Memory-Chip Allocation under the AI-Memory Supercycle

A multi-period MILP study of how a memory manufacturer should allocate scarce HBM3e / DDR5 / DDR4 output across heterogeneous customer classes during the 2024–2026 AI-memory shortage. Built in Pyomo, solved with Gurobi, with reproducible input data as plain CSVs.

1. Quick start

# one-time install (Gurobi ships with a free restricted-size license)
pip install pyomo gurobipy pandas numpy matplotlib

# pipeline
python3 generate_data.py    # rebuilds data/*.csv from a fixed seed
python3 solve.py            # builds Pyomo model → Gurobi → output/results.json
python3 plots.py            # reads results.json → figs/*.pdf

solve.py finishes in a second or two on the shipped instance. Output:

z*_LP   =  7101.74   (transport 998, shortage 5529, holding 570, lane 5)
z*_MILP =  7250.01   (transport 1005, shortage 5533, holding 572, lane 140)
open lanes : 7 / 15,  MILP gap vs LP = 2.09 %

2. What the model captures

The instance is 3 fabs × 5 customer classes × 3 products × 4 planning periods (weeks of Q1 2026).

Symbol	Meaning	CSV
x[i,j,p,t]	units shipped fab i → customer j, product p, period t	decision variable
u[j,p,t]	unmet demand	decision variable
Inv[i,p,t]	end-of-period inventory at fab i	decision variable
y[i,j]	lane (i,j) opened over horizon (binary)	decision variable
S[i,p,t]	supply	supply.csv
D[j,p,t]	demand	demand.csv
c[i,j,p]	transport cost	transport_cost.csv
π[j,p]	shortage penalty	shortage_penalty.csv
φ[j,p]	minimum SLA fill-rate	sla_min.csv
h[p]	per-period holding cost	holding_cost.csv
e[i,j]	kg CO₂ per shipped unit	emissions.csv
F, K, B, M	lane fixed cost / lanes per fab / carbon budget / big-M	params.csv

Constraints: supply balance with inventory carry-over, demand balance, SLA floors for contracted customers, big-M lane linking, lane cardinality per fab, and a global carbon budget.

3. Dataset layout

Everything lives in data/. All CSVs are long-format (one row per tuple), UTF-8, comma-separated.

data/
├── suppliers.csv         supplier_id, name, country, has_hbm_packaging
├── customers.csv         customer_id, name, tier, country
├── products.csv          product_id, name, generation, requires_advanced_packaging
├── periods.csv           period_id, label
├── supply.csv            supplier_id, product_id, period_id, supply_kwe
├── demand.csv            customer_id, product_id, period_id, demand_kwe
├── transport_cost.csv    supplier_id, customer_id, product_id, cost_per_unit
├── shortage_penalty.csv  customer_id, product_id, penalty_per_unit
├── sla_min.csv           customer_id, product_id, min_fill_rate
├── holding_cost.csv      product_id, cost_per_unit_period
├── emissions.csv         supplier_id, customer_id, kg_co2_per_unit
└── params.csv            param_id, value, description

All units: quantities are kWE (thousand wafer-equivalent units); money is $k; CO₂ is kg.

To try a variant, edit any CSV by hand and rerun solve.py. To reset, rerun generate_data.py.

4. Files

File	Purpose
generate_data.py	Writes the 12 CSVs in data/. Seed 42 → deterministic.
solve.py	Pyomo model + Gurobi solver + sensitivity scan → output/results.json.
plots.py	Reads output/results.json → four PDFs in figs/.
data/	Input dataset (above).
output/results.json	Canonical machine-readable output of one run.
figs/	Four figures: allocation.pdf, shadow.pdf, lp_vs_milp.pdf, sensitivity.pdf.

5. Reproducibility notes

• The data seed is fixed at 42 in generate_data.py.
• solve.py calls Gurobi through pyo.SolverFactory("gurobi"); LP duals are imported via pyo.Suffix(direction=pyo.Suffix.IMPORT) on the LP-relaxation solve.
• The LP and MILP share the same build_model() function; relax_binary=True turns y from Binary into [0,1] continuous so the relaxation's dual multipliers are meaningful.
• Sensitivity scan multiplies Fab-KR1's HBM3e supply by a sequence of multipliers and resolves the LP each time.

6. Citation / acknowledgement

This project was built for Prof. Ana Torres' 06-664 / 06-665 (Design and Optimization of Sustainable Processes / Process Systems Modeling) at Carnegie Mellon University. The base allocation formulation follows Ng, Sun & Fowler (EJOR 2010); the multi-period rolling-horizon spirit follows Herding & Mönch (CEJOR 2024); the sustainable / resilient extension is in the style of Tsao, Tesfaye-Balo & Lee (IJPE 2024).