An Application of Equilibrium Size of Plant Analysis to Fluid Milk Processing and Distribution

Abstract

This article reports the results of an empirical study in which a model for equilibrium size of marketing firm in a spatial market is used. This model has received extensive treatment in this JOURNAL, particularly from a theoretical standpoint. The model is applied to the processing and distribution of packaged fluid milk. Solution of the model results in determination of size of plant associated with minimum average processing and distribution costs. Results of the study indicated that where packaged milk is distributed in semitrailers, in most situations increases in distribution cost as plant size is expanded do not offset decreases in processing cost up to the 134,000 quart per day plant. While total average cost declines within this range of plant sizes, most of the economies of size are realized by the 50,000 quart per day level.T HE PROBLEM of estimating the equilibrium size of plant in a spatial market has recently received extensive treatment in the JOURNAL.! Very simply, the solution consists of minimizing (combined) average processing and transportation costs. As larger processing units are put into operation to realize possible size economies, increasing average transportation costs of assembly and/or distribution will be associated with the increased processing plant volume where production or sales density is uniform. The question then becomes, at what point does the increase in transportation cost exceed the decrease in processing cost, in a planning sense? Though the theoretical considerations and empirical applications of this model have generally been confined to assembly, the model applies equally to distribution where the operating conditions do not severely violate necessary assumptions. This paper summarizes the results of a study to determine the equilibrium size of fluid milk plants considering both processing and distribution costs. This type of analysis seems particularly appropriate for the o Journal Paper No. 2154, Purdue Agricultural Experiment Station. The assistance of Joseph Havlicek and Charles Howe in development of the model is gratefully acknowledged.

Cost and Price Effects of Concentration Restrictions in the Plant Location Problem

“…The mathematical configuration of the problem for a single product is as follows: (1) subject to the constraints (2) (3) (4) (5) where S, is the output of raw product in producing area i, D k is the consumption of final product in consuming area k, Ci, and Cik are, respectively, the unit costs of assembly and processing of raw product from area i in plant f and distribution of final product to area k, and Xii and X i k are the quantities assembled, processed, and distributed from area i through plant i to area k.…”

“…Assembly and distribution cost functions were linear with respect to volume, but economies of scale were present in the processing cost function. The processing cost function used was similar to those used by Cobia and Babb [2]. Diary manufacturing was assumed to be supplementary to fluid utilization; all milk not assembled for fluid use was assumed to be available for manufacturing purposes.…”