Optimizing Efficiency-Robustness Trade-Offs in SC-Design

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Efficiency is about trade-offs. Effectiveness is about achieving a goal, making it happen no matter what.
But in reality resources are scarce and efficiently reaching a goal is nearly as important as reaching it at all.

Low-risk supply chains often contradict the efficiency demands of the company’s stakeholders.
Robust strategies, which reduce risks while keeping performance up, are still the holy-grail of supply chain risk management.
Simple strategies are not able to accomplish this goal, only a extensive redesign of the supply chain (as for example using the postponement strategies) may indeed be able to reduce risks while keeping performance up.

How these trade-offs can be optimized according to the goals of the company is the topic of the 2011 paper: “Optimizing efficiency-robustness trade-offs in supply chain design under uncertainty due to disruptions” by Shukla, Lalit and Venkatasubramanian.

Model and robustness metric

The authors use a mathematical model to implement their robustness metric, which “is based on expected losses incurred due to network failures. It defines efficiency and robustness in terms of operational cost and expected disruption cost (EDC), respectively. The EDC is defined in terms of loss of opportunity cost incurred due to not meeting demand on time after a disruption has occurred.”

Decision variables of the mixed-integer linear model are:

  • the assignment of the warehouse to the manufacturing center and
  • the assignment of the warehouse to the customer.

The objective function is defined as the weighted sum of efficiency and robustness. Efficiency is defined in terms of OC of the supply chain and robustness is defined in terms of the EDC [figure 1]:

Objective Function
Figure 1: Objective Function (Shukla et al., 2011)

The authors use secondary data to build a case study with scenarios from the current US.
Figure 2 shows an extract of the demand numbers used.

Demand by state for functional and innovative product
Figure 2: Aggregated Demand as Input for the Model (Shukla et al., 2011)

Figure 3 contains details of the risks experienced by the respective warehouse locations.
Warehouse distances and historical data from FEMA on presidential disasters reported from December 24, 1964 to March 3, 2007
Figure 3: Warehouse Distances and Risk Data (Shukla et al., 2011)

Four case studies are conducted, I picked number one as an example and refer you to the paper for further details.

Case study 1 deals with node failure or failure of warehouses for functional products. Since most of the warehouse locations are far apart we assume that failures are independent of each other and multiple failures can occur simultaneously. The probability of failure of a warehouse depends on the region in which the warehouse is located.


Figure 4 shows the efficient supply chain design for the first case study and figure 5 the corresponding results for more robust results.

Case study 1: most efficient supply chain
Figure 4: Case Study: Efficient Supply Chain Design (Shukla et al., 2011)

Case study 1: most robust supply chain network
Figure 5: Case Study: Robust Supply Chain Design (Shukla et al., 2011)

The authors state that:

The resulting supply chain is much more reliable in the long term since we have shown that a significant amount of robustness can be built into the system without compromising a lot on efficiency.


So there is no free lunch and it seems inevitable to sacrifice some of the efficiency to gain robustness, but this paper shows that in the case studies with only small cost increases risks can effectively be reduced based on supply chain design changes.
So if your customers value reliability this might be the right approach for your chain.


Shukla, A., Lalit, V., & Venkatasubramanian, V. (2011). Optimizing efficiency-robustness trade-offs in supply chain design under uncertainty due to disruptions International Journal of Physical Distribution & Logistics Management, 41 (6), 623-647 DOI: 10.1108/09600031111147844



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