Optimal Sandbag Production for Flood Fighting with Forecast Updates

Some geographical areas in the US face flood fighting every spring due to the melting of surrounding rivers, and forecasts of the flood level evolve dynamically during this period. Thus, we consider the planning problem that determines the timing and amount of sandbag production for flood fighting efforts when more accurate forecasts become available as the time of the flood approaches. Sandbag production can occur only once in the planning horizon as volunteers are expected to answer only the first call for assistance in large numbers. We show that the optimal production quantity follows a newsvendor model. However, determining the timing of production requires balancing the benefits of delaying production to obtain a more accurate forecast of the crest level and the underage risk associated with a shorter production time frame. To achieve this balance, we use dynamic programming to obtain the optimal production policy (timing and quantity) in minimizing the total expected cost, which includes the fixed cost of production as well as overage and underage costs for sandbags. We report extensive numerical results. Particularly, we observe that increasing production capacity allows for delaying of the production so that the production quantity is based on a more accurate forecast and yields less waste.