Optimization modeling
Formulate and solve LP/MIP/scheduling problems to a verified optimum.
20 project-authored proposals · taxonomy v1.1 · 0 new benchmark runs. Verifiers and partial-credit rules below are designs, not executed results.
- Typical applications
- Gurobi · OR-Tools · AMPL · Excel Solver
- Class GUI-need label
CL· CLI-sufficient
Task proposals · 20
Expand to inspect the complete original wording and proposed checks. Original proposal text remains English in both interfaces.
R03.07.01.01-T01 Production planning LP
Original instruction
Using fixtures/opt/products.csv (per-product profit, machine-hours, and labor) and the resource limits in limits.txt, formulate and solve an LP that maximizes total profit. Write the optimal production quantities and objective to solution.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- OR-Tools · Gurobi
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 2 / 5
Proposed verifier
solution.json objective equals the reference optimum within 1e-6 relative; all resource constraints satisfied; reported quantities feasible and matching an optimal vertex. Graded by re-solving and checking objective + feasibility.
Proposed partial credit
30% feasible plan; 30% constraints satisfied; 40% objective = optimum
R03.07.01.01-T02 Least-cost diet blending LP
Original instruction
Given fixtures/opt/ingredients.csv (cost and nutrient content per unit) and nutrient minimums/maximums in diet_reqs.csv, build and solve an LP minimizing cost while meeting every nutrient bound. Output the ingredient amounts and total cost to solution.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- OR-Tools · AMPL
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
Objective within 1e-6 of the reference minimum; all nutrient min/max constraints satisfied; solution re-verified feasible. Graded by re-solve + feasibility check.
Proposed partial credit
30% feasible blend; 30% all nutrient bounds met; 40% cost = optimum
R03.07.01.01-T03 Transportation problem
Original instruction
From fixtures/opt/supply.csv, demand.csv, and cost_matrix.csv, solve the balanced transportation LP minimizing shipping cost. Write the shipment matrix and total cost to solution.json. Handle any supply-demand imbalance with a dummy node if needed.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- OR-Tools · Gurobi
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
Total cost within 1e-6 of the reference optimum; row sums = supply, column sums = demand; shipments nonnegative. Graded by re-solve + balance checks.
Proposed partial credit
30% feasible shipment plan; 30% supply/demand balance; 40% cost = optimum
R03.07.01.01-T04 Assignment problem
Original instruction
Given the worker-task cost matrix in fixtures/opt/assign.csv, solve the assignment problem minimizing total cost (one worker per task, one task per worker). Output the assignment pairs and cost to solution.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- OR-Tools
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 2 / 5
Proposed verifier
Objective equals the reference optimum exactly (integral costs); assignment is a perfect matching. Graded by re-solve + matching validity.
Proposed partial credit
50% valid perfect matching; 50% cost = optimum
R03.07.01.01-T05 0/1 knapsack MIP
Original instruction
From fixtures/opt/items.csv (value, weight) and the capacity in knap.txt, solve the 0/1 knapsack as a MIP maximizing value. Write the chosen item set and objective to solution.json; the model must use binary variables.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- OR-Tools · Gurobi
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
Objective equals the reference optimum; total weight <= capacity; selected variables binary; MIP gap 0. Graded by re-solve + feasibility.
Proposed partial credit
30% feasible selection; 30% within capacity; 40% value = optimum (gap 0)
R03.07.01.01-T06 Cutting-stock minimization
Original instruction
Given stock length and the order of pieces (length, quantity) in fixtures/opt/cutting.csv, minimize the number of stock bars used via a MIP (or column generation). Output the chosen cutting patterns, their counts, and the total bars to solution.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Gurobi · OR-Tools
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 3 / 5
Proposed verifier
Total bars equals the reference optimum; each pattern fits within stock length; piece demands fully met. Graded by re-solve + pattern/demand validation.
Proposed partial credit
30% valid patterns; 30% demand met; 40% bar count = optimum
R03.07.01.01-T07 Capacitated facility location
Original instruction
Using fixtures/opt/facilities.csv (open cost, capacity), customers.csv (demand), and ship_cost.csv, solve a capacitated facility-location MIP minimizing open + shipping cost. Output which facilities open and the customer assignments to solution.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Gurobi · AMPL
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 4 / 5
Proposed verifier
Objective equals the reference optimum (gap 0); capacity not exceeded at any open facility; every customer served; open vars binary. Graded by re-solve + capacity/assignment checks.
