Water Resource Allocation
LINEAR PROGRAMMING
Agriculture accounts for 70% of global freshwater withdrawals, yet optimal allocation can increase water use efficiency by 20–35%. Each irrigation cycle requires deciding how much water to send to each field from a limited reservoir. This is a Linear Programming problem — the most widely applied optimization technique, solvable in polynomial time.
Where This Decision Fits
Agricultural operational chain — the highlighted step is what this page optimizes
The Problem
From reservoirs to optimization theory
You have a fixed volume of water in a reservoir and several crop fields, each needing between a minimum and maximum amount. The constraint is that total water allocated cannot exceed reservoir capacity, and each field must receive at least its minimum requirement. The question is: how much water should each field get to minimize the total cost of pumping and delivery?
This is a Linear Programming (LP) problem: optimize a linear objective subject to linear constraints. LP is solvable in polynomial time using interior-point methods.
| Agriculture Domain | LP Model | |
|---|---|---|
| Water allocation | Decision variable xi | |
| Reservoir (5000 m³) | Resource constraint | |
| Min water need | Lower bound li | |
| Max water need | Upper bound ui | |
| Irrigation cost | Objective coefficient ci |
Try It Yourself
Edit field water requirements & costs, adjust reservoir size, then optimize allocation
Field Water Requirements
6 Fields · Click any cell to edit| Field | Crop | Min (m³) | Max (m³) | Cost ($/m³) |
|---|
The Algorithm
Greedy LP Allocation for Bounded Variables
Assign Minimums
Give each field its minimum required water. This satisfies all lower bound constraints.
Compute Remaining Budget
Calculate remaining reservoir capacity after all minimums are assigned.
Sort by Cost
Rank fields by cost per m³ (ascending). Cheapest fields get extra water first.
Distribute Remainder
Allocate remaining water to cheapest fields up to their maximum, then next cheapest, etc.
Real-World Complexity
Factors beyond the basic LP model
Rainfall Uncertainty
Natural rainfall reduces irrigation needs, but is unpredictable.
Evapotranspiration
Hot weather increases water loss, requiring dynamic allocation adjustments.
Soil Absorption
Sandy vs. clay soils have different absorption rates affecting efficiency.
Time-of-Day Pricing
Electricity for pumping varies by time, making irrigation timing important.
Canal Network
Water must flow through canals with capacity limits between source and fields.
Water Rights
Legal water rights and environmental flow requirements add constraints.
References
Key literature on water resource optimization