How do duality and shadow prices in Linear Programming provide insights into resource allocation in Industrial Engineering?
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Duality and shadow prices in Linear Programming offer insights into resource allocation by revealing the impact of constraints on the objective function. Duality provides an alternative view that focuses on the value of resources, while shadow prices indicate how much the objective (e.g., profit or cost) would change with a one-unit increase in a resource. In industrial engineering, these concepts help identify which resources are scarce and where additional investment would improve efficiency or outcomes.
Duality and shadow prices in linear programming show how variations in resource availability impact the best possible solution, which offers important insights into resource allocation. The dualitynotion provides several viewpoints on resource utilization by illustrating the connection between the original problem and its dual. The value of extra resources is better understood by decision-makers when they use shadow prices, which show how the objective function changes for every unit increase in a resource. These insights help industrial engineers allocate resources more effectively by highlighting the most important restrictions and the areas where capacity or resource expenditures can have the biggest impact.