Proposed partial credit
25% feasible assignment; 25% capacity respected; 20% all demand served; 30% cost = optimum
R03.07.01.01-T08 Capacitated vehicle routing
Original instruction
From fixtures/opt/cvrp.json (depot, customer demands, vehicle capacity, distance matrix), solve the CVRP minimizing total distance with OR-Tools routing. Output the per-vehicle routes and total distance to solution.json; no route may exceed capacity.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- OR-Tools
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
long· Long-horizon- Proposed difficulty
- 5 / 5
Proposed verifier
Every customer visited exactly once; each route starts/ends at depot and respects capacity; total distance is within 2% of the reference best-known. Graded by route validation + distance recompute.
Proposed partial credit
30% all customers visited once; 30% capacity respected; 40% distance within 2 percent of reference
R03.07.01.01-T09 Nurse shift scheduling (CP)
Original instruction
Using fixtures/opt/nurses.json (staff, shifts, coverage minimums, max consecutive shifts, days off requests), build a CP-SAT model that produces a feasible 2-week roster meeting all hard constraints and maximizing satisfied requests. Output the roster to solution.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- OR-Tools
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
long· Long-horizon- Proposed difficulty
- 5 / 5
Proposed verifier
All hard constraints hold (coverage per shift, max-consecutive, rest rules); the satisfied-request count equals the reference optimum (or within the stated bound). Graded by constraint validation + objective.
Proposed partial credit
40% feasible roster (hard constraints); 30% coverage minimums; 30% requests = optimum
R03.07.01.01-T10 Job-shop makespan minimization
Original instruction
From fixtures/opt/jobshop.json (jobs, ordered operations, machine, duration), build a CP-SAT model minimizing makespan. Output the start time of every operation and the makespan to solution.json; no machine may run two operations at once.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- OR-Tools
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
long· Long-horizon- Proposed difficulty
- 5 / 5
Proposed verifier
Precedence within each job respected; no machine overlap; makespan equals the reference optimum (or proven bound). Graded by schedule validation + makespan.
Proposed partial credit
30% precedence respected; 30% no machine overlap; 40% makespan = optimum
R03.07.01.01-T11 Set covering
Original instruction
Given fixtures/opt/cover.csv (candidate sets and the elements each covers) and per-set costs, solve a set-covering MIP that covers every element at minimum cost. Output the chosen sets and total cost to solution.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- OR-Tools · Gurobi
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
Every element covered by at least one chosen set; objective equals the reference optimum (gap 0). Graded by coverage check + objective.
Proposed partial credit
50% full coverage; 50% cost = optimum
R03.07.01.01-T12 Multi-commodity flow
Original instruction
From fixtures/opt/network.json (nodes, arcs with capacity and cost, commodities with source/sink/demand), solve the min-cost multi-commodity flow. Output per-arc per-commodity flows and total cost to solution.json; respect arc capacities shared across commodities.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Gurobi · AMPL
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 4 / 5
Proposed verifier
Flow conservation holds per commodity; shared arc capacities not exceeded; all demands routed; total cost within 1e-6 of the reference optimum. Graded by re-solve + conservation/capacity checks.
Proposed partial credit
25% conservation; 25% capacities respected; 20% demands met; 30% cost = optimum
R03.07.01.01-T13 Bin packing
Original instruction
Given item sizes in fixtures/opt/bins.csv and a fixed bin capacity, solve a bin-packing MIP minimizing the number of bins used. Output the item-to-bin assignment and bin count to solution.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- OR-Tools · Gurobi
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
No bin exceeds capacity; every item assigned once; bin count equals the reference optimum (gap 0). Graded by assignment validation + objective.
Proposed partial credit
30% valid assignment; 30% capacity respected; 40% bin count = optimum
R03.07.01.01-T14 Exact TSP on a small instance
Original instruction
From the symmetric distance matrix in fixtures/opt/tsp.csv (<=15 cities), solve the TSP to proven optimality using a MIP with subtour elimination (lazy constraints) or OR-Tools exact. Output the optimal tour order and length to solution.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Gurobi · OR-Tools
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 4 / 5
Proposed verifier
The tour visits every city once and returns to start (no subtours); length equals the reference optimum exactly. Graded by tour validation + length.
