Random Interval Scheduling Challenge Generator

Description

Generate synthetic positive-duration half-open jobs and solve the declared count or weight objective exactly with finish-time dynamic programming, retaining one optimum with exclusion on objective ties.

An optimization instance defines choices, constraints, and an objective. A feasible witness demonstrates that its stated constraints can be met; it establishes optimality only when the tool actually computes and verifies an optimum.

When to use this tool

Use this generator to create reproducible interval scheduling challenge cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.

How to use the tool and how it works

Supply jobCount, horizon, maximumDuration, objective in the field shapes below. Set seed when you need an explicit replay.
Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
Read jobs, selectedIds, objectiveValue. Use the conventions below and keep answer-bearing fields separate when presenting an exercise.

Draw half-open intervals inside the horizon with positive integer weights. Sort by finish time and use dynamic programming with the latest compatible predecessor to maximize selected count or total weight, retaining the excluded solution on a tie.^[1]

Input field	Meaning and units	Accepted input
jobCount	Job Count	Required. Safe integer; minimum 1; maximum 16.
horizon	Horizon	Required. Safe integer; minimum 1; maximum 64.
maximumDuration	Maximum Duration	Required. Safe integer; minimum 1; maximum 64.
objective	Objective	Required. Text; one of "count", "weight".
seed	Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed.	Optional. Safe integer.

Output field	Interpretation	Returned shape
jobs	Jobs	Required. Array of Object; no unknown keys.; minimum items 0; maximum items 16.
jobs[].id	Literal identifier used to match records, independently of their display labels.	Required. Safe integer; minimum 0; maximum 15.
jobs[].start	Start	Required. Safe integer; minimum 0; maximum 63.
jobs[].endExclusive	End Exclusive	Required. Safe integer; minimum 1; maximum 64.
jobs[].weight	Weight	Required. Safe integer; minimum 1; maximum 9.
selectedIds	Selected Ids	Required. Array of Safe integer; minimum 0; maximum 15.; minimum items 0; maximum items 16.
objectiveValue	Objective Value	Required. Safe integer; minimum 0; maximum 144.
randomness	Replay metadata: source is seed or context; seed is the normalized 32-bit seed or null for a context source.	Required. Object; no unknown keys.
randomness.seed	Optional numeric replay seed; normalization and precedence are explained below.	Required. Safe integer. or Null.
randomness.source	Source	Required. Text; one of "context", "seed".

An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.

json

{
  "input": {
    "jobCount": 3,
    "horizon": 6,
    "maximumDuration": 3,
    "objective": "weight",
    "seed": 42
  },
  "output": {
    "jobs": [
      {
        "id": 0,
        "start": 3,
        "endExclusive": 5,
        "weight": 8
      },
      {
        "id": 1,
        "start": 4,
        "endExclusive": 5,
        "weight": 5
      },
      {
        "id": 2,
        "start": 1,
        "endExclusive": 3,
        "weight": 8
      }
    ],
    "selectedIds": [
      2,
      0
    ],
    "objectiveValue": 16,
    "randomness": {
      "seed": 42,
      "source": "seed"
    }
  }
}

Limitations and assumptions

Touching end and start times are compatible. The answer is optimal for this generated single-resource objective, not for extra precedence, setup, multiple-resource, or real scheduling constraints.
A replay requires the same complete input and implementation. Randomized construction does not guarantee uniform coverage of every feasible output; finite samples can repeat unless a distinct-selection rule is explicitly stated.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.

References

Tool behavior and example: Random Interval Scheduling Challenge Generator — tool.io

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