BULLETIN 603 October 1977 OPTIMUM NUMBER, SIZE, AND LOCATION OF FLUID MILK PROCESSING PLANTS IN SOUTH CAROLINA

Transcription

1 BULLETIN 603 October 1977 OPTIMUM NUMBER, SIZE, AND LOCATION OF FLUID MILK PROCESSING PLANTS IN SOUTH CAROLINA

2 ABSTRACT This study was concerned with determining the optimum number, size, and location of milk processing plants to assemble, process, and distribute Class I milk in South Carolina. Earlierstudies have indicated that increased efficiency can be realized by movement toward fewer, but larger, processing plants in a market. This study investigated the validity of this hypothesis for South Carolina conditions. Transshipment linear programming models using the MPSX algorithm were applied to determine the plant system that would simultaneously minimize assembly, processing, and distribution costs for specific sets of conditions. Two cost functions were used in the transshipment models. One was an updated version of a function developed by Earl Alexander Stennis to describe the costs of processing milk in the Southeast. The second was a processing cost function developed by the Case and Company consulting firm, based on a study of the South Carolina dairy industry. Basically, two least-cost transportation models were formulated. Model I, a transshipment model with processing costs based on the average-size South Carolina plant, estimated processing costs of 1.78 and cents per pound with the Stennis and Case formulas, respectively. The least-cost plant organizations were identical for the two cost functions. The results included processing plants with capacities ranging from an upper limit of 191,350 pounds to a low of 34,239 pounds per day. The expected pattern of market-oriented processing plants did not materialize. Introduction of processing cost functions permitting size economies in Model II prod uced a major shift to larger processi ng plants. The Case function which at first allowed size economies, but resulted in diseconomies at larger outputs, reduced the number of plants in an optimum organization of the industry from 14 to nine. The Stennis function did not show any diseconomies of size throughout the range required and produced an optimum solution with plants at Columbia and Spartanburg. Even though two cost functions used in the study resulted in different optimum organizations, the study showed that the economies of size in milk processing were sufficient to offset increased transportation costs. The dairy industry of South Carolina was not operating at a least-cost position, and a general move toward fewer, but larger, processing plants was one way to decrease total cost, or to increase the well-being of the citizens of South Carolina.

3 TABLE OF CONTENTS ABSTRACT INTRODUCTION Objectives Procedure Data Sources and Characteristics South Carolina Milk Production and Milk Production Areas Assembly and Raw Milk Transfer Costs Processing Locations and Costs Distribution Costs Fluid Milk Consumption and Consumption Areas ANALYSIS of EMPIRICAL DATA Model I Model IA Model IB Model II Model IIA Sensitivity of Optimum Organization to Processing Cost Changes Model lib Pricing Efficiency LITERATURE CITED APPENDIX

4 OPTIMUM NUMBER, SIZE, AND LOCATION OF FLUID MILK PROCESSING PLANTS IN SOUTH CAROLINA William A. Thomas and R. Kenneth DeHaven * INTRODUCTION The dairy industry of South Carolina is important to the economy of the state. During the past several years, cash receipts from the sale of milk have ranked among the top six sources of farm receipts in South Carolina, amounting to over $55 million in In addition, dairy farms are the underlying foundation to the revenues produced directly by a broader-based industry consisting of individuals, cooperatives, and corporations involved in assembling, processing, and distribution of dairy products important to the health and well-being of the people of South Carolina. This important agriculturally based industry contributes more than $100 million to the economy of the state. Historically, South Carolina has been deficient in milk production. That is, the consumption of dairy products exceeds production within the state. As a result, a high percentage of South Carolina-produced milk is allocated to Class I uses. During 1975 over 88 percent of the milk marketed by South Carolina producers was consumed as whole milk, buttermilk, flavored milk drinks, or other Class I items. The remaining milk was Class II, or manufacturing milk, which is valued well below the Class I price. In 1975 the Class II price for milk with 3.5 percent butteriat averaged $8.60 per hundredweight, compared to a Class I price of \ $11.25 (;t8). q For most states, the price received by producers would have been below the $10.14 per hundredweight received by South Carolina producers during This price was dueto a combination of high Class I and II prices and a high percentage of Class I utilization. These favorable price relationships have convinced many people in the dairy industry that there is both an opportunity and a need for expansion of milk production in South Carolina. Such expansion must evolve in response to a consideration of both present and expected future price and cost factors. These include obtaining maximum operational efficiency within all sectors of the industry - production, processing, and distribution - in order to minimize costs, and to maintain or enhance pricing efficiency within the sectors. This study was primarily concerned with optimizing the operational efficiency of the industry by improving the assembling, processing, and distribution system within the state. ' Extension Marketing Economist, University of Georgia and Asssociate Professor, Department of Agriculture Economics and Rural Sociology, South Carolina Experiment Station, Clemson University, Clemson, South Carolina. 3

