Choosing Robust or Stochastic Optimization with Uncertain Prices

Summary

The document frames a product-selection problem over multiple weeks. Binary decision variables indicate which products are chosen, while the objective sums production quantities multiplied by prices across weeks. Future prices are unknown, and the question notes that historical data are limited. It asks whether robust optimization or stochastic optimization is better suited to maximizing future profit under these conditions.

No answer or implementation method is included, so the document does not establish a preferred approach, describe constraints in detail, or provide a price model, uncertainty set, scenarios, or performance evidence. It serves as a problem statement that highlights the central modeling choice: how to represent price uncertainty when selecting products. A practical solution would depend on information not supplied here, including the structure of the constraints, the plausible range or distribution of future prices, and the decision maker’s tolerance for downside risk.

Key ideas

• The decision is modeled with binary variables that indicate whether each product is selected.
• The objective aggregates production quantities and uncertain prices across weeks.
• Limited historical data and unknown future prices make the treatment of uncertainty central to the optimization.
• Robust and stochastic optimization are raised as alternatives, but the document does not compare or implement them.
• Choosing an approach would require additional detail about constraints, price uncertainty, and risk tolerance.

Tags

# Robust or Stochastic Optimization Approach for Maximizing Profit with Limited Price Information


# Robust or Stochastic Optimization Approach for Maximizing Profit with Limited Price Information












I am tackling a linear maximization problem where I need to select the optimal product among several options over a series of weeks, given certain constraints, in order to maximize future profit. The decision variables are binary, indicating whether or not a particular product is chosen.

The objective function is expressed as:

$$ \max_{j} \sum_{i} choice(j) \cdot c_{i,j}^T p_{i,j}$$

Where:

$c_{i,j}$ represents the production quantity of product $j$ in week $i$, $p_{i,j}$ represents the price of product $j$ in week $i$, $choice(j)$ is a binary variable indicating the selection of product $j$, and The summation is over all weeks $i$.

However, I encounter a challenge because $p_{i,j}$ is not fully known. It is a time series, and I lack future values as well as extensive historical data. To address this issue, I'm considering either Robust Optimization or Stochastic Optimization techniques. Which approach should I pursue, and how can I implement it effectively to maximize profit in this scenario?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.