Resource Allocation
Assign limited resources (people, equipment, budget) to tasks or projects to maximize output or minimize cost under capacity constraints.
NP-hard (integer), Polynomial (continuous)Complexity
Why Resource Allocation Is Hard
Integer requirements
You can't assign half a crew or half a machine. Integer constraints make the problem NP-hard even when the continuous relaxation is trivial.
Multi-period coupling
Today's allocation affects tomorrow's options. A crew sent north today can't serve the south tomorrow. Decisions are temporally coupled.
Competing priorities
Balance workload fairness, minimize cost, maximize coverage, maintain reserve capacity. These objectives conflict with each other.
Real-World Example
What This Looks Like in Practice
A utility company has 120 field crews serving 80 service regions. Some regions need specialized skills. Emergency capacity must be maintained. Travel time between regions varies from 20 minutes to 3 hours. A storm just moved two crews offline. How do you re-allocate the remaining 118 crews to maintain SLA compliance while minimizing total travel time? There are 118 to the power of 80 possible assignments. Your operations manager has 30 minutes.
Approach
How kint Solves Resource Allocation Problems
Formulate as MIP or LP
Continuous resources use LP. Discrete assignments (people, machines) use MIP. kint selects the right formulation automatically.
Rolling horizon for dynamic problems
Multi-period allocation re-optimizes as conditions change. Each planning window overlaps with the next for smooth transitions.
Warm-starting from current state
Yesterday's allocation seeds today's optimization. The solver converges faster because the starting point is already good.
Sensitivity analysis
kint reports which constraints are binding. You see where adding one more crew or one more hour would have the biggest impact.
Technical Details
Resource allocation problems are modeled as linear programs or mixed-integer programs depending on whether resources are divisible. kint supports multi-period allocation with rolling horizon optimization for dynamic environments.
Impact
What Changes
Crew travel time
4.2 hours/day average
3.1 hours/day (-26%)
Jobs completed
Baseline
+18% more per day
SLA compliance
88%
95%
Re-allocation time
2 hours
Minutes
Workload balance
High variance
Equalized within 10%
Example
Input
Allocate 120 field crews across 80 service regions, balancing workload, travel time, skill requirements, and emergency capacity.
Output
Optimal crew assignment with 26% less travel time, 18% more jobs completed, and 95% SLA compliance.
-26%
travel time
+18%
jobs completed
95%
SLA compliance
Connections
Related Problem Types
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