Solving a Discrete Optimization Problem

Objectives

After completing this lesson, you will be able to:
  • Maintain master data for discrete optimization.
  • Configuring the PPO Profile for discrete optimization.
  • Solving a discrete optimization problem with PPO.

Master Data for Discrete Optimization

A problem is not continuous (and is therefore discrete) in production planning, when the model contains:

  • Discrete (integer-value) lot sizes for transportation or PDSs
  • Discrete increase of production capacity
  • Minimum lot sizes for transportation or PDSs
  • Fixed PDS resource consumption
  • Fixed PDS material consumption

If you want the optimizer to consider any of the preceding constraints, you must use the discrete optimization method in the PP optimizer profile. The discrete optimization method can significantly increase runtime requirements.

A prerequisite for using any discrete constraints in the optimization profile is that you have defined discretization as part of your master data.

The figure shows a screenshot of transaction PDS_MAINT. The header data of the PDS shows a field Discretize PDS that allows you to decide, whether a PDS should be considered as discrete or not.

For any production data structure (PDS) for which you want to use discrete constraints, you have to define this in the header data of the PDS. Only this allows the PPO to consider integral production lots, minimum production lot sizes, and fixed material and resource consumption, if any of these are activated in the PP Optimizer profile.

Configuration of the PPO Profile for Discrete Optimization

In the PP Optimizer Profile, you can select whether you want to use the Linear Optimization method or the Discrete Optimization method. Only, if you choose the discrete optimization method, you can maintain, which discrete constraints are to be considered by the optimizer in the Discrete Constraints tab. You have learned in previous lessons that this will significantly increase the runtime requirements due to the nature of the planning problem and the algorithm used to solve it.

On the Discrete Constraints tab, you can define discrete constraints relating to:

  • Capacity Constraints
  • Lot Sizes
  • Fixed Consumption
  • Extended Lot Size Planning

For each type of constraint, you can define the duration (starting from today's date) for which the constraint is to be considered discrete.

Discrete Production Capacity Increase is valid for all production resources for which a capacity increase has been defined in the master data. You must define the corresponding extended capacity utilization rate in the Extended Capacity (%) column which can be found under Change Work CenterCapacityAPO ResourcePPO Capacity Constraints. If you have chosen the discrete optimization method and activate this indicator, the algorithm increases the capacity either for the full or zero amount of the capacity increase as defined in the work center or resource master and the corresponding cost for increasing production capacity gets applied.

You can define the horizon for which you want this discrete constraint to be considered. You can define a specific horizon, for example, in days or weeks. The discretization horizon starts from today's date, even if the planning horizon starts in the future or the past.

Regarding lot sizes, you have four options to define discretization in the Discrete Constraints tab:

  • Minimum Production Lot Size
  • Integral Production Lots
  • Minimum Transportation Lot Size
  • Integral Transportation Lots

If you choose Minimum Production Lot Size, you specify that you want the PP Optimizer to consider the minimum production data structure (PDS) lot size. You can define the horizon for which you want this discrete constraint to be considered. The discretization horizon starts from today's date, and can be defined in, for example, days or weeks. As a prerequisite, you must have defined either the minimum lot size in the PDS, or if a larger minimum lot size has been defined in the material master, the optimizer considers the value from the material master.

The PP Optimizer proposes production quantities per bucket as integral multiples of PDS lot sizes, if you have selected Integral Production Lots. The basis for integral multiple is that if a rounding value has been defined in the material master, the optimizer considers this value. If not, the PP Optimizer uses the typical lot size. The typical lot size is based on the following logic:

  • If a fixed lot size is maintained, the corresponding quantity is returned.
  • If a minimum lot size is maintained either in the material master or in the source of supply, the maximum of both minimum lot sizes is returned.
  • If none of the above is applicable, the typical lot size is considered as 1 (fallback).

If you choose Minimum Transportation Lot Size, you specify that you want the optimizer to consider the minimum lot size calculated from the transportation lane lot size profile and transportation lanes. How the minimum transportation lot size is calculated depends on the option that you have chosen for Optimizer Transport Lot Size on the General Constraints tab. There, you have two options:

  1. Transportation lane

    The algorithm calculates the transportation lot size based on the rounding values defined in the lot size profile of the transportation lane.

    The minimum lot size is calculated as the highest value between the two: Minimum Lot Size from the Transportation Lane Lot Size Profile and Minimum Lot Size from the Transportation Lane.

    The maximum lot size is calculated as the least value between the two: Maximum Lot Size from the Transportation Lane Lot Size Profile and Maximum Lot Size from the Transportation Lane.

