Discrete Commitment Optimization¶
Choose among indivisible options or commitments when partial allocation is impossible.
The Diagnostic Story¶
Symptom: Each option looks attractive on its own, so the team picks the highest-ranked items one at a time — only to discover that the chosen set is over budget, incompatible, or leaves critical needs unmet. Rounding a fractional plan creates overruns. Selections that seemed independent turn out to share constraints, and the bundle that emerges fails even though every individual component passed review.
Pivot: Represent the decision in whole, indivisible units from the start; define the coupling constraints that link choices; and compare complete feasible bundles against an explicit objective rather than ranking options one at a time.
Resolution: The selected commitment bundle is globally feasible rather than locally appealing: budget, compatibility, and coverage constraints are satisfied together, and the tradeoffs among bundles are documented and visible. Fewer choices require emergency reversal after implementation begins.
Reach for this when you hear…¶
[capital budgeting] “We approved the three highest-NPV projects independently and then realized they all need the same engineering team in the same quarter — we have to re-run this as a bundle problem, not a ranking.”
[hospital staffing] “Shift scheduling looks fine on paper until you notice that three of the approved assignments require the same specialist to be in two places at once.”
[procurement] “The fractional relaxation said buy 2.7 of this equipment unit, which is not a thing, and when we rounded up we blew the budget and when we rounded down we missed minimum capacity.”
Mechanisms / Implementations¶
- Assignment Model
- Branch-and-Bound Procedure
- Constraint Satisfaction Search
- Crew Scheduling Model
- Facility Location Model
- Integer Programming Model
- Integer Programming Solver
- Project Selection Matrix
- Selection Review Board
- Solver Dashboard
Related Abstractions¶
Abstractions this archetype builds on — directly (a source ingredient) or as a related pattern. Links follow the typed catalog namespace.
Built directly on (3)
- Discreteness: Countable steps.
- Integer Linear Programming (ILP): Discrete optimization with integer variables.
- Optimization: Finds best solution under constraints.
Also references 6 related abstractions
- Cardinality: Size of sets.
- Complexity (Time/Space): Resource scaling with input size.
- Constraint: Limits possibilities to guide outcomes.
- Coupling: Interdependence among subsystems.
- Resource Management: Allocation of finite assets.
- Scheduling: Organizing tasks over time.
Variants¶
Narrower or domain-specific specializations that share this archetype's core structure. Recognized variants are established; candidate variants are provisional.
Binary Project Selection · subtype · recognized
Choose which indivisible projects, proposals, features, or initiatives to accept when each candidate is essentially yes-or-no.
Integer Quantity Commitment · subtype · recognized
Choose whole-number quantities of units, slots, staff, licenses, batches, or assets when fractional quantities are impossible or meaningless.
Assignment / Matching as Discrete Commitment · subtype · candidate
Assign agents, tasks, slots, resources, or roles to one another when each match is a discrete commitment constrained by capacity and compatibility.
Facility Location Commitment · domain variant · recognized
Choose which physical or logical sites to open, close, place, or reserve when each site is an indivisible commitment with network effects.