Proposed partial credit
30% valid Hamiltonian tour; 30% no subtours; 40% length = optimum
R03.07.01.01-T15 Mean-variance portfolio optimization
Original instruction
Using fixtures/opt/returns.csv (expected returns) and cov.csv (covariance), solve the QP that minimizes portfolio variance for a target expected return of 8% with weights summing to 1 and no shorting. Output the weights and resulting variance to solution.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Gurobi
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 4 / 5
Proposed verifier
Weights sum to 1, all nonnegative, expected return >= 8%; variance within 1e-6 of the reference optimum. Graded by re-solve + constraint checks.
Proposed partial credit
30% feasible weights; 30% return target met; 40% variance = optimum
R03.07.01.01-T16 Blending LP with dual/sensitivity report
Original instruction
Solve the blending LP in fixtures/opt/blend.mod (AMPL/Pyomo) and, in addition to the optimal cost, report the shadow price of each binding constraint and the objective-coefficient ranging for two named variables. Write values to sensitivity.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- AMPL · Gurobi
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
Optimal cost matches reference; reported shadow prices and coefficient ranges match the reference duals/ranges within 1e-4. Graded by re-solve + dual comparison.
Proposed partial credit
40% optimum; 35% shadow prices; 25% coefficient ranges
R03.07.01.01-T17 Workforce LP in Excel Solver (control pair of T01)
Original instruction
Control pair of T01: in Excel, open fixtures/opt/workforce.xlsx and use the Solver add-in (GUI) to set up and solve the staffing LP (decision cells, objective cell, constraint ranges) that minimizes weekly labor cost meeting daily coverage. Save with the solved values and the Solver model stored.
- Platforms
win· Windowsmac· macOS- Applications
- Excel Solver
- Interfaces
desk· Desktop GUI- GUI need · task setting
G2· GUI-essential- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
click· Point & clicktype· Text & formsnav· Pan/zoom/scroll- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 2 / 5
Proposed verifier
The solved decision cells meet all coverage constraints and the objective cell equals the reference optimum within tolerance; the saved workbook contains the Solver model definition (set via the GUI, not a pasted answer). Graded on cell values + stored model. Agent VM has no terminal or Python and Excel macros/VBA are disabled by Trust Center policy, so the Solver model can only be built in the Solver dialog.
Proposed partial credit
30% model set up in Solver; 30% constraints met; 40% objective = optimum
R03.07.01.01-T18 Capacitated lot-sizing
Original instruction
From fixtures/opt/lotsize.json (per-period demand, setup cost, holding cost, production capacity), solve the single-item capacitated lot-sizing MIP minimizing setup + holding cost. Output the production and inventory per period and total cost to solution.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Gurobi · OR-Tools
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
Inventory balance holds each period, demand met, capacity respected, setup binaries consistent with production; total cost equals the reference optimum (gap 0). Graded by re-solve + balance checks.
Proposed partial credit
25% inventory balance; 25% demand met; 20% capacity+setup logic; 30% cost = optimum
R03.07.01.01-T19 Constraint feasibility (Sudoku/CP)
Original instruction
Given the partially filled grid in fixtures/opt/sudoku.txt, model it as a CP satisfaction problem in OR-Tools CP-SAT and output the unique completed grid to solution.txt. The model must encode row/column/box all-different constraints.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- OR-Tools
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
- None declared
- Proposed difficulty
- 3 / 5
Proposed verifier
solution.txt is a valid completion satisfying all all-different constraints and matching the puzzle's unique solution. Graded by constraint validation against the given clues.
Proposed partial credit
40% model constraints correct; 60% valid unique completion
R03.07.01.01-T20 Bi-objective goal programming
Original instruction
For the planning model in fixtures/opt/biobj.json with objectives (minimize cost, minimize emissions), compute 5 Pareto-efficient points via the epsilon-constraint method and output the trade-off frontier (cost, emissions) plus the chosen weighted-goal solution to solution.json.
- Platforms
lin· Linuxmac· macOSwin· Windows- Applications
- Gurobi · AMPL
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro applong· Long-horizon- Proposed difficulty
- 5 / 5
Proposed verifier
The 5 reported points are each feasible and non-dominated, matching the reference frontier within 1%; the goal-programming solution meets the stated target deviations. Graded by re-solve at each epsilon + dominance check.
Proposed partial credit
30% feasible points; 30% non-dominated frontier; 20% matches reference; 20% goal solution correct
Mapped research references
Existing benchmark-to-class links from the research catalog. They are not record-level annotations, executions or product endorsements.