NVD ObjectivesObjectives

Overview

This section provides a high-level description of the objectives used in the NVD model.

Applicable models

• NVD nvd-hap0j2y4zlm1

Cost Objective

The most common objective used in optimisation problems is one which attempts to minimise the cost of a particular solution. In the context of an NVD model, this would be to perform the visits specified (with their prescribed frequency) at a minimum cost meaning that routes should be efficiently sequenced and visits allocated to days which allow for other visits on the same day to be performed effectively.

Intra-Balance Objective

So while we often want to minimise the cost of performing a set of visits, we may also want to ensure that a plan for a period is balanced. Unfortunately, a balance measure is not dimensionally compatible with cost as one may find it difficult to specify the exact tradeoff between balance and cost. As a simple example, if we said we could reduce the standard deviation by 12 units, how much would you be willing to pay in additional routing cost?

It is also straight forward to construct a thought experiment which illustrates that balance and routing cost are actually competing objectives. By this, we mean that as you try to decrease one objective, the other objective tends to increase (or vice versa). So we are inherently having to trade off the one objective for the other. The marginal cost of performing a visit is strictly decreasing with the more visits on a particular route so, in a perfect world, if all visits could be performed on a single day, then that would result in the absolute minimum routing cost. It should also be clear that performing all visits on the same day, while cost effective, also results in a solution with the worst balance, because the workload is not being spread over the period.

There are many advantages to a balanced schedule. One advantage is that, by spreading the workload over the period, one budgets for spare capacity in the future. Sales-reps often find themselves in a position where new customers are being on-boarded throughout the month. A highly cost-centric schedule will tend to leave little room to manoeuvre throughout the period, whereas a balanced schedule will leave an even amount of capacity through the period, increasing the likelihood that, should new customers be added to the schedule, they can be placed cost-effectively into the schedule.

Another reason to smooth the workload through the period is to create what we would call robust schedules. There is often volatility in the execution of schedules where estimated parameters for a future state of the world are put to the test. Budgeting for capacity to be introduced into the schedule over the period improves the probability that the schedule can be performed in reality.

The intra-balance objective term aims to measure the balance of the schedule assigned to a sales-rep or within a territory. Schedules with a lower balance term are considered more smooth. The total intra-balance term is the sum of individual balance terms for each territory.

Inter-Balance Objective

When tackling a territory assignment problem it is often desirable to assign workloads to sales-reps in a near-equal manner. In an ideal world, each rep should service the same number of customers and have identical workloads. In reality, this is rarely possible due to the geographic nature of these problems. In such instances, a tradeoff is being made once again against cost and intra-territory balance. As an example, I may be able to assign all territory workloads to a single territory and achieve a reasonably low routing cost and low balance score. However, in this example, we then have a second territory which has been assigned no work whatsoever - which would be a poor solution. Instead, targeting the balance between territories as an objective term for the solver can be enabled (setting the inter-balance parameter to 1.0 in the configuration) which allows the user to visualise the tradeoff in the search space between the cost and the inter-territory balance (as well as intra-territory balance if specified).