Hot-Rolled Steel Pipe Batch Planning Method Considering Machine Maintenance

Literature Overview

This paper by Wu Zixuan, Li Tiekke, Zhang Wenxin, and Wang Bailin, published in Control Theory and Applications (2017, Vol. 34, No. 9, pp. 1250–1259), addresses the hot-rolled steel pipe batch planning problem under periodic machine maintenance constraints. The research was conducted at the Dongling School of Economics and Management, University of Science and Technology Beijing, and the Ministry of Education Engineering Research Center for Steel Production Manufacturing Execution System Technology. The paper extracts the batch planning problem from actual seamless steel pipe production and formulates it as a single-machine scheduling problem with maintenance and setup time considerations.

Problem Formulation

The seamless steel pipe hot-rolling production process involves multiple pipe specifications that require different machine settings. When transitioning between batches of different specifications, machine adjustment time is required to change rollers, calibers, and other tooling. Additionally, periodic machine maintenance is mandatory for equipment reliability and safety.

Key Problem Characteristics

Characteristic	Description	Engineering Significance
Machine maintenance	Periodic downtime for inspection and repair	Non-negotiable constraint
Machine setup time	Depends on specification change magnitude	Major source of idle time
Single machine	One hot-rolling mill	Scheduling complexity
Batch processing	Multiple pipes of same specification per batch	Production efficiency
Order due dates	Customer delivery requirements	Service level constraint

The mathematical model minimizes the total machine idle time and machine adjustment time, subject to maintenance constraints and order fulfithe writing systement requirements.

Algorithm Development

Minimum Adjustment Time Sequencing Rule

The paper proposes a minimum adjustment time sequencing rule that orders batches to minimize total setup time between consecutive batches. The rule is proven to be optimal when maintenance constraints are not considered. The adjustment time between two batches depends on the specification change magnitude, particularly:

Outer diameter change: Requires roller diameter adjustment
Wall thickness change: Requires caliber adjustment
Material grade change: May require temperature and speed parameter changes

Two-Stage Heuristic Algorithm

The proposed algorithm operates in two stages:

Stage 1 - Maintenance-integrated scheduling: The scheduling framework incorporates maintenance windows as fixed constraints and partitions the production horizon into sub-intervals between maintenance events.
Stage 2 - Batch sequencing within intervals: Within each sub-interval, batches are sequenced using the minimum adjustment time rule, with a cyclic solving framework that iteratively improves the solution.

Experimental Validation

The algorithm was validated using actual production data from a seamless steel pipe plant with multiple problem scales:

Problem Scale	Number of Batches	Maintenance Windows	Solution Quality	Computation Time
Small	20-50	1-2	Near-optimal	Seconds
Medium	50-150	2-4	Good	Minutes
Large	150-300	4-6	Acceptable	Minutes

Engineering Practice Integration

Application to Seamless Pipe Production

The batch planning problem directly impacts the following aspects of seamless pipe production:

Roller wear management: Frequent specification changes accelerate roller wear, increasing maintenance costs and reducing production capacity.
Energy efficiency: Maintaining stable rolling conditions minimizes energy consumption per ton of pipe produced.
Quality consistency: Minimized setup changes reduce the risk of dimensional deviations and surface defects associated with parameter adjustments.
Delivery performance: Optimized scheduling improves on-time delivery rates and reduces work-in-progress inventory.

PDCA Cycle Application

The batch planning methodology can be integrated into a PDCA (Plan-Do-Check-Act) quality management cycle:

Phase	Application to Batch Planning	Key Activities
Plan	Develop optimized batch schedule	Algorithm execution, constraint definition
Do	Execute the production schedule	Mill operation, changeover management
Check	Monitor actual vs. planned performance	Idle time tracking, quality inspection
Act	Refine scheduling parameters	Rule updates, constraint adjustments

Key Reflections

This research bridges the gap between operations research theory and steel pipe manufacturing practice. The seamless steel pipe production environment presents unique scheduling challenges that are not adequately addressed by general scheduling literature:

Specification-dependent setup times: Unlike discrete manufacturing where setup times are often uniform, seamless pipe setup times vary significantly based on the magnitude of specification change. This makes the sequencing problem particularly important.
Maintenance as a hard constraint: In steel pipe production, machine maintenance cannot be deferred indefinitely without risking equipment failure. The periodic maintenance requirement fundamentally changes the scheduling problem structure.
Batch size optimization: The interaction between batch size and setup time creates a trade-off that must be optimized for each specific production scenario.

The minimum adjustment time sequencing rule provides a practical and provably optimal solution for the setup-time-minimization sub-problem. Its integration into a cyclic solving framework with maintenance constraints demonstrates a practical approach to complex scheduling problems that balances computational tractability with solution quality.