5 In recent years the South Carolina dairy industry has switched from a nonregulated pricing system to a system of administered prices. The South Carolina Dairy Commission was created in 1953 and assigned the job of policing the importation of milk into the state. By1959, its role had been expanded to include setting minimum prices at producer, distributor, and retailer levels. Although the future role of the Dairy Commission in pricing is unclear at this time, price-setting power, coupled with controls over most forms of non price competition, has cast the industry into a competitive structure different from that which prevailed earlier. It has been charged that an administered price fixed above minimum ATC for efficient firms acts as a floor price and allows inefficient firms to remain in the industry* This can result in misallocation of resources, both within the dairy industry and in relation to alternative industries. The physical organization of the processing sector greatly influences potential supplies. The current regulatory system has, without question, brought about an orderly adjustment from conditions existing at the inception of the Dairy Commission. However, a great deal of emphasis has been placed on maintaining the status quo. In the interest of objectivity, it should be pointed out that the Commissiv:l has been provided with very little hard research information to aid its decision-making. This problem is brought into focus by the results of this study, which indicates the direction that economic forces are leading certain segments of the industry. As such: the research provides objective data that could aid in decision-making by firms and regulatory bodies. Objectives The general objective of this study was to evaluate alternative patterns of assembling, processing, and distributing fluid milk in South Carolina. It involved determination of the optimum number, size, and location of plants needed to handle the quantity of milk demanded in the state at minimum total cost. The study was concerned with efficient assembly, processing, and distribution of existing supplies at current cost relationships. Specifically, the study attempted to determine: (1) the volume and location of Grade A milk produced in South Carolina, (2) the cost of transporting milk from production points to existing and potential processing plants, and from there to distribution points throughout the state, (3) the number, size, and location of fluid milk processing plants that would minimize the total costs of assembling, processing, and distributing 1971 supplies of Grade A milk, and (4) the effects of an optimal processing industry structure on the pricing system in the state. 'ATe includes a normal profit. A normal profit is a return to the factors of production sufficient to keep them in their current use. 4

6 Procedure The dairy industry of South Carolina may be conceptualized as a set of raw product or supply locations, a set of various size processing plants at different locations, and a set of distribution points. The problem considered here was to ascertain the most efficient number, size, and location of processing plants for the state, rather than to maximize the profit of individual processors. That is, the minimum point on the long-run industry cost curve for assembling, processing, and distribution was sought. Such a point can be approximated through the use of linear programming techniques. Linear programming allows a product to be shipped from a number of origins or assembly points, through a number of intermediate processing stops, to a number of consumption centers in such a way as to minimize total cost. The model formulated for use in this study consisted of the following: 46 assembly points, 14 possible processing sites, and 66 consumption centers. For the year studied, 1971, each assembly and consumption point had a fixed availability or requirement based on actual conditions for that year. Restrictions were also placed on the pricequantity relationships for each of the processing plants. The objective was to minimize total cost subject to the given constraints. Linear programming, with the Mathematical Programming System-Extended (MPSX) algorithm, was used to obtain optimum solutions incorporating both linear and separable objective functions. Several approaches or models were used, but the overall objective was to find an optimum organization for the South Carolina dairy industry in terms of the number, size, and location of processing plants needed to minimize total cost of assembling, processing, and distributing. Data Sources and Characteristics Data obtained for this study were divided into five major categories : (1) milk production for South Carolina base holders and production areas, (2) bulk milk transportation cost, (3) processing costs, (4) packaged milk distribution cost, and (5) fluid milk consumption in South Carolina. South Carolina Milk Production and Production Areas For 1971, there were 566 South Carolina base holding producers.' There were 499 producers in 39 South Carolina counties (Figure 1). In addition, 67 North Carolina and Georgia producers held South Carolina bases. Estimates of supply totals for 1971 were taken from data collected by the South Carolina Dairy Commission. Estimates 'Any person approved by the South Carolina Dairy Commission who produces Grade A raw milk for pasteurization and who owns a base established in accordance with the rules and regulations of the Commission. 5

7 were based on Grade A production by South Carolina base holders. Producers who ceased production during the year were not included, while the production estimates for producers who started in mid-year were projected for the full year. The production figures represent the total Grade A production of South Carolina base holding dairymen. Although Class I utilization had averaged about 88 percent of milk production, this was believed to be a consequence of the use of the individual handler base plan. South Carolina base holders do not produce sufficient milk to supply the fluid milk demands of the state. Therefore, it seemed reasonable to assume that virtually all Grade A milk could be sold as Class I, if it could be correctly allocated to markets within the state. For this reason, it was assumed in this study that all Grade A milk was sold as Class I. Another source of milk that had to be considered was the milk produced by Dairymen Incorporated, a regional producer cooperative operating in South Carolina. These producers do not have South Carolina production bases; therefore, the Dairy Commission does not maintain production records on them. It was assumed that the cooperative would furnish sufficient milk to meet demands in excess of the production of South Carolina base holders. Assembly and Raw Milk Transfer Costs Milk from the 566 producers was collected at the closest of 46 production centers, Figure 1. These centers served no function other than as points from which milk could be transported to various processing plants. Distances from the producers to the production centers, or assembly points, and from there to various processing sites, were calculated by the same method. First, air distance were determined from maps, and then converted to road miles by a formula developed by McAlhany for use in South Carolina (8) p. 111). The model used was: Y = X where Y = distance in road miles, and X = distance in air miles. The method used for computing bulk milk transportation cost is shown in Table 1h The functions were based on those derived in 1966 by ERS, USDA &tf1:lnd were updated using the transportation services series of the Consumer Price Index. The ERS study included an allowance for the cost of reloading milk from small to large trucks. This 5.7 cents per hundredweight reloading cost was deducted, since the size of South Carolina dairy herds made it possible for most milk to be loaded on large over-the-road tankers. 6

