How deals with discrete data for the reduction of simulation models using neural network

Simulation is useful for the evaluation of a Master Production/distribution Schedule (MPS). Also, the goal of this paper is the study of the design of a simulation model by reducing its complexity. According to theory of constraints, we want to build reduced models composed exclusively by bottlenecks and a neural network. Particularly a multilayer perceptron, is used. The structure of the network is determined by using a pruning procedure. This work focuses on the impact of discrete data on the results and compares different approaches to deal with these data. This approach is applied to sawmill internal supply chain

💡 Research Summary

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The paper addresses the problem of reducing the complexity of discrete‑event simulation models used for evaluating Master Production/Distribution Schedules (MPS) in manufacturing systems. Building on the Theory of Constraints (TOC), the authors propose a reduction methodology that retains only the bottleneck work‑stations and replaces the material flow between them with a multilayer perceptron (MLP). The reduced model therefore consists of a small set of critical resources (structural bottlenecks, conjunctural bottlenecks, and synchronization work‑stations) plus a neural network that predicts the time needed to traverse the aggregated sections of the line.

The reduction algorithm proceeds in four steps: (1) identify structural bottlenecks that have historically limited capacity; (2) identify conjunctural bottlenecks that are saturated for the current MPS; (3) select synchronization work‑stations that are frequently used together with bottlenecks; (4) model the remaining “aggregated blocks” with an MLP. The MLP architecture uses a single hidden layer with a hyperbolic‑tangent activation function and a linear output. Because the optimal number of hidden neurons is unknown, the authors start with an over‑parameterized network (10 hidden units) and apply a weight‑elimination pruning algorithm (Setiono & Leow, 2000) after training. Training follows a three‑stage procedure: Nguyen‑Widrow weight initialization, Levenberg‑Marquardt optimization with a robust criterion, and finally pruning of insignificant weights.

The methodology is illustrated on a real sawmill (SIAT) internal supply chain. Logs enter the system, are directed to one of two conveyors (RQM4 or RQM5), processed by a series of cutting machines (Canter, CSMK, MKV) and finally by a trimmer. The authors collect 12 input variables for each log: ten continuous variables (log length, three diameter measurements, queue lengths, utilization rates, etc.) and two discrete variables – the product type (T_piece) and the conveyor choice (RQM). The target output is the elapsed time ΔT between log arrival at the line and its entry into the trimmer queue.

Two strategies for handling the discrete conveyor variable RQM are examined. In the first approach the raw numeric values 4 and 5 (corresponding to RQM4 and RQM5) are fed directly to the network. Over 30 runs with different random weight initializations, the mean residual error on training data is 78 s (standard deviation ≈ 586 s) and on validation data 74 s (≈ 582 s). Correlation analysis shows that only the diameter “diaPB” and RQM have noticeable influence on the residuals; the others are negligible. Statistical tests (Student’s t‑test and Fisher’s F‑test) reveal that the two RQM groups have significantly different means and variances (99 % confidence), indicating that the network fails to learn the relationship associated with this discrete input.

In the second approach the RQM variable is recoded as a binary indicator (0 for RQM4, 1 for RQM5). This simple encoding reduces the mean residual to about 45 s and the standard deviation to ≈ 350 s. The correlation between RQM and the residual drops, and the statistical tests still show a difference between the two groups but with reduced magnitude. Nevertheless, the network still exhibits non‑negligible errors, especially related to the continuous diameter variable “diaPB”.

The results lead to several key insights:

1. Model reduction via bottleneck identification combined with an MLP can dramatically shrink simulation models while preserving essential dynamics.
2. Discrete inputs must be treated carefully; feeding raw categorical numbers leads to poor learning because the network interprets them as ordinal values.
3. Binary or one‑hot encodings improve the network’s ability to capture the effect of categorical variables, but they do not completely eliminate prediction errors.
4. Pruning can inadvertently remove useful continuous variables, highlighting the need for a careful variable‑selection strategy.

The authors conclude that while the proposed reduced‑model framework is promising, further work is needed to enhance the handling of discrete data. Potential extensions include using embedding layers or dedicated categorical processing units, integrating rule‑based logic for the most critical discrete decisions, and developing online learning schemes to adapt the neural model to changing production conditions. Such improvements would increase the robustness and applicability of reduced simulation models in real‑time production planning environments.