A model for the evaluation of selected inventory policies for the feed blending problem

Abstract

The purpose of this research is to provide analytical methods for inventory control in the feed blending business. The application of simulation techniques is currently used by large feed mills to plan inventory control policies; however, the expense of these simulations in terms of computer time is often quite large. Also, these simulations rely chiefly on planning from period to period which may not yield the least costly inventory policies over the total planning horizon. This research first applies traditional continuous inventory models to the feed blending problem. Linear programming is used to determine the demands for each ingredient such that ingredient costs are minimum and specified nutritional demands are satisfied. The unconstrained simple lot size model is formulated to analyze inventory control decisions when each ingredient is stored in separate bins. For the case, where ingredients may share joint storage space, the constrained simple lot size model is used as an analytical decision tool. The solution of the constrained model is also discussed using both the Lagrange multiplier technique and dynamic programming. Examples of both the constrained and unconstrained models are presented. For the case where the planning horizon must be broken into planning periods, a discrete inventory model is presented. This model may be applied in cases where ration changes are frequently necessary. The model is presented as an inventory network and linear programming is used to determine the costs of the various paths of the network. Orthogonal contrasts are used to determine the combinations of ingredient inventory levels to begin and end each planning period. In order to reduce the number of possible inventory levels, each ingredient is considered to be at either a maximum or minimum amount in inventory. Both forward and backward recursion dynamic programming, are used to determine the minimum cost inventory policies for various beginning and ending inventory conditions. Examples of the model are also presented and discussed. ...