8 , -...J.,~ ~. --- If/' 'l'ft '1'/ Figure 1. Milk Producing Counties, South Carolina Key: = number of producers = average annual production (1.000Ibs,) production centers

9 Table 1. Bulk milk transportation cost functions, 1973 One-way mileage a Estimating Equations and over b TC = TC = TC = I TC = a. where: TC total cost in cents per cwl, and o = one-way mileage in road miles. b. Two drivers were required for distances of 200 miles or more. Source: (7, p. 10). Processing Locations and Costs The initial selection of processing plant sites was based on the actual location of plants in South Carolina. Twelve locations chosen on this basis are listed in Tab Ie 2. Analysis of 1975 plant locations, with the knowledge that transporting costs are slightly higher for packaged than for bulk milk. led to the hypothesis that processing sites generally would be limited to population centers. Additional processing sites were designated at Newberry and Rock Hill. the largest towns without processing sites. Two different processing cost functions were used. The first was based on actual South Carolina processing costs; the second was based on the cost functions developed for other studies. Table 2. Selected fluid milk processing sites in South Carolina Plant site Anderson Charleston Columbia Florence Gaffney Greenville Lake City Plant site Newberry North Augusta Orangeburg Rock Hill Seneca Spartanburg Sumter In Case and Company. Incorporated. cooperating with Clemson University. completed a report forthe Dairy Study Committee of the South Carolina Legislature on the dairy industry of South Carolina. Producing. processing. distributing. and retailing sectors of the industrywere covered (3). To obtain processing costs for this study. six plants were sampled statistically to obtain an equal representation of plants in respect to location, ownership. and size. The survey was intended to determine costs from the time the milk was received at the processing plant until it was available to the consumer. 8

10 Data from the sample plants were combined, and average costs were presented for each product and package size. Plant expenses were classified into the following functional groups: (1) general and administration, (2) selling, (3) processing, (4) raw product costs, and (5) containers and ingredients. In the form in which they were presented, the costs could not be used in the analysis of economies of size. First, the costs did not include any allowance for profit or return on investment and, therefore, did not measure the full economic cost of processing (3, pp. 1-2). Measurement of costs may be done in several ways. Typically, businesses are interested mainly in their outlay or explicit costs. These are the objective and tangible expenses listed in company records. A more basic concept used by economists measures not only explicit costs, but also implicit costs such as return to owned resources. The resulting economic cost is more than a measure of outlay; it includes a measure of the opportunity cost of the firm. A second problem was that, although the cost figures reflected costs incurred during 1973, there was no effort to determine the level of plant utilization and efficiency, nor any change in the rate of expenditures that might raise or lower per-unit cost. This type of data does not provide adequate basis for comparison of the costs of different plants. Differences in age, rate and method of depreciation, product mix, level of plant utilization, and organizational structure are other aspects that must be considered in using this type of survey data. When none of these factors are specified, the reliability of any comparative analysis is open to questions. A third critical problem was that the data were aggregated to such an extent that processing costs were not differentiated by size of plant. Although the Clemson University Departments of Agricultural Economics and Rural Sociology and Dairy Science participated in the collection of data for the study, all processing cost data were collected by Case and Company and remained under their exclusive control. One of the main determinants of the method in which the data were presented was the effort by Case to prevent disclosures of the costs of anyone firm. Therefore, the costs obtained from the six participating firms were weighted and averaged and only this averaged cost was revealed. To obtain costs in a form suitable for this study, Case requested that the participating firms allow their data to be used. Five firms responded positively to the req uest with the stipu lation that ind ivid ual-fi rm costs not be divulged; therefore, Case would only consent to release data in the functional form. Due to lack of information, no adjustment was made to the data to allow for a return on investment orto set a criterion concerning the desired level of efficiency within plants. A least-squares analysis was performed to obtain the function that best fitted the data. Simple linear and second-degree polynomial re- 9

