A Lot Aggregation Optimization Model for Minimizing Food Traceability Effort
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This paper proposes a lot aggregation optimization model for minimizing the traceability effort at a grain elevator. The problem involves blending of bulk grain to meet customer specifications. A mathematical multi-objective mixed integer programming (MIP) model is proposed with two objective functions. The objective functions allow in calculating the minimum levels of lot aggregation and minimum discounts that need to be applied to a shipment when the customer contract specifications are not met. Constraints on the system include customer contract specifications, availability of grain at the elevator and the blending requirements. The solutions include the quantities of grain lots from different bins to be used for blending for a shipment while using the minimum number of storage bins and the total discounts to be applied. The numerical results are presented for two shipment scenarios to demonstrate the application of this model to bulk grain blending. The Pareto optimal solutions were calculated that represent the different optimal solutions for the blending problem. This provides the elevator management with a set of blending options. This model provides an effective method for minimizing the traceability effort by minimizing the food safety risk. Besides minimizing the lot aggregation, this model also allows in using the maximum volume of grain present in a given bin which leads to emptying of the storage bins and the extent of aggregation of old grain lots with the new incoming lots can decrease considerably. Use of fewer bins for blending shipments is also easier logistically and can lead to additional savings in terms of grain handling cost and time.