14.7 Decision Rule
In decision theory, a decision rule is a formal function that maps observed data or conditions to a specific course of action. It plays a central role in fields such as statistics, economics, and game theory, where decisions must be made under uncertainty. A decision rule typically operates within the framework of a loss function, which quantifies the cost or penalty associated with each possible action under various states of nature. The goal is to select the action that minimizes expected loss.
Linear Decision Rule (LDR)
The Linear Decision Rule (LDR) is a mathematical approach to aggregate production planning developed by Holt, Modigliani, Muth, and Simon in the 1960s. It provides a systematic method for determining optimal monthly production levels, workforce size, and inventory levels, with the objective of minimizing total operational costs.
LDR is particularly useful in environments where demand fluctuates over time and where costs are associated with:
- Changing production rates (e.g., hiring, layoffs)
- Holding inventory
- Using overtime or idle capacity
The Linear Decision Rule uses a set of linear equations derived from cost functions and operational constraints. These equations relate:
- Forecasted demand
- Current inventory levels
- Workforce availability
- Production capacity
The model then computes the optimal values for decision variables (e.g., production quantity, workforce size) that minimize the total cost while satisfying demand and operational constraints. Key Features of LDR are;
- Cost Minimization: Balances trade-offs between inventory holding, labour adjustments, and production changes.
- Dynamic Planning: Adjusts decisions month-by-month based on updated forecasts and system states.
- Managerial Relevance: Offers a structured yet flexible tool for production managers to make informed decisions.
LDR is particularly effective in industries with:
- Seasonal or cyclical demand.
- High labour or inventory costs.
- Need for coordinated planning across multiple time periods.
It remains a foundational technique in operations research and is often integrated into more complex planning systems such as ERP and advanced planning and scheduling (APS) tools (Holt, 1955).
