By
Abdul Ali Khan, Assistant Chief, API
1. Abstract
2. Importance of Industry Location
Traditionally, industries display one of three location orientations with respect to their markets and resources i.e. resource-oriented; market oriented; and intermediate point oriented. Among the most important factors that influence the choice of location for manufacturing industries are nearness to market, source of raw materials, availability of fuel or power, and labor supply. The general principle governing the location of manufacturing industries, in terms of transportation costs, is that an industry will tend to locate where the aggregate transportation charges are the least. This may be at the source of supply of some important raw material; it may be at the market for the finished product; it may be at the source of fuel supply; or it may be at some intermediate point. It must also be recognized that the importance of transportation charges will vary with different industries. If transportation costs are a larger factor in the cost of production, and large relative to the value of the commodities produced, they may be the controlling factor in the location of industry. If transportation costs are but a small part of the cost of production, and small relative to the value of the commodities produced, they may have little or no influence in the selection of locations.
Whether the industry will be drawn toward the raw materials or toward the market for finished products will depend upon the relative cost of transporting the raw materials and the finished goods. If the rates on the raw materials are higher than on the finished product, there will be an advantage in locating near the raw materials. If the rates on the finished products are higher than on the raw materials, there will be an advantage in locating near the centers of consumption, unless this advantage is offset by loss of weight in the manufacturing process. It should be noted that normally the rate on the raw materials are lower than on the finished product. Also industries may be expected to locate near the source of raw materials which shrink in weight in the process of manufacture. This explain, in part, why sawmills penetrate into the wilderness and why wood-using industries are commonly located near the supplies of growing timber.
The aggregate-travel or transportation-cost model serves a plant. It is a means of finding an optimal location for a plant. It is a means of finding the relative cost of collecting an input to a location of known spatial distribution, based on the measurement of the total cost or coverage of distance.
The aggregate travel (transport cost) model was used in the Mississipi Delta Area to collect the gin waste at a minimum cost. This model can be replicated in Pakistan for choosing location for any industry. Mathematically the model can be expressed as:
n
|
Zi=∑ QiTij
|
i=j
|
Where zi
|
=
|
is the aggregate cost involved of moving gin waste from all sites to plant location;
|
Qi
|
=
|
number of truck loads of gin waste at each site;
| |
Tij
|
=
|
cost per trip of gin waste from site i to plant location j.
|
This simple mathematical model can be used to determine the optimal location by deriving the values of Zi, which is the aggregate cost of hauling gin waste from all sites to a given location. The site with the least value in the output matrice is the optimal location for the processing plant.
3. Assumptions of the Model
The basic assumptions of the model are as follows:
1. The processing plant uses only gin waste, and converts it into a homogenous product.
2. The unit cost of waste at any gin is constant, irrespective of quantity transported to plant j.
3. The amount of gin waste is fixed at each site.
4. Unit production costs at any plant location are constant, irrespective of scale and capacity of the plant.
5. Transportation cost varies, depending upon the milage covered.
The disposal of cotton gin waste is a significant problem in the cotton ginning industry. For spindle-picked cotton, 100 to 150 lbs of cotton gin waste per bale of lint must be handled. Cotton gin waste is already collected at the gins, but needed to be transported from the gins to a central location where it could be further processed and converted into a useful product. Since gin waste is a bulky and low value density material, therefore more emphasis should be placed on its transportation cost.
Sakashita (1967) examined the location problem of a firm in one dimension. Using a linearly homogeneous production function, he considered the case of a firm utilizing two inputs. Assuming the transportation rates on the inputs to be constant and that on output to be zero, he established that a cost minimizing firm would only locate at one of the fixed location of its inputs, and never at an intermediate point. Woodward (1973) found that under cost-minimization, the firm's location is independent of the output level when the transportation cost of output is positive (zero), if the production function is linearly homogeneous.
Khalili et. al. (1974) considered the location problem of a firm in two dimensions that is the two inputs of the firm and the output market are located at the vertices of a triangle. He established three propositions:
(i) Homotheticity of the firm's production function (which is equivalent to the firm's expansion path being a ray through the origin) is the necessary and sufficient condition for the optimum production location to be invariant with respect to the output level when the firm is constrained to remain at a specified distance from the market;
(ii) With the distance from the market variable, the necessary and sufficient condition is linear homogeneity of the production function; and
(iii) With a homogeneous production function, the firm would move towards (away from) the market under increasing (decreasing) return to scale.
