From my doctoral course
This note comes from the doctoral course “Supply Chain Network Design”. I rewrote the explanations in my own words and recomputed the numerical example. The course’s main sources include Watson et al. (2013), Chopra and Meindl, and Dekker et al. (2004).
From one objective to several
Network design usually starts with minimum cost. But the decision maker wants simultaneously:
- low cost,
- low response time (distance from the customer),
- high reliability (rate of meeting demand),
- low environmental impact (emissions, energy use),
- low disruption risk.
These conflict (more warehouses cut time and raise cost). Multi-objective models (MODM) make this explicit and give a set of efficient solutions (the Pareto front).
Common objective functions
- Cost: the sum of fixed, production, transport, inventory.
- Response time: the sum of (flow × delivery time), or the maximum time.
- Reliability: the rate of meeting demand (fill rate), or the probability of meeting demand.
- Environmental: carbon emissions of transport and production, waste.
Solution methods
- Weighted sum: (simple, but it misses solutions on non-convex parts of the front).
- ε-constraint: minimise one objective and control the rest with constraints ; the Pareto front is built by varying .
- Goal programming: set a goal for each objective and minimise the deviation.
- Metaheuristics such as NSGA-II for large problems.
- After reaching the Pareto front, for the final choice MADM methods (such as TOPSIS) are used; that is, MODM and MADM are complementary.
Sustainable supply chains
Today’s world thinks in terms of the “triple bottom line” (economic, social, environmental; Elkington, 1997). A sustainable supply chain measures, besides cost, environmental and social impact: reducing transport carbon, recyclable packaging, suppliers’ working conditions. Large retailers have announced such policies; assessing them precisely is hard, so models usually bring in quantitative indicators (carbon emissions, employment).
Resilient supply chains
Resilience is the ability to withstand and recover after a disruption. Sources of risk: supply (supplier bankruptcy), demand (volatility), operations (breakdown), and environment (sanctions, disasters). Strategies:
- Redundancy (a second supplier, safety stock), which costs money.
- Flexibility (a plant that makes several products).
- Agility (quick change).
- The balance between being lean (removing waste) and resilient: a lean chain is efficient but fragile; the middle way is to combine lean, agile and flexible at the same time.
To model it: stochastic programming (disruption scenarios with probabilities) or robust optimisation (the worst case within an uncertainty set).
My note
I think the conclusion of this part is simple: when the objective is only cost, the most optimal network is usually the most fragile. Resilience cannot be “added later”; it must be in the objective and constraints from the start, and its cost seen plainly.
Related: Introduction: what is multi-attribute decision making? and The multi-product, multi-period model.