Material Procurement Planning
Lot Sizing · Wagner-Whitin Algorithm
Construction material waste from poor procurement timing runs 8–12% of total material cost, with storage fees adding €15–€40 per cubic meter per week on congested urban sites. Every project phase, a procurement manager must decide when and how much to order — balancing setup/delivery costs against holding costs and storage constraints. This is the dynamic lot sizing problem — solvable exactly by Wagner-Whitin in O(T²) — where ordering too early wastes storage and too late causes delays.
Where This Decision Fits
Construction planning chain — the highlighted step is what this page optimizes
The Problem
Dynamic lot sizing for construction material procurement
Consider a 12-week project horizon for an office tower construction. Each week has a known demand for structural steel measured in tonnes. Every delivery incurs a fixed setup cost of €2,500 (truck dispatch, crane time, inspection, and paperwork) regardless of order size. Holding unused material on-site costs €45 per tonne per week in storage space, weatherproofing, and insurance. The procurement manager must decide the order quantities for each week to satisfy all demand at minimum total cost.
The key trade-off: order frequently and pay high setup costs with minimal inventory, or batch orders and pay lower setup costs but carry inventory. The Wagner-Whitin algorithm finds the exact optimum by exploiting the zero-inventory property — it is always optimal to begin a new order only when inventory reaches zero.
subject to
It = It-1 + xt − dt // inventory balance
xt ≤ M · δt // order only when setup is paid
It ≥ 0 // no backorders
δt ∈ {0, 1} // binary setup indicator
Where K is the fixed setup/delivery cost, h is the per-unit holding cost per period, dt is the demand in period t, xt is the order quantity, and It is the ending inventory.
Try It Yourself
Optimize material procurement across the project horizon
Lot Sizing Optimizer
12 Weeks · K=€2,500Ready. Click “Solve & Compare All Algorithms” to run.
| Algorithm | Total Cost | Deliveries | Avg Inventory |
|---|---|---|---|
| Click Solve & Compare All Algorithms | |||
The Algorithms
From exact dynamic programming to simple heuristics
Wagner-Whitin Algorithm
O(T²) | Optimal solution guaranteedA dynamic programming approach that exploits the zero-inventory ordering (ZIO) property: in an optimal plan, a new order is placed only when ending inventory is zero. The algorithm builds a cost matrix C(i, j) representing the minimum cost of covering demands from period i through j with a single order placed in period i, then finds the globally optimal partition of the horizon into order intervals. Published by Wagner & Whitin in 1958, it remains the gold standard for uncapacitated lot sizing.
Silver-Meal Heuristic
O(T) | Myopic forward passA greedy forward-pass heuristic that decides how many future periods to cover with each order. Starting from the current period, it extends the order horizon one period at a time, computing the average cost per period (setup cost plus cumulative holding cost divided by the number of periods covered). It stops extending when the average cost begins to increase and places the order covering all periods up to that point. Simple, fast, and often near-optimal for smooth demand patterns.
Lot-for-Lot (L4L)
O(T) | Zero inventory policyThe simplest possible policy: order exactly what is needed each period. Every period with positive demand triggers a separate delivery, resulting in zero holding cost but maximum setup cost. L4L serves as the upper bound baseline — any reasonable batching heuristic should do at least as well. It is optimal only when setup costs are negligible relative to holding costs.
Real-World Complexity
Why construction procurement goes beyond textbook lot sizing
Beyond the Basic Model
- Capacity constraints — Limited site storage, truck payloads, and crane availability cap order sizes per delivery
- Quantity discounts — Suppliers offer tiered pricing; larger orders reduce per-unit cost but increase holding expense
- Lead times — Materials must be ordered weeks in advance; lead times vary by supplier and material type
- Perishability & shelf life — Ready-mix concrete sets within hours; adhesives and sealants have limited shelf life
- Multi-material coordination — Steel, concrete, and formwork must arrive in sync with the construction schedule
- Weather uncertainty — Rain delays shift demand forward; procurement plans must accommodate schedule slippage
- Cash flow constraints — Progress billing cycles and payment terms limit when materials can be purchased
Key References
Foundational works in lot sizing
- (1958). “Dynamic version of the economic lot size model.” Management Science, 5(1), 89–96.
- (1973). “A heuristic for selecting lot size quantities for the case of a deterministic time-varying demand rate and discrete opportunities for replenishment.” Production and Inventory Management, 14(2), 64–74.
Need to optimize your construction procurement?
From lot sizing to project scheduling and resource leveling, mathematical modeling can transform your construction supply chain. Let’s discuss how Operations Research can work for you.