Further, Khalili et. al. (1974) demonstrated that the firm would never locate on the line joining the market to either of the two inputs.
Moses (1958) investigated how changes in a firm's
location at a constant distance from the market point affect the efficiency conditions governing the firms consumption of inputs which needed to be transported from two different points. He concluded that a production function homogeneous of degree one is sufficient to ensure an optimum location independent of the level of output, as long as the transportation rates are constant or depend solely on haulage distances. However, if transport rates are also allowed to vary with haulage volume, then the condition sufficient for an output-independent optimum location solution must be extended to cover not only the necessary nature of the production function, but also the necessary nature of both the elasticity of transport rates with respect to quantities shipped and the marginal productivities of the inputs. The reason for this is that changes in transport rates with respect to quantities shipped will demand changes in the total number of ton-miles hauled and, with variable proportions coefficients, this could lead to factor substitution in either direction. The actual impact of changes in transport rates with respect to haulage volume will depend not only on their elasticities with respect to haulage volume, but also on their absolute levels.
location at a constant distance from the market point affect the efficiency conditions governing the firms consumption of inputs which needed to be transported from two different points. He concluded that a production function homogeneous of degree one is sufficient to ensure an optimum location independent of the level of output, as long as the transportation rates are constant or depend solely on haulage distances. However, if transport rates are also allowed to vary with haulage volume, then the condition sufficient for an output-independent optimum location solution must be extended to cover not only the necessary nature of the production function, but also the necessary nature of both the elasticity of transport rates with respect to quantities shipped and the marginal productivities of the inputs. The reason for this is that changes in transport rates with respect to quantities shipped will demand changes in the total number of ton-miles hauled and, with variable proportions coefficients, this could lead to factor substitution in either direction. The actual impact of changes in transport rates with respect to haulage volume will depend not only on their elasticities with respect to haulage volume, but also on their absolute levels.
Weber approached the location problem by making three basic assumptions, in order to eliminate many of the complexities of the real world. First, the geographical basis of materials is given (that is, fuel and other raw materials are found in some localities only). Second, the situation and size of places of consumption are given, with the market comprising a number of separate points. Condition of perfect competition are implied, with each producer having an unlimited market with no possibility of deriving monopolistic advantages from choice of location. Third, there are several fixed labor locations, with labor immobile and in unlimited supply at a given wage rate.
There are three factors that influence industrial location, two general regional factors of transport and labor costs, and the local factor of agglomerative or deglomerative forces. Weber (1929) first examined the manner in which the point of minimum transport costs can be found and then the circumstances in which labor or agglomeration advantages will operate. Transport costs are viewed as the primary determinant of plant location. Costs are not considered directly, however, but as a function of weight to be carried and distance to be covered. Weber demonstrated the derivation of the least transport-cost location by using the locational triangle. He took from his simplified space economy one point of consumption (C) and the most advantageous deposits of the two necessary materials (M1 and M2) as framework within which to examine the way any factory will be located. The least transport-cost location is the point at which the total ton miles involved in getting materials to a place of production and the finished product to the market is at a minimum; each corner of the triangle exerts a pull on the point, measured by the weight to be transported from or to the corner (in the case of market) . The point can be found by a simple application of the theorem of the parallelogram of forces. It can also be discovered by the use of Varignon's mechanical model, in which weights of appropriate size attached to the pieces of string passing over pulleys are suspended from the corners of the triangle; the three pieces of string are tied together, and the position within the triangle where the knot comes to rest indicates the point of compromise between the three forces.
Palander (1935) used Weber's isodapane technique to demonstrate the effect of transport costs on location. He made an important distinction between rates that rise evenly with distance and the more realistic arrangement under which the rate tends to fall off with distance travelled. The uniform rate will produce a series of isovectors around a given point taking the form of concentric circles spaced at regular intervals, whereas the variable rate makes the isovectors successively further apart as cost per unit of distance falls. A uniform increase in the transport costs in relation to distance from each point makes isodapanes interpolated from the three sets of isovectors reveal a least-transport-cost point within the triangle whereas with variable freight rates locations at the corners are more attractive.
