanges the assumptions for “real” data whose impact is to be studied.
• One gets an optimal result at the push of a button.

In parts 1 and 2, we show how time-space networks can be used to optimize demand-driven delivery schedules. The same model can be used without customization to compare scenarios. But what does this mean in practice?

## The common baseline

Every comparison lives from a common baseline to which we can refer. This actual or “baseline” scenario frequently reflects the current state. In our example, this could be the customer demand over time.

In the comparison, the assumptions are now adjusted and their effects on the optimal plan are calculated: what if the customers’ demand were to increase?

We know from the baseline scenario how many trucks we can plan with and how the customers’ stocks will develop over time. For the comparative scenario (target scenario), the demand is adjusted accordingly and analyzed to see what happens. For the same fleet size, the result could be that you cannot meet all demands over time.

This is where the strategy now comes into play: which customers are affected the most? Should the stock capacity be increased or the fleet of trucks?

## The comparison provides for discussion

An analysis is easy: you develop two new scenarios, namely “Stock” and “Fleet”. For “Stock”,  the customers’ maximum stock capacity is increased, for “Fleet” the number of trucks is increased. Needless to say, these both cost money.

For both scenarios the cost-optimal delivery plan can be calculated  at the touch of a button using mathematical optimization. Only the additional costs for stocks or fleet expansion need to be added afterwards.

All three scenarios can be compared as a result: the actual status and the extended variants “Stock” and “Fleet”. Which one provides the best result?

## Experts automatically find the best expansion

While performing these comparison calculations requires little effort, experts go one step further by integrating the costs for warehouse or fleet expansions directly into the model. This is performed by softening the warehouse restrictions at the customers’ end and adding a cost rate to the additional storage space. By doing so this storage space becomes possible, but it is unappealing – unless, of course, it is cheaper than deploying extra trucks.