Non-linear scaling and discount rate adjustments

Targets can be toggled between linear and non-linear tradeoffs by using the linear scaling or non-linear scaling icons along the target chart tool bar.

The goal programming formulation uses the difference between the target and the achieved value as a penalty value. Linear weights use the difference between target and achievement as is. Non-linear weights use the square of the difference, thus greatly favouring values that are further from the target above those that are close to the target. If the model has a choice to improve a value that is far away from its target, it will prefer doing so to improving a value that is already close to the target.

If you want to 'satisfice' your targets, trying to balance them all evenly, then use non-linear since this will give an extra boost to targets that are far below the target. If you want to get the overall best achievement, without caring how it is spread through time, then use linear targets.

Non-linear targets seem to work best at getting evenflow values, or balancing non-equivalent targets (e.g. ecological vs timber vs budgets). Linear works best for NPV type analysis.

Discount rates can be applied to target values by using the window on the far right of the toolbar. A default value of 1 implies no discounting. By using the up arrow the discount rate can be increased by 1% at a time (1.01 = 1% discount rate, 1.03 = 3% discount rate). Likewise, the value can be decreased by one percent at a time using the down arrow. Use values of less than 1.0 for compounding.

The discount value will be computed at the mid-point of each planning period, and then multiplied against the previously set weighting value. For example, a discount rate of 1.03 will result in a discount factor of 0.2456 in period 10. This value will then be multiplied against whatever weight value had previously been set for the planning period.

Discount rates express an attitude towards risk. When used with a net value account the effect will be to balance the stream of benefits to mazimize the discounted value, similar to a net present value analysis. Compunding rates can be used to implement targets where the goal is to 'move towards' achievement over time.