Hoover's (1936) early work on industrial location is still among the most useful particularly for those who seek a clue to the general nature of the location problem. He started with the assumption of perfect competition between producers or sellers at any one location and perfect mobility of factors of production and transportation costs and extraction or production costs as the determinants of location. In case of extractive industries with known location of deposits, the delivered price to any buyer will be the cost of extraction plus transport costs. Buyers will obtain the commodity from the source that offers the lowest delivered price and the boundary between the market area of two producers will be a line joining points at which delivered price is the same from both sources. He also pointed out that in the absence of production cost differences the best location will be at the minimum transport cost, which may be at a material source, at the market, or at an intermediate point. The least-transport cost location is found by constructing isotims (lines joining points where a commodity costs the same) around given material and market points, from which lines of equal total transport cost (isodapanes) can be constructed.
August Losch (1954) approached the location problem by seeking the location at which revenue is the greatest i.e. total revenue exceeds total cost by the greatest amount. He determined the total attainable demand and the best volume of production as a function of factory price for a number of virtual factory locations separately. The greatest profit attainable at each of these points were determined from the cost and demand curves, and from this place the greatest money profits, the optimal location were found.
Martine Labbe and s. Louis Hakimi {1991) considered a two-stage location and allocation game involving two competing firms. The firms select the location of their facility on a network. Next the firms optimally select the quantities each wishes to supply to the markets, which are located at the vertices of the neb10rk. The criterion for optimality for each firm is profit maximization, which is the total revenue minus the production and transportation costs. Under reasonable assumptions regarding the revenue, the production cost and the transportation cost functions, they showed that there would be a Nash equilibrium for the quantities offered at the markets by each firm. \'lhen the quantities supplied (at the equilibrium) by each firm at each market are positive, there would be a Nash location equilibrium, i.e. no firm would find it advantageous to change its location.
Dennis 0. Olson and Yeung-Nan Shieh {1990) examined the theoretical implicationsof quantity-discounted transportation rates on the optimum location decision of the firm. In a two dimension, n-input space, when the transportation rate is independent of quantity of distance shipped, the linearly homogeneous production is easily generalized to the case where transportation rates depend upon distance shipped. When transportation rates depend upon quantity shipped, the firm's location decision cannot be made independently from its production decision unless (1) the elasticities of transportation rates with respect to quantity shipped are constant and identical, and (2) the ratio of marginal products to the marginal transportation costs are equal for each input.
Melvin Greenhut (1956) studied various important factors which influence plant location. He listed these as transportation, processing costs, the demand factor, and "cost reducing" and "revenue increasing" factors. Greenhut felt that transportation is the major determinant of plant location. An entrepreneur will tend to economize on transportation if freight costs comprise a large part of total costs, but only if transfer costs vary significantly at different locations. Material orientation as a product of transport costs is considered, and it is concluded that it occurs in two special cases: (1) where the materials are perishable, and (2) where transport cost on the material is much greater than on the finished product.
Walter Isard (1956) analyzed the locational equilibrium of the firm under transport orientation and showed how the substitution approach is applied. The framework is the familiar locational triangle, with the market at one corner (C), sources of two materials at the other corners (Ml and M2). The initial problem is to find the optimum location, given certain assumptions regarding freight rates and quantity of material needed, for a plant at some distance form one corner of the triangle. The arc, which represents a locus of possible points, is transposed into a transformation line on a graph in which distance from Ml is plotted against distance from M2. Moving along the transformation line distance from one source point decreases while from other point of source increases; in other words, transport inputs from one point are being substituted for transport inputs from another. To find the optimum or least-cost location along the curve, it is necessary to add equal outlay lines and the optimum point will be the one at which it is tangential to the lowest value equal outlay line.
4. Summary
The overall objective of the this study was to determine an optimal location for two cotton gin waste disposal facilities so that this waste produced could gin waste disposed off in an acceptable way. Cotton acreage, production, and number of bales ginned at the country level were obtained from the National Agricultural Statistics Service (NASS). Locations of the existing gins in the study area were identified by using the Cotton Ginners Association Blue Book. Since the actual number of bales processed per gin was not available, this figure was derived by dividing the number of gins into the number of bales processed at the country level. The amount of waste was estimated using three conversion rates – 100, 125, and 150 pound waste per bale.
