Robust beats optimal: deciding when the future is uncertain

Why does the optimal plan so often fail?

The optimal plan is optimal only for the assumptions it was built on; when the future is uncertain, the better choice is a robust plan that performs acceptably across many possible futures. Most supply chain plans are tuned to a single forecast of demand, lead times and prices. When reality differs, and it always does, the tuned plan can be the one that breaks first.

Sam Savage calls this the "flaw of averages": plans built on average assumptions are, as he puts it, "wrong on average" [1]. A plan that sets stock to average demand, books capacity for the average lead time and buys at the average price can look efficient on paper and still run short, late and over budget when demand, lead times or prices land above their averages.

Operations research has long offered alternatives. Stochastic programming builds the uncertainty into the model as scenarios with probabilities, so the plan is chosen for its performance across them rather than for one forecast [2]. Supply chain disruptions in particular have been studied in depth: one review of the operations research literature covers nearly 150 works, from sourcing and inventory decisions to facility location [3].

What is the difference between an optimal and a robust decision?

A robust decision is not a cautious guess. It is a deliberate trade: accept a little less in the expected case in exchange for much less exposure to the bad cases.

What does robustness cost?

Robust optimization goes back to Soyster's work in 1973, which found solutions that stay feasible for every value of the data within a set [4]. That protection was very conservative. Later work, summarized by Ben-Tal, El Ghaoui and Nemirovski, made robust optimization practical for large problems [5]. Bertsimas and Sim gave the trade a name: "the price of robustness" [6]. Their approach is "willing to accept a suboptimal solution for the nominal values of the data in order to ensure that the solution remains feasible and near optimal when the data changes," and it lets the decision-maker "flexibly adjust the level of conservatism." The point for managers is that robustness is not all or nothing. You choose how much protection to buy, and you can see what it costs.

Supply chain research shows the same trade in sourcing. Tomlin studied a firm that can buy from an unreliable supplier or a reliable but more expensive one [7]. The best strategy, whether carrying extra inventory, sourcing from the reliable supplier, or simply accepting the risk, depended on the supplier's uptime and on the nature of disruptions: for the same uptime, sourcing mitigation was "increasingly favored over inventory mitigation as disruptions become less frequent but longer." There is no single right answer; there is an answer that fits the risks you face.

How does robust decision making work?

Robust decision making (RDM) was developed at RAND for long-term policy problems where the future cannot be predicted with confidence [8]. It is one of several methods for "deep uncertainty", where experts cannot agree on the probabilities of key outcomes; an open-access book edited by Marchau, Walker, Bloemen and Popper sets them out with real-world applications [9]. Lempert and colleagues describe it as an iterative process that "first suggests candidate robust strategies, identifies clusters of future states of the world to which they are vulnerable, and then evaluates the trade-offs in hedging against these vulnerabilities" [10]. In supply chain terms:

1. 01

   List the options

   Single or dual sourcing, more or less stock, near-shore or offshore, one site or two.

2. 02

   Describe the uncertainty as ranges

   Demand, lead times, prices, exchange rates and supplier reliability, from history and expert judgement.

3. 03

   Run every option across many futures

   A model or digital twin tests each option against thousands of combinations.

4. 04

   Find where each option fails

   The useful output is not one number but the conditions that break each plan.

5. 05

   Choose, hedge or adapt

   Pick the option that holds up, strengthen it where it is weak, or set the signals that tell you when to switch.

The last step matters. Robust plans are often adaptive: they say what to do now and what to watch for, so the plan changes before the problem arrives.

What does a robust answer look like in practice?

Our own work offers an example. Building Resilience developed a stochastic optimization approach, enhanced by genetic algorithms, for multi-step supply chains spanning several countries, currencies and risk factors. Instead of stopping at the first good answer, it explores alternative assumptions so the solutions it returns are robust rather than locally optimal. A finding from that work was that for some businesses, concentrating on domestic markets can reduce risk and give better long-term outcomes than pursuing volatile international opportunities. Read the case.

On a single forecast, the international option may look better. Across many futures, with currency swings, longer lead times and more ways to be disrupted, the domestic option can hold up better. That is the difference between optimal and robust.

Early warning works with robustness. An early warning algorithm that spots sudden departures from normal patterns, such as ours, which identified a significant spike in deaths in early January 2020, weeks before the first official COVID-19 case was reported in the UK, tells you when the world is moving toward the futures where your plan is weak.

When should you use robust decision making?

Use it when the decision is hard to reverse, the stakes are high and the key inputs cannot be forecast with confidence: network design, sourcing strategy, long-term contracts, capacity and infrastructure investments. For routine, easily reversed choices with stable inputs, a standard optimization is usually enough.

What to do next

Take one plan you rely on and ask: which assumption, if wrong, would hurt most? Then test the plan with that assumption 20% higher and 20% lower. If the answer changes sharply, the plan is optimal but not robust. Our decision support work does this systematically across many futures, with the assumptions visible so the people accountable for the decision can challenge them. Talk to us.

References

1. Savage, S. L. (2009). The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty. Hoboken, NJ: Wiley.
2. Birge, J. R., & Louveaux, F. (2011). Introduction to Stochastic Programming (2nd ed.). New York: Springer. doi:10.1007/978-1-4614-0237-4
3. Snyder, L. V., Atan, Z., Peng, P., Rong, Y., Schmitt, A. J., & Sinsoysal, B. (2016). OR/MS models for supply chain disruptions: A review. IIE Transactions, 48(2), 89–109. doi:10.1080/0740817X.2015.1067735
4. Soyster, A. L. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research, 21(5), 1154–1157. doi:10.1287/opre.21.5.1154
5. Ben-Tal, A., El Ghaoui, L., & Nemirovski, A. (2009). Robust Optimization. Princeton, NJ: Princeton University Press. doi:10.1515/9781400831050
6. Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations Research, 52(1), 35–53. doi:10.1287/opre.1030.0065
7. Tomlin, B. (2006). On the value of mitigation and contingency strategies for managing supply chain disruption risks. Management Science, 52(5), 639–657. doi:10.1287/mnsc.1060.0515
8. Lempert, R. J., Popper, S. W., & Bankes, S. C. (2003). Shaping the Next One Hundred Years: New Methods for Quantitative, Long-Term Policy Analysis (MR-1626). Santa Monica, CA: RAND Corporation. rand.org: MR-1626
9. Marchau, V. A. W. J., Walker, W. E., Bloemen, P. J. T. M., & Popper, S. W. (Eds.) (2019). Decision Making under Deep Uncertainty: From Theory to Practice. Cham: Springer (open access). doi:10.1007/978-3-030-05252-2
10. Lempert, R. J., Groves, D. G., Popper, S. W., & Bankes, S. C. (2006). A general, analytic method for generating robust strategies and narrative scenarios. Management Science, 52(4), 514–528. doi:10.1287/mnsc.1050.0472