11 'l- gression equations were calculated with the polynominal having the best fit. Logarithmic transformations were performed on the data, and a better fit was obtained. Again, the second-degree logarithmic polynomial regression equation provided the best fit, based on comparison of the standard errors of estimate. This least-sq uares estimate of the processing-cost function was provided by: \ b ( ~ () tr lj ) Log (TCx100) = : Log V ( Log r where TC = total unit cost, in(gents;r-arict ;1 Of) ((..." It.. S V = volume, in qua-tis per operating day. This equation had a multiple correlation coefficient (R) of It was assumed that plants were homogenous in all respects except size. The average package size and type percentages for the five plants in the study are shown in Table 3. Table 3. Average percentages of fluid milk processed, by size and type of container, five South Carolina plants, 1973 Container size and type 1 gallon plastic V2 gallon plastic '12 gallon paper Quart paper Pint paper 10-ounce paper '/2 pint paper ounce Tetra Pak Bulk (3 sizes) Total Percent of plant output \ I' Source: (3). This function did not reflect the expected relationship between size and cost. Cost per unit declined as quantity increased; but cost reached a minimum and started to increase at a much smaller quantity (about 87.,200 quarts per day) than other stud ies have shown, Fig u re 2. Due to the anonymity of the processing firms, the reason for the upturn Cents per unit Figure 2. Unit cost of processing fluid milk in five South Carolina plants,

12 J could not be determined, although several hypotheses as to why the larger plants might have higher costs than smaller plants are possible. Inefficient management or operation at less than optimal capacity could explain such higher costs. Even in an efficient operation, an accelerated capital depreciation schedule easily could increase perunit cost sufficiently to cause the function to increase. Because of these unexpected results, a second processing-cost function was included in the study. A publication by Stennis, under Southern Regional Dairy Marketing Project SM-28, presented a processing-cost function applicable to the South (~~ p. 13). That formula was based on both actual and estimated proje'ssing costs in the region. For this study, the Stennis formula was updated to 1973 using the Wholesale Price Index. The adjusted formula was : C =_6':L629 V-O.24B where PC = processing cost, in cents per quart, ~nd V = volume processed, in quarts per day.? 1-',,). I.. I'. j, IV lr v. t - From Figure 3, it can be seen that this function indicated economies of size. Per-unit cost declined at a decreasing rate, and eventually the rate of decline approached zero as plant size was increased and the cost curve became asymptotic to the horizontal axis at some minimum positive value. For the purposes of Model IIA used later, 3.0 cents Qer ' quart was selected as a plausible lower limitfor per-unitcostsain Mo~ a, r!:r/oa,/ I, it was assumed that all processing plants were operating at an average cost above this lower limit. Optimum shipping patterns were determined solely on the basis of transportation costs, with historical processing charges and plant sizes ignored. With respect to processing charges, a separable function derived from the nonlinear functions presented was utilized in Model II. Linear cost segments were developed between the following daily volumes: 0; 1,274; 2,548; 12,742; 25,485; 38,228; 100,000; and 200,000 quarts. Cents per quart Quarts processed per day Figure 3. Relationship between cost of processing packaged fluid milk and volume of milk processed 11

13 J Distribution Costs 7 The costs of transporting packaged fluid milk by truck are.2i.9.b1.!y..-- higher than those of moving a like volume of raw milk in bulk, because packaged milk requires more space, more handling and loading labor, and more equipment than bulk milk. As with bulk milk, the cost of transportation of packaged milk is a function of the distance shipped. The packaged milk transportation cost functions used in this study are shown in Table 4. These functions assumed a 35,000-pound load and were based op functions developed by Kerchner, indexed to reflect 1973 costs (-?' 'P. 19). This function included the costs of loading at the processing plant, transportation, and unloading at a distribution plant. No additional marketing expenses were included. Any additional costs, such as in-store costs, home delivery, and promotion costs, would occur regard less of the organization and scale of the processing sector, and therefore would not affect decisions on processing acilities, utilization, or location. Table 4. Packaged milk transportation cost functions, 1973 One-way distance a Estimating equations a. where: TC = total cost, in cents per cwt., and D : one-way distance, in road miles. Source: (7, p. 19). TC = ' D TC = D TC = D Various other aspects of the cost of processing have not been included for the same reason. The costs of packages, flavoring, and additives were not included in the processing-cost function, therefore; precaution must be exercised in comparing the functions presented here to those from other studies. Fluid Milk Consumption and Consumption Areas The adjusted South Carolina demand for fluid-milk products (total sales and utilization minus out-of-state sales) amounted to 522,499,919 pounds of milk in 1971 (9). The latest census figures place the state population at 2,590,516 and, considered with the adjusted demand, imply a per ~pita consuli1p.ti.on o.l2 l2 PQuo.ds.oLmilk per year. This is little below the lli!1io al gyerage ot223..po_uods _ pecyeacbut is in line with the historical relationship in South Carolina. The populations of the 263 incorporated places in South Carolina, plus shares of the rural population in proportion to their sizes, were used to calculate area demands for fluid milk products in the state. The resulting daily consumption for some of the smaller towns amounted to less than 20 gallons. For this reason, the number of consumption sites was reduced to 66 of the largest towns in the state. The consump- 12

