TS-Based Supply Optimizer finishes before Maximum Solving Runtime with Technical Gap (1 iteration)

[vincentverheyen]

What could be the reason that a TS-Based Supply Optimizer (Profit Maximization Mode, Technical Weeks, Discretization of 20 weeks) finishes before Maximum Solving Runtime, with a Technical Gap (Average technical gap created by product decomposition > 2.7 ... e-05)?

How to reconcile this (the fact that there is a technical gap) with the # Number of subproblems in product decomposition solved to optimality being equal to the # Number of subproblems in product decomposition?

We switched on "Product Decomposition" as well as "Use Remaining Runtime for Non-Optimal Subproblems". Additional Parameter OPT/SNP_PRODUCTDECO/BUSEUPREMAININGRUNTIME is set to YES. "Pre-Optimization" is enabled. "Local Optimization for Discrete Problems" is set to "Use as start solution'.

We monitor that there has only been one iteration of the Planning Run. Why did the run not create more iterations &/or a longer Optimizer solving time, since there was a Technical Gap)?

In our case, the Optimizer solving time was 2500 seconds, which is far below the Maximum Solving Runtime for Optimizer maintained as 15000.

This is a case of MIP due to the lot sizes, while binaries are used for Minimal Lot Size and integers for Incremental Lot Size:
- Continuous Variables: 8 million
- Discrete Variables: 28000
- Binary Variables: 16000
- Linear Constraints: 2 million

Since this is MIP indeed we expect a parameter to decide when to stop searching for a solution, since there is no mathematically optimal solution like with LP. What is the cut-off parameter to determine when a solution is 'optimal' enough?

[Marlene2]

Hi Vincent and TS-SCM End-Users,

I want to thank Vincent asking an important Time Series Based SC-Inventory. Here are my thoughts after reading all responses.

 Analysis of Time Series-Based Supply Optimizer Behavior

Scenario Overview

- Optimizer: TS-Based Supply Optimizer
- Mode: Profit Maximization
- Time Horizon: Technical Weeks
- Discretization: 20 weeks
- Product Decomposition: Enabled
- Use Remaining Runtime for Non-Optimal Subproblems: Enabled
- Pre-Optimization: Enabled
- Local Optimization for Discrete Problems: Set to "Use as start solution"

Observed Behavior

1. Optimizer finishes before Maximum Solving Runtime
2. Technical Gap present (Average technical gap > 2.7e-05)
3. Number of subproblems solved to optimality equals the total number of subproblems

Analysis

1. Early Termination

Reasons for finishing before Maximum Solving Runtime:

a) Convergence: The optimizer might have reached a point where further improvements are minimal.
b) Subproblem Optimization: All subproblems were solved to their individual optimality criteria.
c) Discretization Effect: The 20-week discretization might limit the solution space, allowing faster convergence.

2. Technical Gap Presence

The technical gap indicates that while individual subproblems are solved to optimality, the global solution might not be perfectly optimal. Reasons include:

a) Decomposition Limitations: Product decomposition can introduce small inaccuracies in the global solution.
b) Discretization Effects: The 20-week discretization might introduce small approximations.
c) Numerical Precision: The gap might be within the solver's numerical tolerance.

3. Reconciling Gap with Optimal Subproblems

This apparent contradiction can be explained by:

a) Local vs. Global Optimality: Subproblems are optimal individually but may not yield a globally optimal solution when combined.
b) Decomposition Artifacts: The process of breaking down and recombining subproblems can introduce small discrepancies.
c) Numerical Issues: Rounding and precision limitations in calculations can lead to small gaps.

Potential Solution to Improvements

1. Adjust Decomposition Strategy: Fine-tune the product decomposition parameters.
2. Increase Precision: Tighten numerical tolerances if computational resources allow.
3. Extend Runtime: Allow more time for the "Use Remaining Runtime for Non-Optimal Subproblems" phase.
4. Refine Discretization: Experiment with different discretization intervals.

The observed behavior is not uncommon in complex supply chain optimization problems. The technical gap, while present, is very small (2.7e-05), suggesting that the solution is likely very close to optimal for practical purposes.