Two processing plants were proposed for the study area. A total of 66 gins located in the Upper Delta and North Central districts would deliver the gin waste to the first plant. The actual number of bales processed by these gins were estimated at 668.4 thousand bales during the period 1988-92, and produced 30,317 tons of waste based on a 100 pound conversion rates. A second plant was proposed for the Lower Delta and Central districts. Here, 73 gins located at 42 sites would deliver the gin waste to the second plant. These gins produced 46,082 tons of gin waste based on a 100 pound conversion rate.
Since transportation cost is a function of distance and weight or volume to be shipped, the distance between waste producing sites was determined using a software called “Auto Map”. A road map was also used where the requisite information was not available from the Auto Map program. It was assumed that the distance between the gins within each site/town is negligible and has little or no affect on the transportation charges. Dump tracks will be used to move the waste from each site to the processing plant. Transportation charges were obtained from the Mississippi Public Service Commission. For first processing plant, a 43x43 matrix consisting of transportation costs was multiplied by a 43x1 matrix showing the number of truck loads at each site. The elements in the output matrix showed the total transportation costs from each site to the plant. The same methodology was used for the second plant.
5. Conclusions
An aggregate travel cost model was used to determine the optimal locations for both plants. The first plant would process cotton gin waste from 66 gins located in the Upper Delta and North Central districts. The results showed that Lyon was the optimum site because it had the lowest transportation costs. A total of 3,013 truck loads would be shipped to site at a cost of $445,423. The average cost per truck was estimated as $151.15 and the cost of building per bale was 69 cents. These estimates were the lowest compared to the remaining 42 sites.
Similarly, for the second facility, Silver City had the lowest hauling cost. This site would handle 4,591 truck loads at a cost of $580,314. The average cost per truck was estimated as $126.40 and the per bale cost was 57 cents.
6. References
1. Khalili, Amir, Vijay K. Mathur, Diran Bodenhorn. 1974. “Location and the Theory of Production: A Generalization, “Journal of Economics Theory, 9, pp 467-475.
2. Olson O. Dennis, Shieh Yeung-nan “A note on Transportation Rates and Location of the Firm in a Two-Dimension, n-Input Space” Journal of Regional Science, Vol. 30, No. 3, 1990, pp 427-434.
3. Fryrear, D.W. and D.V. Armbrust. 1969. “Cotton gin trash for wind erosion control”. Texas Agricultural Experiment Station, Texas A&M University, Publication MP-928, 7pp.
4. Beck, S.R. and L.D. Clements. 1982. Ethanol production from cotton gin Trash”. In: Proceeding of the Symposium on cotton Gin Trash Utilization Alternatives, National Science Foundation et. Al., pp.163-181.
5. Jerger, D.E., M.P. Henry, S. Ghosh, D.Q. Tran, S. Babu, and D.P. Chynoweth 1982. “Gasification of land-based biomass”. Gas Research Institute report no. GRI-81.0080, 186pp.
6. Parnell, C.B., Jr. 1981. “Gin trash cotton utilization research in Texas-an update”. In: Proceedings of the gin waste utilization Roundup and tour, University of California at Davis, pp. 37-43.
7. Williams, G.F., P. Piumsomboon, and C.B. parnell, Jr. 1982B. “A systems engineering model for cotton gin trash utilization”. Transactions of the ASAE, pp. 802-810.
8. Biblis, E.J. 1977. “The manufacture of building materials from ginning wastes”. In: Proceddings of the Gin-Waste-Utilization and Stick-Separation Seminar, Cotton Incorporated, pp. 41-42.
9. Dernovich, A.V. and L.A. Priz. 1987. “On the potential for use of cotton gin trash in the hydrolysis industry”. Hydrolysis of Wood into chemical s (USSR), Allerton press, New York, no. 6, pp. 58-59.
10. Kenneth B. young and Mesbah U. Ahmed (1978). “Economics of Using Cotton Gin Trash as a Supplemental Feed for Range Cattle”. Journal of Range Management 32 (2), March 1979.
