Date of Award
Doctor of Philosophy
Joe A. Martin
T.J. Whatley, Charles Sappington, Joe A. Martin, Hans E. Jensen, Allen H. Keally
This study was designed to achieve the following objectives: (1) to determine the optimum number, sizes and locations of major corn handling facilities in the Southeast under 1964 and projected 1975 conditions, (2) to impute costs of employing sub-optimum routes in each case, and (3) to estimate the stability of each of the solutions obtained above relative to decreases in transportation costs. A secondary objective was to determine the validity of a reactive programming plant location model when applied to a wide-area problem.
The Continental United States was divided into 36 domestic and four export markets. Surpluses or deficits of corn were determined in every market for 1964 and 1975. The trading system for 1964 consisted of 12 surplus markets and 24 deficit markets. Projections for 1975 indicated 13 surplus markets and 23 deficit markets. For both years the number of potential sites for corn handling capacity remained constant at 23.
Data collection and processing were carried out under the auspices of the Southern Regional Grain Marketing Committee Project SM-29 entitled "Optimal Adjustments of Marketing Facilities to Present and Future Conditions." Results of this study are expected to contribute to the Committee's regional objectives.
Data required for 1964 and 1975 included assembly and distribution costs from each origin through every plant site and to all markets. For 1964 the following modes of transport were considered: Least-cost mode, barge least-cost rail, barge weighted-average rail, barge-truck, least-cost rail, weighted-average rail, truck and highest-cost mode. Transportation modes for 1975 remained the same except for least-cost rail which was dropped in favor of Gainesville rail rates and Rent-ATrain rates. The new rates resulted in decreased rail shipping costs and were expected to be available in major southern markets by 1975, There were a total of eight modes considered for 1964 and nine for 1975,
Plant costs were obtained through the Southern Regional Grain Marketing Committee for 2,500, 5,000 and 10,000 bushels per hour corn handling facilities. These costs were used as relevant plant costs throughout the study, A 300-day operating season was assumed in all cases,
Three separate computer programs were employed in the analysis. The first program utilized assembly and distribution costs for each mode to compute the minimum-cost route from each origin through a plant and to each market. Output from this program was fed into a conventional transportation model to obtain optimum flows of corn under each set of transfer cost and market demand assumptions. Equilibrium price differentials and imputed costs of utilizing suboptimum routes were calculated from these transportation model solutions ,
The transport modes were then re-examined, and four were selected as being indicative of changes occurring in transfer costs for corn. These modes were least-cost mode 1964, least-cost mode 1975, Rent-A Train rate 1975 and Gainesville rail rate 1975. The effects of these modes on the optimum number, sizes and locations of corn handling capacity was then investigated by means of a plant location model.
This plant location model employed corn supply estimates, market demand functions, plant costs and transfer costs to determine the optimum number, sizes and locations of corn handling facilities from the set of pre-selected potential plant sites.
An absence of demand functions for corn at all markets required the creation of pseudo demand curves from actual corn requirements and equilibrium market price differentials. These pseudo demand curves were required to allocate the proper amount of corn to the several markets and maintain the price differentials between them. These curves were not assumed to possess any additional economic significance, however.
Together the 1964 and 1975 plant location solutions included four transportation modes and two sets of corn surplus-deficit assumptions. The quantity of corn in the system also nearly doubled due to increased production in the Midwest. Two market points shifted from deficit to surplus, and one market point changed from surplus to deficit .
With the least-cost mode of transportation 1964,the model indicated that corn should be handled at 13 of the 23 potential sites. The 1975 plant location solution which utilized the Gainesville rail rate indicated that 16 of the 23 locations would be active. In the 1975 Rent-A-Train rate solution corn handling capacity was distributed among 12 of the 23 locations. According to the plant location solutions which utilized the least-cost mode 1975, corn should be handled at 15 of the 23 possible locations.
Only six of the 23 possible Southeastern corn handling locations were active In every case. Three locations remained Inactive under all conditions considered. Three other locations were utilized with only one mode of transportation. Four sites appeared twice In the optimum solutions, and seven sites appeared three times. The 13 sites which were active In three or more solutions were concluded to possess the highest potential from the viewpoint of transportation.
To estimate the sensitivity of computed corn flows to general changes In the freight rate structure, optimum flows of corn with the least-cost mode and the highest cost mode were obtained from transportation models and compared for 1964 and 1975.
It was concluded that a high degree of stability existed within plant location solutions for 1964 and 1975. This stability declined rather sharply, however, as the location determinants were allowed to vary over time.
Average cost of utilizing sub-optimum routes with each type of transportation was between five and six cents per bushel of corn. Since the maximum operating margin assumed for corn handling facilities In this study was eight cents per bushel. It was concluded that considerable pressure existed for firms to employ minimum-cost routes to move their corn.
Empirical application of a reactive programming plant location model to a problem of practical size was a secondary objective of this study.
The theoretical basis of the reactive programming plant location model appeared sound. Plant number and size determinations depended on supply estimates, market demand functions, plant costs and transfer costs. The solution was obtained from a set of preselected potential plant sites on the basis of a spatial equilibrium criterion.
Shortcomings of the computer formulation of the model concerned its treatment of fixed plant costs, however. Only one plant cost could be considered in a given computer run. This resulted in considering only one size of plant at all potential locations. Interarea differences in plant costs were also neglected. Closely allied with these problems was the requirement of only one plant per location. This would preclude determination of optimum plant number when requirements at any site exceed the capacity of one plant.
This model, however, is an advantage over current formulation of the Stollsteimer Plant Location Model in economizing computer time. The Stollsteimer model computes all possible combinations of assembly and distribution costs for origins, plants and markets. These computations can become very substantial with large problems.
Strawn, Harry B., "The effects of alternative modes of transportation on the optimum number, sizes and locations of major corn handling facilities in the southeast. " PhD diss., University of Tennessee, 1969.