Multichoice Modeling: Exploring Decision Configuration Space under Uncertainty

Mariia Kozlova; Roman Stepanova; Alexander Walzer; Andrea Saltelli

cs.AIOct 22, 2026

Multichoice Modeling: Exploring Decision Configuration Space under Uncertainty

Authors: Mariia Kozlova, Roman Stepanova, Alexander Walzer, Andrea Saltelli

Organizations: LUT University, LUT Business School, Lappeenranta, Finland · University of Applied Sciences and Arts Northwestern Switzerland FHNW, Switzerland · UPF Barcelona School of Management, Barcelona, Spain

Abstract

Decision support has become sophisticated at exploring uncertainty, but much less so at representing the architecture of the decision itself. As a result, the decision space is often narrowed before uncertainty is analyzed, leaving interactions among choices and the effects of alternatives they imply largely invisible. This paper introduces multichoice modeling, a framework for making large decision configuration spaces explicit and computationally explorable under uncertainty. Drawing on the logic of rugged landscapes, we conceptualize such problems as contingent performance landscapes, where interdependent choices generate configuration-specific outcomes whose value changes across uncertain futures. The computational framework combines multidimensional decision and uncertainty spaces in a single simulation. Further, variance-based sensitivity analysis is used for identifying influential choices, and conditional distribution analysis for comparing configuration-specific performance profiles. We demonstrate the framework through three case studies: a manufacturing process upgrade, M&A strategy, and mortgage design. By contrasting conventional uncertainty-only analysis with multichoice modeling, the cases show how opening the decision configuration space can reveal unexpected complementarities, near-best configurations with different risk profiles, and strategies that were not apparent as alternatives at the outset.

Figures & tables

Figure 1: Implementation workflow for multichoice modeling.

Table 2

Figure 2: Ten simulated paths of interest rate evolution under the mean-reverting process (left) and the resulting distribution of cumulative interest-rate expenses (right).

Choice	Dependency	Effect in the model
Rate type	None	Fixed 4.1% / stochastic process
Interest rate cap	Variable rate only	5% cap at 0.05% premium / no cap
Payment scheme	Variable rate only	Fixed payment / fixed term
Reference rate	Variable rate only	3-month / 12-month Euribor

Table 3: Strategy table for mortgage choices

Table 5

Figure 3: Conditional distributions produced by the combination of the dominant uncertainty variable and two mortgage choices.

Table 7

Figure 4: One-at-a-time sensitivity analysis (left) and Monte Carlo simulation (right) results.

Area/upgrade	Cost, K€	Effect	Sensitivity index
Material			3%
Concrete 2	40	Price 301 €/ton; available with Mixer upgrade.
Concrete 3	40	Price 223 €/ton; available with Mixer and Pump upgrades.
Hardware
Mixer	90	Enables self-compacting concrete up to 300; enables Concrete 2.	20%
Printing head 1	50	Reduces labor by one worker.	0%

Table 8: Upgrade options, effects, and computed sensitivity indices

Figure 5: Conditional distributions of unit cost across configurations defined by the three most influential choices.

Figure 6: Conditional distributions for material choices within the subset of configurations with Pump and Mixer upgrades.

Table 12

Figure 7: Five sample realizations of the stochastic equipment and service market attractiveness processes (left) and distribution of simulated net present value (NPV) outcomes for the M&A case (right).

Choices	Dependencies	Effects	Numeric assumptions
Staged acquisition $\bullet$ No $\bullet$ Yes	None	Delays full commitment and enables learning about integration success before the remaining stake is acquired.	First-stage price is €35M. Learned integration success takes values low (40–60%), medium (60–80%), or high (80–100%).
Buying trigger $\bullet$ Low $\bullet$ Medium $\bullet$ High	Relevant only if staged acquisition = Yes	Determines the threshold of learned integration success required to proceed with full acquisition.	Directly tied to the levels of learned integration success. If learned integration success $\geq$ trigger, then buy the remaining stake and integrate fully. Second-stage price is €55M with a one-year delay.
Integration $\bullet$ Partial $\bullet$ Full	If buy remaining stake = Yes, only Full integration is possible	Full integration increases market synergy realization and enables operational flexibility, but incurs higher integration costs.	Full integration cost (M€): $5+30(1-\text{integration success})$ .
Operational flexibility $\bullet$ No $\bullet$ Yes	Available only if integration = Full	Allows capacity reallocation between equipment manufacturing and service activities in response to changing market conditions; incurs recurring flexibility costs dependent on integration success.	Investment cost is €10M. Recurring costs are $10(1-\text{integration success})$ M€/year.
Market development $\bullet$ Passive $\bullet$ Active	None	Determines the extent to which potential market synergies are pursued through cross-selling and market expansion; active development incurs additional costs.	Cost of active market development is €2M/year.

Table 11: Choice structure of the M&A case

Figure 8: Joint analysis of M&A profitability and operational flexibility value: simulated outcomes (left) and sensitivity indices (right).

Figure 9: Conditional distributions of acquisition NPV by integration and operational flexibility choices.

Figure 10: Conditional distributions of acquisition NPV by market type, acquisition staging, and buying trigger choices.

Figure 11: Conditional distributions of acquisition NPV by acquisition staging, integration, operational flexibility, and market development choices.

Case	Uncertainty-only analysis	Rugged landscape	Global sensitivity analysis	Optimization
Mortgage	Limits attention to the default decision configuration	Even independent choices can change their relative performance under uncertainty	A choice with a near-zero sensitivity index may still matter if uncertainty explains most variance	The best-performing configuration is not necessarily the most robust across uncertainty
Manufacturing upgrade	Cannot represent the decision space, as each uncertain model input is influenced by multiple alternative actions.	Focus on partial configurations prioritizes the most critical choices first	A choice with high sensitivity is not necessarily advisable if it has a negative effect or its positive effect overlaps with another influential choice; a low-sensitivity choice can still be critical locally (within an appealing partial configuration)	The best-performing configuration is implementing all upgrades, while the practical decision problem is prioritizing a smaller subset that creates most of the improvement
M&A	Limits attention to a single strategy	Same choice configurations can perform differently in different regions of uncertainty	Choices may earn low sensitivity indices if they only make a difference in a certain configuration of other choices	Optimality of a learning threshold may depend on uncertainty and choice configuration

Table 12: How the cases extend established decision-support perspectives

Decision-Making under Uncertainty

Decision-making under uncertainty studies how to choose actions when outcomes, states, or models are imperfectly known.

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Abstract

Decision-Making under Uncertainty

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