14 tion sites listed in Table 5 included at least one town from each county. Costs of distribution to stores within a town and to smaller towns would be approximately the same no matter what the size and location of processing plants. In many cases, the milk is shipped from processing plants to local distribution points in large, over-the-road trucks and then transferred to smaller route trucks for delivery. Such del ivery costs would occur irrespective of processing plant size and would not affect optimal plant location. Disregarding the consumption sites receiving full loads, the average daily delivery was 51 percent of a full load ~ thus a truck would average two stops per trip. The average distance between adjacent consumption sites was determined to be 13 miles, and half of this distance was charged to each of the sites as its share of this additional route cost. Linear programming with the Mathematical Programming System Extended (MPSX) algorithm was used to apply the economic theory related to dairy processing outlined in this section to the above data. Several approaches or models were used, but the overall objective was to find an optimum organization forthe South Carolina dairy industry. Table 5. Selected South Carolina milk consumption centers and daily volumes, by county, 1971 Adjusted County Center population consumption (number) (pounds) Abbeville Abbeville Aiken Aiken 46,289 25,579 N. Augusta 40,641 22,458 Allendale Allendale Anderson Anderson ,514 Honea Path 21,217 11,725 Belton 27,295 15,083 Bamber9 Bamberg 21, Barnwel Barnwell ,123 Beaufort Beaufort 34,197 18,897 Berkeley Moncks Corner 21, Calhoun SI. Matthews 7, Charleston Charleston 186, ,201 Mt. Pleasant 29,532 16,319 Cherokee Gaffney 40, Chester Chester Chesterfield Chesterfield ,750 Cheraw 15,001 8,289 Clarendon Manning 16, Colleton Walterboro 19, Darlington Darlington ,326 Hartsville 21,372 11,810 Dillon Dillon 25,187 13,918 Dorchester Summerville ,347 Edgefield Edgefield 15,099 8,344 Fairfield Winnsboro Florence Florence 77,392 42,766 Lake City Georgetown Georgetown 35,423 19,575 Greenville Greenville 177,386 98,023 Greer Simpsonville 27,981 15,462 Greenwood Greenwood 63, Hampton Hampton 21, Horry Myrtle Beach 33,419 18,467 Conway ,362 Jasper Ridgeland 5,380 2,973 13

15 Table 5. (Continued) Selected South Carolina milk consumption centers and daily volumes, by county, 1971 Adjusted County Center population consumption (number) (pounds) Kershaw Camden 25,091 13,865 Lancaster Lancaster 31,881 17,617 Laurens Laurens 31,585 17,454 Clinton 21,694 11,988 Lee Bishopville 10,530 5,819 Lexington Cayce 41,530 22,950 West Columbia 31,694 17,514 McCormick McCormick 6,062 3,350 Marion Marion 38,790 21,435 Marlboro Bennettsville 30,068 16,615 Newberry Oconee Newberry Seneca 34,728 17,013 19,190 9,401 Orangeburg Orangeburg 18,320 42,152 10,123 23,293 Walhalla Pickens Bowman Easley 16,080 37,415 8,886 20,675 Richland Clemson 36,828 20,351 Columbia 302, ,261 Saluda Spartanburg Spartanburg 118,752 65,622 Forest Acres Saluda 25,451 19,386 14,064 10,713 Inman 17,262 9,539 Woodruff 16,637 9,194 Cowpens 17,981 9,936 Sumter Sumter 69,309 38,300 Union Union 34,642 19,143 Williamsburg Kingstree 15,086 8,336 York York 25,405 14,039 Rock Hill 102,829 56,823 State Total 2,590,516 1,431,506 14

16 ANALYSIS OF EMPIRICAL DATA In this section, the cost estimates developed above were used in several models to determine optimum organizations of the South Carolina milk processing industry under different assumptions. An optimum solution, as defined here, is a solution to a set of processing and transportation cost equations, given the product availability and demand, that minimizes the value of the objective function. It is not necessarily a unique solution as it is possible for more than one combination of processing plant sizes and locations to yield the same optimum solution. The programming algorithm employed does not ~ y ~<;, specify the existence of such alternatives. '::> 0 ~.5, Model I Modell was a least-cost model for the fluid milk industry based on conditions in Data concerning the actual movement of milk during this period were not available; thus specific comparisons of the optimum with the actual movements of milk were not possible. This model can be used, however, ~s a basis of comparison for Model II. As previously stated, South Carolina base-holding producers d~oot produce sllfficieoi r::n.il.iu.o_roee1jbe--1nstatedemand...to r...j.luld..ml n ::.N71, production amoljn1:e.d..iq..5q.1,4~s, a6s.pow:ids.-w.bi1e_cqnsumption ~22, 4_9.9~B9Lp0.uJ:lQs,o.r,"2.1..,06~.,325. po.uod.s ethan.prod uction.. In this model, the additional milk needed to meet demand was furnished by a regional cooperative, Dairymen Incorporated, located at Spartanbu rg. The point was thus assumed to represent a large regional producer cooperative which could supply any amount of milk needed. All models required that milk produced by South Carolina base holders be used first, even though its cost of transportation might exceed that for milk supplied from out-of-state. Model I was used as a basis to compare typical South Carolina processing plants to an optimum organization when economies of size in processing were considered. The 16 processing plants in South Carolina had an average output of 89,000 quarts, or 191,350 pounds, per day during January This quantity was used as the upper limit of processing plant size for Modell. The model was further specified as to the processing cost function used. In Model la, the processing cost per unit was calculated from the Stennis model for 89,000 quarts of output per day. Model 18 used the Case cost function. ModellA A constant processing cost of 1.78 cents per pound was used in ModellA for all processing plants, independent of volume processed. Results from Model IA indicated that all 14 possible processing sites would enter the optimum solution, but only two plants would reach the upper limit imposed. This was primarily due to the fact that South Carolina plants were built with sufficient capacity to meet their weekly share of the market with 4 or 5 days of production. It was assumed in this study that plants would be operated 7 days per week in order to minimize capital investment and to fully utilize processing capacity. Results from ModellA are presented in Appendix Table 1. Each of the 14 processing plant sites is shown separately. The production centers 15,"';

