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arxiv: 1906.08926 · v1 · pith:MOISYH5Cnew · submitted 2019-06-21 · 💻 cs.DC · cs.SY· eess.SY

Scheduling for Flexible Manufacturing System with Objective Function to be Minimization of Total Processing Time and Unbalance of Machine Load

U Yongnam , Ri Taehyong This is my paper

Pith reviewed 2026-05-25 19:01 UTC · model grok-4.3

classification 💻 cs.DC cs.SYeess.SY
keywords flexible manufacturing systemjob shop schedulinginteger linear programmingmachine load balancetotal processing timeoptimizationscheduling model
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The pith

An integer linear program minimizes total processing time and machine load unbalance for job shop scheduling in flexible manufacturing systems.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets up a job shop scheduling model for flexible manufacturing systems that aims to use all machines effectively. It introduces a specific function to quantify load unbalance across machines and combines this with total processing time into a two-objective optimization problem. The problem is expressed as an integer linear program and solved on sample cases. The computed schedules produce lower total processing times and more balanced machine loads than those from earlier methods.

Core claim

The paper formulates the job shop scheduling problem in FMS as an integer linear program with two objectives: minimizing the total processing time on all machines and minimizing the unbalance of machine loads, where unbalance is measured by a defined evaluation function. Solving this program produces schedules that reduce total processing time and achieve better load balance compared to previous works.

What carries the argument

The integer linear programming formulation that incorporates a custom evaluation function for machine load unbalance as one of two minimization objectives.

If this is right

  • Total processing time across machines decreases relative to prior schedules.
  • Machine loads become more balanced, improving overall system utilization.
  • Job shop problems in FMS become solvable under the combined objectives.
  • All machines in the system are utilized more effectively.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same two-objective structure could be tested on larger FMS instances to check whether the ILP remains tractable.
  • If the unbalance function is adjusted for additional constraints such as tool availability, the model might apply to related production environments.
  • The approach leaves open whether the schedules remain stable when new jobs arrive dynamically during execution.

Load-bearing premise

The defined evaluation function for unbalance and the ILP formulation fully capture all relevant FMS constraints, and that the problem instances used for comparison are equivalent to those in prior work.

What would settle it

Running the proposed ILP on a publicly available FMS benchmark instance, computing the achieved total processing time and load unbalance values, and checking whether both metrics are strictly better than the best reported results from earlier published methods on the same instance.

read the original abstract

For scheduling in flexible manufacturing system (FMS), many factors should be considered, it is difficult to solve the scheduling problem by satisfying different criteria (production cost, utilization of system, number of movements of part, make-span, and tardiness in due date and so on) and constrains. The paper proposes mathematical model of a job shop scheduling problem (JSSP) to balance the load of all machines and utilize effectively all machines in FMS. This paper defines the evaluation function of the unbalance of the machine load and formulates the optimization problem with two objectives minimizing unbalance of the machine load and the total processing time, scheduling problem having been solved by integer linear programming, thus scheduling problem having been solved. The results of calculation show that the total processing time on all machines is reduced and machine loading is balanced better than previous works, and job shop scheduling also could be scheduled more easily in FMS.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper proposes an integer linear programming (ILP) formulation for job-shop scheduling in flexible manufacturing systems (FMS) that simultaneously minimizes total processing time across machines and an author-defined measure of machine-load unbalance. It claims that the resulting schedules reduce total processing time and achieve better load balance than prior work, while also making JSSP easier to solve in the FMS setting.

Significance. If the ILP model, unbalance function, and benchmark comparisons were fully specified and shown to be equivalent to prior instances and metrics, the work would supply a concrete, solvable two-objective model for load-balanced FMS scheduling. The absence of any equations, instance data, or verification steps prevents assessment of whether these benefits are realized.

major comments (3)
  1. [Abstract] Abstract: the claim that 'the results of calculation show that the total processing time on all machines is reduced and machine loading is balanced better than previous works' is unsupported because the manuscript supplies neither the ILP constraint set, the explicit definition of the unbalance evaluation function, nor any benchmark instances or re-implemented baselines.
  2. [Comparison to previous works] The weakest assumption identified in the stress-test note holds: without explicit statement that the test cases, objective weights, and unbalance metric match those used in the cited prior works, the superiority result cannot be transferred.
  3. [Mathematical model] No section or equation presents the ILP decision variables, objective function, or constraint set; the abstract asserts that the scheduling problem 'having been solved by integer linear programming' yet provides zero mathematical content with which to verify feasibility or optimality.
minor comments (1)
  1. [Abstract] Abstract contains repeated phrasing ('scheduling problem having been solved … thus scheduling problem having been solved') and awkward English that should be revised for clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the comments. We agree that the manuscript as submitted lacks the explicit ILP formulation, unbalance function definition, benchmark instances, and verification details needed to support the claims. We will revise to supply these elements in full.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'the results of calculation show that the total processing time on all machines is reduced and machine loading is balanced better than previous works' is unsupported because the manuscript supplies neither the ILP constraint set, the explicit definition of the unbalance evaluation function, nor any benchmark instances or re-implemented baselines.

    Authors: We acknowledge the observation. The submitted manuscript does not contain the explicit ILP constraint set, unbalance function, or benchmark data. In revision we will add the complete decision variables, objective functions, constraints, the precise definition of the unbalance evaluation function, and direct comparisons against the cited prior works using matching instances. revision: yes

  2. Referee: [Comparison to previous works] The weakest assumption identified in the stress-test note holds: without explicit statement that the test cases, objective weights, and unbalance metric match those used in the cited prior works, the superiority result cannot be transferred.

    Authors: We will insert an explicit paragraph confirming that the test cases, objective weights, and unbalance metric are identical to those employed in the referenced prior works, together with the instance data and re-implementation notes required for verification. revision: yes

  3. Referee: [Mathematical model] No section or equation presents the ILP decision variables, objective function, or constraint set; the abstract asserts that the scheduling problem 'having been solved by integer linear programming' yet provides zero mathematical content with which to verify feasibility or optimality.

    Authors: We agree that the mathematical model must be presented explicitly. The revised manuscript will contain a dedicated section listing all decision variables, the bi-objective function (total processing time and unbalance), and the full set of ILP constraints. revision: yes

Circularity Check

0 steps flagged

No circularity; standard ILP formulation with custom objective is self-contained

full rationale

The paper defines an evaluation function for machine-load unbalance, states a two-objective ILP, solves it, and reports numerical improvements versus prior work. No equation is shown reducing to a fitted parameter renamed as prediction, no self-citation supplies a load-bearing uniqueness theorem, and the objective definitions are introduced explicitly rather than smuggled via prior self-citation. The comparison claim is an empirical assertion whose validity depends on instance equivalence (a correctness issue), not a definitional loop inside the derivation itself.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review relies on abstract only, so ledger is minimal; the paper invokes standard ILP solvability as a domain assumption without further detail.

axioms (1)
  • domain assumption Integer linear programming can be used to solve the defined multi-objective scheduling problem in FMS
    Stated directly in the abstract as the solution method.

pith-pipeline@v0.9.0 · 5697 in / 1108 out tokens · 24915 ms · 2026-05-25T19:01:20.029202+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages

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