  2. Transportation lane/location product

    The algorithm calculates the transportation lot size based on the rounding value defined in the lot size profile of the transportation lane. If this value is not defined or is maintained as zero, then transportation lot size is used from the material master where the first preference is given to Fixed Lot Size and the second preference to the Rounding Value.

    The minimum lot size is calculated as the highest value of the three: Minimum Lot Size from the Transportation Lane Lot Size Profile, Minimum Lot Size from the Transportation Lane and Minimum Lot Size from Product Master.

    The maximum lot size is calculated as the least value between the two: Maximum Lot Size from the Transportation Lane Lot Size Profile and Maximum Lot Size from the Transportation Lane.

You can define the horizon for which you want this discrete constraint to be considered. The discretization horizon starts from today's date, and can be defined in, for example, days or weeks.

Finally, if you have chosen Integral Transportation Lots, you want the optimizer to use integral (integer-based) transportation lots during optimization. Transportation lots are also calculated based on the Optimizer Transport Lot Size selection on the General Constraints tab. If you have selected 1 (Transportation Lane), then the transportation lot size is picked from the Rounding Value from the transportation lane lot size profile. If you have selected 2 (Transportation Lane/Location Product), then the transportation lot size is picked from the Rounding Value from the transportation lane lot size profile. If that is not maintained, the transportation lot size is picked from the material master, first priority given to the fixed lot size followed by the rounding value.

If you want to consider the fixed consumption of material and production resources that was defined in the production data structure (PDS), you choose Fixed Material and Resource Consumption. You must have defined the fixed material and resource consumption in the corresponding PDS master data as a prerequisite.

In some rare cases, it may be required to consider sequence-dependent lot sizes as a constraint in the PPO. For this purpose, you can define the setup costs and setup times in the setup matrix. The PP Optimizer then considers the data entered there and optimizes the setup costs. In the results log of the optimization, an order sequence number is displayed for the planned orders. A prerequisite for this option is that you have maintained the corresponding master data as follows: In the resource or work center master data, you must set the Period Lot Size indicator (which is in the PPO Capacity Constraints tab of the APO Resource) to Sequence-Dependent Lot Size Planning. Furthermore, the production data structure (PDS) must contain a setup group.

Solve a Discrete Optimization Problem with PPO

To understand the impact of discrete constraints to the planning result, you want to run the PPO with the consideration of discrete constraints.

The figure shows that discrete constraints can be passed to the PPO together with the location products and horizons. Simultaneous product and resource planning will create feasible receipts, that are planned orders, transfers and purchase requisitions.

In a first run, you want to analyze how the result changes, if you consider a minimum lot size for the first semifinished material in your example and if you consider an integral lot size for the second semifinished material.

Watch the Run the Production Planning Optimizer with Discrete Constraints simulation to learn how to run the PPO, review the planning result in the product planning table, and compare the results of two optimization runs with linear and discrete constraints. By completing this simulation, you can experience the look and feel of the solution and explore the supported business processes. The simulations serve as an entry point for the exercises that you can complete by yourself in the SAP Practice System, in which you can explore the features and functions in greater depth. Even though the simulations in this course are labeled exercises, they are not as comprehensive as the end-to-end exercises offered through SAP Practice Systems. They are merely intended to provide initial hands-on practice before attempting the end-to-end exercises.

You must have noticed that the discrete constraints are observed by the PPO, if you activate them and that this can have a significant change to the planning result.

Extend the Resource Capacity for the PPO

To understand the impact of discrete constraints to the planning result, you want to run the PPO with the consideration of discrete constraints.

The figure shows that discrete constraints can be passed to the PPO together with the location products and horizons. Simultaneous product and resource planning will create feasible receipts, that are planned orders, transfers and purchase requisitions.

In a second run, you want to analyze how the result changes, if you also consider the option of extending the resource capacity of your bottleneck resource.

Watch the Run the Production Planning Optimizer with Capacity Extension simulation to learn how to run the PPO with capacity expansion, review the planning result in the product planning table, and compare the results of different optimization runs. By completing this simulation, you can experience the look and feel of the solution and explore the supported business processes. The simulations serve as an entry point for the exercises that you can complete by yourself in the SAP Practice System, in which you can explore the features and functions in greater depth. Even though the simulations in this course are labeled exercises, they are not as comprehensive as the end-to-end exercises offered through SAP Practice Systems. They are merely intended to provide initial hands-on practice before attempting the end-to-end exercises.