Optimal Storage Capacity Allocation in Grain Merchandizing

Grain storage is an important problem for both farmers and grain merchants; however, it is especially central to the success of the grain merchandizing companies because the time, price, and quantity of both the commodity purchases as well as sales determine the company’s profitability over a specific time. Since commodity storage is a finite resource, merchandizers have to dynamically allocate its capacity among competing commodities in face of uncertainty, considering opportunity cost at all times. Important decision making steps can be described as follows: which grain, how much of it, and at what price one should buy in order to sell it profitably in the future while at the same time lining up the capacity for the next commodity’s quantity with a given price. Studies focus on on-site storage for farmers, and many research and extension programs investigate the optimal timing of sales (Musser, 1996; Lai et al., 2003; Kadjo, 2013). However, no studies analyze the storage allocation problem for a grain merchandizing line of business, with such attributes as handling more than one grain and operating under price volatility, various harvesting cycles, and a limited storage capacity. This study incorporates price distributions based on historical data to solve the optimal grain storage problem for a grain merchandizer. An optimal partial selling rule is derived in the model allowing optimal allocation to spread sales out over the storage period.