17 from which the fluid milk was obtained and the consumption centers to which the processed milk was shipped are listed under each processing location. For each production and consumption center the amount of milk involved and the distance to the processing plant are listed. In addition, the total amount of milk processed and the average distances milk was shipped to the plant and to the consumption centers are shown. For example, the processing plant at Gaffney received 18,490 pounds of milk from Chester, which was 45 miles away. Milk was also shipped from Union and Gaffney. Although no transportation cost was included for the Gaffney production area, a handling charge of 0.2 cent per pound was charged in this and all similar cases. A total of 34,239 pounds of milk per day was received at the Gaffney plant from an average distance of 24 miles. Two-thirds of this milk was consumed in Gaffney, while one-third was shipped to Laurens, even though Laurens was more than 57 miles away. Milk processed at Gaffney was shipped an average of 20 miles. Further analysis of results from ModellA showed that the total cost of shipping milk from assembly points to the processing point, plus the processing costs at a constant 1.78 cents per pound and transporting the packaged product to consumption centers, amounted to $30,904 per day. Half of the 14 processing plants were closer to their markets than to the prod uction centers. Processing plants were located in each of the four largest metropolitan areas, but only the Columbia and Charleston plants marketed all their milk in the immediate area. These two plants definitely were market-oriented. The Greenville plant supplied six cities with milk, located as far as 60 miles from the processing plant. Most of the milk from the Spartanburg plant was processed for local consumption, but it also supplied milk to York and Chester. The supply point for out-of-state milk furnished 57,707 pounds of milk, all of which was processed in Spartanburg. Again, itwas assumed in the model that no transportation cost was incurred, although a handling fee was charged. The total cost of the model should be increased by the cost of bringing the nearest available out-of-state milk to the proper plant. The two smallest plants in the optimum organization were located near the borders of the state. These plants at Gaffney and North Augusta were market-oriented, although their processing volumes were relatively small. The average pound of milk handled by this model system for South Carolina was shipped 22 miles to be processed and 23 miles to a consumption point. Therefore, the analysis provided no clearcut support for the hypothesis that processing plants would be marketoriented. To further investigate this point, the upper limit on processing plant size was removed from the model and a second optimum organization was derived. In this organization, the Columbia plant increased its processing by over16,000 pounds. This was milk which was processed at the Orangeburg plant in the organization with a ceiling on plant size. This reallocation of resources from the product-oriented plant at Orangeburg to the market-oriented plant at Columbia resulted in a net reduction in daily transportation cost of $ At least for the two 16

18 largest processing plants, removal of all constraints resulted in a shift of processing toward the market. Model IS In ModellB, the Case cost function estimated a per unit cost of cents per pound for a plant processing 191,350 pounds per day. Forthis model, daily transportation and processing costs were $20,569. This was a reduction of $10,335 from the organization provided by ModellA; and it resulted from a lower per-unit processing cost. As per-unit processing costs decrease, transportation charged became more important and at some point would affect the optimum organization of the industry. This point was not reached in ModellB and the optimum size and location of processing plants did not vary between the models. The primary objective was the same for both models. Since no economies of size in processing were considered, the problem was minimizing assembly and distribution costs subject to model con-. straints. Model II Model II was a least-cost distribution model which included economies of size in milk processing. The separable programmi t),9 feature of the MPSX algorithm was used to introduce the processing cost relationship to determine the effect of economies of size on processing locations. This subroutine divided a curvilinear cost function into linear segments for use in linear programming. This allowed larger plants to process milk at a lower unit cost than smaller plants. It was anticipated that introduction of this function would lead to larger processing plants and reduce the number of active processing locations. ModelliA Model!lA, based on the Stennis cost function incorporating economies of size, provided an optimum shipping pattern different from that of Model la, Appendix Table 2. The size and location of the active processing plants were changed significantly from Model IA. Only the plants at Columbia and Spartanburg entered the least-cost solution. The Columbia processing plant was the largest, with a daily output of 908,127 pounds, with Spartanburg processing 523,379 pounds, Appendix Table 1. These outputs were 5.75 times and 5.71 times the outputs of the plants at these sites under Model IA. There were specific reasons why the plants at Columbia and Spartanburg entered the optimum solution. Columbia, the largest city in the state, required 267,261 pounds of processed milk daily to supply its population. S.lDJ:<~Jh~Ldistribution. costin the city where th~. Q ~9pe_s.ing ~ant W qs..j.q.ge~ dwgsa.ss_umed to be.zero in the model,.a,si.gnitic_c!.d.! portion of the distribution cost for the plant and for the state was ~ 1m te~ : his provided a reason for locating a processing plant intended to minimize processing and transportation costs at that location. Spartanburg was selected as a second site for a similar reason. As stated before, itwas assumed that the regional producer cooperative at Spartanburg would supply sufficient milk to compensate for any pro- \Jonl! "" 'r r l" S T /~Y ~ /l fv Y""" \If f! " (, P, ;" 0, 17

