Mixed Integer Optimization Modeling
In mixed integer optimization modeling a fundamental consideration is the representation of time. How long should the planning horizon be? Should the model encompass multiple time periods or is the definition of just one time period representing the entire planning horizon sufficient? What are the trade-offs between ease of use, data maintenance, solve time, increased accuracy and manageable insights in a single period model verses multiple time periods? These are all very important questions that can have significant impact on the value derived from modeling for business planning purposes.
Define the Planning Horizon
The first consideration is defining the planning horizon of interest. This can be thought of in general, broad terms:
Strategic planning is long-term, typically more than one year. Strategic decisions typically include harvest planning, capacity planning, network design, investment planning, etc.
Tactical planning generally ranges in the mid-term of a month to a year in duration. Tactical decisions typically include, capacity planning, supply chain optimization, order allocation, product mix, shift configuration, etc.
Operational planning is everything from real time to a month in length. These decisions are much more focused on what to do today. What should each processing center be doing today or this week. What product should be shipped on which truck, ordering of production runs, size of production runs, etc.
It should be noted that the definition of the planning horizon should also affect the way costs are portrayed in the model. In the short run — i.e. operational planning — all costs are fixed. You can’t lay off a crew today and expect them back to work tomorrow. In tactical planning, more of the costs become variable, and in the long run all costs should be variable. When I say variable, this means they are based on a per unit or per hour basis or even a binary decision of spend this get that or spend nothing and get nothing. These binary decisions are variable and are a very powerful use of mixed integer optimization.
Determine How Many Periods to Use
Once the planning horizon has been determined, the decision of how many periods to model needs to be addressed. The greater the number of time periods, the larger the data set and the slower the solve time. Because of this you always want to make sure you're not wasting efforts by trying to model at to fine of a level of detail. A model is a simplification of reality that yields useful insights into the nature of reality.
In determining how many periods to use, you should consider data availability. One of the easiest considerations for data availability is the accounting cycle. Financial, production, sales and inventory data is usually available on a set schedule such as monthly reports and annual reports. Because of this, modeling a strategic planning horizon is usually best done in one year time buckets. A tactical model is usually best handled with monthly time buckets.
However, when examining operational issues, the decision around time-period definition becomes much more difficult. The key issues here are how rapidly things fluctuate. In scheduling a detailed process, it might make sense to model a day in fifteen-minute increments. When focusing on meeting a shipping schedule, it might make more sense to model a week in daily time increments. This way you can make sure you have the product you need ready for shipping on the day the truck arrives.
Clearly, the defining of time period and planning horizon is key when designing a model for a specific use case. Improper time period structure can render a model incapable of answering fundamental questions of a specific use case. Equally noteworthy, proper time period definitions can enable the model to actually answer questions beyond the original scope of the intended use of the model. It's safe to say that determining how time will be represented in enterprise modeling is a task worth (you guessed it) making a little time for.