Week 8 | Session 3: Demand Allocation Model & Capacitated Plant Location Problem
Course: Supply Chain Digitization — Module 3: Analytics in SCM
Session Agenda
Section titled “Session Agenda”1. Recap — Week 8 So Far
Section titled “1. Recap — Week 8 So Far”
| Session | Topic | Method / Tool |
|---|---|---|
| W8 S1 | Facility Selection | Break-Even Analysis |
| W8 S2 | Facility Location | Centre of Gravity + Excel Solver (GRG Nonlinear) |
| W8 S3 | Demand Allocation + CPLP | LP formulation + Excel Solver (Simplex LP / Binary) |
2. Case Study — Two Telecom Equipment Manufacturers
Section titled “2. Case Study — Two Telecom Equipment Manufacturers”The Companies: Maxxio (North+East India) and Wavie Communications (South+West India). Both companies have enough capacity to fulfill all market demand. The decision is HOW to allocate, not whether.
3. Demand Allocation Model
Section titled “3. Demand Allocation Model”Question: How much quantity should be shipped from which plant to which market to minimize total cost?
Notation
Section titled “Notation”Cij= unit cost of production + transportation from plant i to market jXij= quantity to be shipped from plant i to market j (decision variable)Si= supply capacity of plant iDj= demand at market j
LP Formulation — Demand Allocation
Section titled “LP Formulation — Demand Allocation”- Minimize Z:
Σi Σj (Cij × Xij)(total production + transportation cost) - Supply constraint:
Σj Xij ≤ Sifor all i (supply ≤ capacity) - Demand constraint:
Σi Xij = Djfor all j (demand fully met) - Non-negativity:
Xij ≥ 0for all i, j
Key Insight from Solution (Maxxio)
Section titled “Key Insight from Solution (Maxxio)”The Kolkata facility is barely utilized despite fixed cost being incurred because of high production + shipping costs. But the fixed cost is still paid → inefficiency. This signals a need for a smarter model that also decides which plants to open.
4. Merger Scenario — Maxvie (Maxxio + Wavie)
Section titled “4. Merger Scenario — Maxvie (Maxxio + Wavie)”Management merges the companies into a new company: Maxvie.
- Now has 5 plants and needs to serve 6 markets.
- New question: Which plants to keep open? Can any be shut to reduce cost?
This is a Capacitated Plant Location Problem (CPLP).
5. Capacitated Plant Location Problem (CPLP)
Section titled “5. Capacitated Plant Location Problem (CPLP)”What Changes from Demand Allocation?
Section titled “What Changes from Demand Allocation?”- Add a binary decision variable
yifor each plant i:yi = 1→ plant i is openyi = 0→ plant i is closed
- Add fixed cost
fifor each plant to the objective function.
LP Formulation — CPLP
Section titled “LP Formulation — CPLP”- Minimize Z:
Σi Σj (Cij × Xij) + Σi (fi × yi)(variable cost + fixed cost of open plants) - Supply constraint:
Σj Xij ≤ Si × yifor all i (plant can only supply if open) - Demand constraint:
Σi Xij = Djfor all j - Binary variable:
yi ∈ {0, 1}for all i
Solving in Excel — Solver Settings
Section titled “Solving in Excel — Solver Settings”- Solving Method: Simplex LP (model is linear — yi is handled via integer constraint).
6. Results & Cost Comparison
Section titled “6. Results & Cost Comparison”CPLP Solution (Maxvie — Merged):
- Optimal plants to keep open: Chennai, Gurugram, Kolkata (only 3 out of 5).
- Plants closed: Delhi and Mumbai (saving their fixed costs).
| Cost Component | Maxxio | Wavie | Combined (Pre-merger) | Maxvie Merged (CPLP) |
|---|---|---|---|---|
| Total Monthly Cost | 3.20 Cr | 2.53 Cr | ~5.73 Cr | 5.22 Cr |
Monthly saving from merger + network redesign: approximately ₹50 lakhs / month.
Session Summary
Section titled “Session Summary”- Demand Allocation Model: Decides
Xijto minimize variable cost — plants are fixed. (Simplex LP) - CPLP: Decides BOTH
Xij(flow) ANDyi(open/close plant) — minimizes variable + fixed cost. (Simplex LP with binary constraint) - Merger result: MaxV operates 3 plants instead of 5 → ~₹50L/month saving.