19 duction deficit in the state. The deficit amounted to over 57,000 pounds daily. This, plus the 22,000 pounds produced daily by South Carolina base holders and assembled at Spartanburg, was assigned a zero assembly cost. As at Columbia, this low assembly cost, coupled with a low distribution cost for the relatively large Spartanburg population, offset any advantages of a more central location. The state was divided between the two processing plants about as one would expect. Newberry was on the dividing line between the two plants. The milk produced at Newberry was processed at the Columbia plant which supplied about one-third of the consumption needs at Newberry. The remainder of the demand at Newberry was met by the Spartanburg plant. All towns above Newberry shipped to and received milk from Spartanburg. All towns below Newberry were served by the Columbia plant. As stated in the discussion of the Stennis cost function above, a lower limit of 1.4 cents per pound was included in the model for quantities over 82,000 pounds. In the absence of such a limit, the cost function would produce unrealistically low unit processing costs at large quantities. If processing costs had been allowed to continue to decrease, the Columbia plant would have been the only active plant in the model. The two-plant solution resulted in a cost of $28,637 for assembling, processing, and distributing a one-day supply of fluid milk for South Carolina. This was a reduction of $2,267 from the results of ModellA. Since both the Columbia and Spartanburg plants operated at quantities over 82,000 pounds, their per unit cost was 1.4 cents per pound. Obviously, the distance milk was shipped increased significantly for the two-plant industry. When the sources and destinations of fluid milk for the hypothetical plant locations in Models IA and IIA were compared, utilization of only the Columbia and Spartanburg plants increased the average distance milk was assembled from 40and 10 miles to 59 and 42 miles, respectively. On the distribution side, the same situation existed. The distribution radii for the two plants were increased from 1 and 16 to 71 and 45 miles, respectively, for Columbia and Spartanburg. Sensitivity of Optimum Organization to Processing Cost Changes Ranges within which processing costs could vary in each center without changing the patterns and flows of the ModelliA solution were calculated. These ranges were subject to all other costs remaining constant. In the active processing centers, the most that processing costs could have increased or decreased without changing the solution was less than 0.01 cent per pound. A reduction in cost as small as cent per pound would have altered the optimum flow in the Spartanburg plant. A negative cost would have had to prevail before any of the other plants would have entered the optimum solution. In other words, for processors at the other locations to have attracted milk, they would have had to pay forthe privilege of using their plants. 18

20 Model lib Model lib was revised to make unit processing costs a function of output. Using the Case study cost function, a total cost for the model of $13,422 was obtained. This was a reduction per day for South Carolina of $7,147 from Model lb. This reduction was due to the fact that the cost function allowed plants to realize most available economies of size at a relatively small volume. The least-cost solution included nine plants, ranging from a daily production of 100,000 pounds at Gaffney to 190,211 pounds at Columbia, with an average of 159,056 pounds, Appendix Table 3. The reason that Model lib included more and smaller plants than Model IIA was that the cost function for lib reaches a minimum and then begins to rise. This prevented two large plants, such as those obtained in Model IIA, from entering the organization. There was no clear cut trend in the Model lib solution toward market-oriented plants. The production-oriented Orangeburg plant was not in the least-cost solution, but neither was the Charleston plant. For the state as a whole, the average distance milk was assembled, 28 miles was less than the average distribution distance of 37 miles. The explanation for the greater distribution radius is obvious when the locations of the majority of the state's dairy production is considered. Major production areas are located in Orangeburg, Bamberg, Newberry, and Saluda Counties in the central part of the state, while dairy farms are almost non-existent in the Coastal counties. Therefore, the distance from the dairy farms to the optimal processing plants was fairly short. On the other hand, some of the state's most populous counties, such as Anderson and Charleston, are located in the periphery of the state away from the processing plants. Considered in its entirety, such a situation led to distribution costs greater than assem bly costs. Cost ranges for which the results of Model lib would apply were determined and resulted in conclusions similar to those for Model IIA. Because of the function used, the overall cost of processing was lower for lib than for IIA, but the sensitivity of the optimum organization to industry cost changes was about the same. For several processing sites, a change in cost of.01 cent per pound would have caused a change in the size of plant; and all plants would have been changed by cost changes of less than one-half cent. As with Model IIA, it would have been necessary for the five possible sites not in the least-cost solution to have had negative costs before they would have entered the solution. From the results of Model II, it can be concluded that economies of size in milk processing, even when tempered by increased transportation costs, provide economic reasons to expect fewer processing plants in South Carolina and changes in the market that the remaining plants serve. Pricing Efficiency It should be emphasized that the major thrust of this study has been to determine the organization of the milk processing industry resulting in the highest possible level of technical efficiency. Previous studies 19

