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The ins and outs of a planning calculation


When resources have to be assigned to activities, a planning needs to be made.  This area really is an excellent opportunity for digitalization and optimization as it will help organizations to make a big leap forward in efficiency.

Creating a planning or schedule comes down to assign resources to a list of activities. To properly do this, information has to be provided: activities, resources, rules & constraints and an objective function. In return, the calculation will typically deliver a planning schedule and a cost & benefit report.


Input 1: list of activities

The most obvious example of activities is a list of tasks that have to be executed (e.g. shifts need to be done in a factory, flights have to be flown by an airline, … ).

Other use cases can have a different aim. The goal can be to calculate what can be the maximum and most beneficial activities that can be fulfilled. E.g. optimize a (logistics) network to maximize the number of customers or goods that can be handled, delivered or sold. Such a challenge is also a planning calculation where the list of activities rather is a description of potential business activities, their benefits and monetization opportunities.

Input 2: list of resources

The resource list passed as input can be the available workforce that can be used and assigned to the activities to make them happen. Typically, additional information is included, such as qualifications, availability, preferences, age and other properties of the resources. These properties can be required to verify rules and constraints when assigning resources to the activities. E.g. a pilot has to be qualified to fly a specific airplane type, a pilot aged 60 or older must be paired with a pilot younger than 60, …

Other types of resources can be equipment that is necessary to execute tasks (airplanes, trains, …) or more “conceptual” resources (airport slots, …)

Input 3: list of rules & constraints

A number of rules and constraints have to be taken into account when assigning resources. For example, a resource has to be qualified to perform an activity, a resource needs to be available, sufficient rest between different activities has to be foreseen, ….

There are two types of rules & constraints that have to be taken into account when assigning resources to activities: the hard rules & constraints: the must-haves and the soft rules & constraints: the nice-to-haves.

If all required activities are covered and all hard rules & constraints are respected, the planning (aka schedule or roster) is considered to be “legal”. Ideally, next to this, the planning also takes into account as many “soft” rules & constraints as possible. Examples of such soft rules are: fair distribution of work, annoying tasks and work abroad; take into account requests of employees (e.g. to regularly work on preferred tasks or together with a friend, to keep some specific time-slots as some free time , …). For every soft rule & constraint, a penalty is defined to take into account if the soft rule is not respected.

Input 4: objective function (aka cost function)

The planning solution tries to maximize the benefits and minimize the costs for the organization. To describe the costs and benefits, an “objective function“ (sometimes just named “cost function”) has to be defined. This brings together the list of costs and benefits that can be linked to the planning. For example: travel and transport-related costs, cost of overtime, hotel cost, cost to hire freelancers, salary cost, … Next to these “financial costs”, also non-financial costs (and benefits) can be included. E.g. the virtual cost of not taking into account employee requests, assigning “annoying” work non-evenly, …

Putting together such an “objective function” for an organization typically requires the involvement and expertise of domain experts.


Output 1: a planning / roster / schedule

A legal and optimized planning respects all rules and constraints and assures a minimum of financial and non-financial costs and maximum benefits. Examples are:

A workforce and equipment schedule which indicates which resources are assigned to the different given activities. Also all “supporting” actions that have to be included to realize the schedule (e.g. required transportation, intermediate storage, rest facilities, hotel stays, …) are included.
An optimized logistics network which indicates which routes to take, which resources to use to run the operations and how to assign them to all activities.

Output 2: a cost and benefit report

Any planning / schedule / roster implies a certain financial and non-financial cost. If the planning is optimized, this total cost is the global minimum: the mathematically best possible planning.

The cost report gives a detailed overview of all individual cost components related to every single activity and resource. These fine-grained numbers can typically be used as input for an analytics tool to give schedulers, operators and management a good idea of where money is spent and benefits are generated.

Also, thanks to these reporting capabilities, an organization can fine-tune the configuration of the planning calculator. E.g. If employees are allowed to indicate preferred “free-time time-slots”, the planning calculation will take into account these individual ‘free-time requests” as long as the cost for the organization does not exceed a configured value. The cost report and analytics tool can then be used to fine-tune this configured free-time-request-cost-limit to make sure there’s a healthy balance between workforce well-being and cost for the organization.

How to get a maximum benefit from planning

Until very recently, automated solutions and certainly (semi-)manual calculations were typically limited because only a subset of all rules and constraints could be taken into account and most of the time, they even had to be significantly simplified to make it technically possible to do the calculation. Most of the time, manual intervention, trial & error and multiple iterations of a simplified version of the planning challenge were needed to end up with a “local optimum”.

A new, modern, state-of-the-art optimized planning engine uses the power of the cloud and advanced mathematical solvers to calculate a legal and global optimal planning which takes into account all rules, constraints and costs without any manual intervention. People working in the planning department can focus on fine-tuning the objective function and configuring the calculation engine to take into account what is really important and efficient for the organization: find a good balance between optimizing for more business, cost reduction and employee well-being.

Our company, MOTULUS, offers advanced optimized planning solutions, built on unique, proprietary solvers. Do not hesitate to get in contact if you want to align on how we can work together – always very eager to discuss and all feedback is really appreciated!