21 have indicated that available economies of size in milk processing would make it technically efficient to have a few large plants supply a large market area with fluid products (1, 2, 4, 6,12,14, and 15). Thisstudy has shown this to be the case for South Carolina. The number of plants that gave the least-cost solution varied with the cost function used; but all studies, whether they concluded that one, or several plants, provided the optimum organization, have assumed that each plant had a monopoly within its market area. Such an organization would appear to attain maximum efficiency both in operation and pricing. However, one point related to pricing efficiency must not be overlooked. If the optimum-size processing plant is determined first, and then the proper margin set, there is no possible way to increase efficiency, ceteris paribus. The problem arises when a margin is set so that an existing plant earns a normal profit, irrespective of its size. This would produce technical efficiency for that plant but not necessarily pricing efficiency. A larger plant might be much more efficient; therefore, to obtain a social optimum, the margin should be reduced, forcing processors to go to larger plants to realize. ormal profit. In order to set the proper fclrm price and processing margin, sufficient information is of paramount importance. If accurate cost data are not available on a continuing basis, the probability of obtaining an optimum in either pricing or technical efficiency is extremely small. 20

22 LITERATURE CITED 1. Ashley, Calvin R., and William H. Alexander. Optimum Number, Size, and Location of Milk Manufacturing Plants in Louisiana and Mississippi. DAE. Research Report 418, Department of Agricultural Economics and Agribusiness, Louisiana State University and Agricultural and Mechanical College. Agricultural Experiment Station, Baton Rouge, Louisiana. December Carley, D. H. Factors Affecting the Location and Size of Fluid Milk Plants. Bulletin N.S. 155, Department of Agricultural Economics, Georgia Experiment Station, Experiment, Georgia. April Case and Company, Inc. A Report on the Cost of Producing, Processing, Distributing and Selling Milk in South Carolina. Authorized by the Dairy Study Committee of the South Carolina Legislatu reo March DeHaven, R. Kenneth, "Connotations of Market Structure in Fluid Milk Pricing. " Paper presented at Annual Meeting of the South Carolina Academy of Science, Columbia, South Carolina. April 4, Devine, Gary, Alex Bradfield, John Mengal, and Fred Webster. Economies of Size in Large Fluid Milk Processing Plants. MP 62, Vermont Agricultural Experiment Station, University of Vermont, Burlington, Vermont. May Kerchner, Orval. Cost of Transporting Bulk and Packaged Milk by Truck. Marketing Research Report No. 791, Economic Research Service, U. S. Department of Agriculture. May McAlhany, John W. The Optimum Size Cotton Gin as Related to Assembly and Ginning Costs in South Carolina. Unpublished Doctoral Dissertation Clemson University, Clemson, South Carolina South Carolina Crop and Livestock Reporting Service. South Carolina Cash Receipts from Farm Marketings. CRS cooperating with Department of Agricultural Economics, South Carolina Experiment Station, Clemson University. September South Carolina Dairy Commission. Monthly Report. January December South Carolina Dairy Commission, unpublished production data Spenser, Milton H. Contemporary Economics. New York, Worth Publishers, Inc Stennis, Earl A., Verner G. Hurt, and Blair J. Smith. Levels and Locations of Fluid Milk Production, Processing and Consumption in the South, 1965 and Southern Cooperative Series, Bulletin No January Tung, T. H., Leon Reu and Ronald H. Millar. A Location Programming Model of the Colorado Dairy Industry. Technical Bulletin 99, Agricultural Experiment Station, Colorado State University, Fort Collins, Colorado. May Webster, Fred, Alex Bradfield, J. R. Browning, H. C. Moore, and K. A. Taylor. Economies of Size in Fluid Milk-Processing Plants. Bulletin 636, Vermont Agricultural Experiment Station, University of Vermont, Burlington, Vermont, June Wonncott, Thomas H. and Ronald J. Wonncott. Introductory Statistics. New York. John Wiley and Sons, Inc

23 Appendix 22

24 Appendix Table 1. Least-cost transportation patterns for fluid milk in South Carolina: Producing to processing centers and processing to consumption centers, Model la, 1973 Production center Consuml2tion center Location Distance shil2ment Location Distance shil2ment (miles) (pounds) (miles) (pounds) Gaffney Chester 45 18,490 Gaffney 0 22,436 Gaffney 0 8,294 Laurens 57 11,803 Union 30 7,455 Total milk 34,239 34,239 Average miles Spartanburg f\) Landrum 20 8,845 Chester 72 15,977 VJ Laurens 40 22,280 Cowpens 16 9,936 Spartanburg 0 22,286 Inman 7 9, ,706 Spartanbu rg 0 65,622 York 57 10,043 Total milk 111, ,117 Average miles Greenville Easley 17 13,641 Greenville Gray Court Greer Greenville Simpsonville 15 4,940 Landrum Woodruff 27 9,194 Piedmont 22 15,669 Greenwood Union Total milk ,825 Average miles 14 20