Annexure-I
Transportation Cost of Gin Waste to Potential Sites
Town/Site
|
Total cost ($)
|
Cost/Bale ($)
|
Town/Site
|
Total Cost ($)
|
Cost/Bale ($)
|
Silver City
|
580314
|
0.57
|
Bentonia
|
907084
|
0.9
|
Belzoni
|
627378
|
0.62
|
Drew
|
925989
|
0.91
|
Inverness
|
635171
|
0.63
|
Chatham
|
929120
|
0.92
|
Holly Ruidge
|
672076
|
0.66
|
Goodman
|
944979
|
0.93
|
Panther Burn
|
678007
|
0.67
|
Schlater
|
956194
|
0.94
|
Midnight
|
689320
|
0.68
|
Vaughan
|
961826
|
0.95
|
Isola
|
692742
|
0.68
|
Satartia
|
995264
|
0.98
|
Indianola
|
704881
|
0.7
|
West
|
1012176
|
1
|
Hollandal
|
708563
|
0.7
|
Canton
|
1033160
|
1.02
|
Delta City
|
715643
|
0.71
|
Rome
|
1076291
|
1.06
|
Tchula
|
720902
|
0.71
|
Flora
|
1226958
|
1.21
|
Arcola
|
725752
|
0.72
| |||
Yazoo City
|
734824
|
0.73
| |||
Anguilla
|
735067
|
0.73
| |||
Greenwood
|
746845
|
0.74
| |||
Leland
|
763684
|
0.75
| |||
Itta Bena
|
765787
|
0.76
| |||
Avon
|
775144
|
0.77
| |||
Rolling Fork
|
799072
|
0.79
| |||
Cruger
|
814639
|
0.8
| |||
Stoneville
|
820054
|
0.81
| |||
Morgan City
|
820750
|
0.81
| |||
Greenville
|
821975
|
0.81
| |||
Lexington
|
824450
|
0.81
| |||
Cary
|
824515
|
0.81
| |||
Glen Allan
|
826747
|
0.82
| |||
Benton
|
832411
|
0.82
| |||
Sidon
|
838942
|
0.83
| |||
Holly Bluff
|
892063
|
0.88
| |||
Minter City
|
897979
|
0.89
| |||
Winterville
|
903253
|
0.89
|
Source: National Agricultural Statistics Service (NASS), Mississippi.
Annexure-II
Hauling Cost of Gin Waste Per Bale to Second Plant
Town/Site
|
No. of Gin
|
Distance from Plant
|
Cost per
Trip ($)
|
Cost per Bale ($)
|
Silver City
|
1
|
1
|
100.00
|
0.45
|
Midnight
|
1
|
6
|
100.00
|
0.45
|
Belzoni
|
2
|
9
|
100.00
|
0.45
|
Isola
|
1
|
15
|
100.00
|
0.45
|
Inverness
|
2
|
21
|
100.00
|
0.45
|
Morgan City
|
3
|
24
|
100.00
|
0.45
|
Yazoo City
|
1
|
24
|
100.00
|
0.45
|
Anguilla
|
1
|
25
|
100.00
|
0.45
|
Sidon
|
1
|
26
|
100.00
|
0.45
|
Holly Bluff
|
2
|
27
|
100.00
|
0.45
|
Hollandal
|
4
|
28
|
100.00
|
0.45
|
Tchula
|
4
|
29
|
100.00
|
0.45
|
Benton
|
1
|
30
|
100.00
|
0.45
|
Indianola
|
5
|
30
|
100.00
|
0.45
|
Panther Burn
|
1
|
31
|
100.75
|
0.46
|
Rolling Fork
|
2
|
31
|
100.75
|
0.46
|
Delta City
|
1
|
33
|
107.25
|
0.49
|
Itta Bena
|
2
|
34
|
110.5
|
0.50
|
Cruger
|
1
|
37
|
120.25
|
0.55
|
Greenville
|
2
|
37
|
120.25
|
0.55
|
Holly Ruidge
|
1
|
38
|
123.5
|
0.56
|
Lexington
|
1
|
40
|
130.00
|
0.59
|
Cary
|
2
|
40
|
130.00
|
0.59
|
Satartia
|
2
|
41
|
133.25
|
0.60
|
Arcola
|
1
|
41
|
133.25
|
0.60
|
Avon
|
1
|
44
|
143.00
|
0.65
|
Chatham
|
1
|
45
|
146.25
|
0.66
|
Glen Allan
|
1
|
45
|
146.25
|
0.66
|
Canton
|
2
|
46
|
149.50
|
0.68
|
Bentonia
|
1
|
47
|
152.75
|
0.69
|
Leland
|
3
|
48
|
156.00
|
0.71
|
Schlater
|
2
|
49
|
159.25
|
0.72
|
Flora
|
2
|
49
|
159.25
|
0.72
|
Vaughan
|
1
|
53
|
159.00
|
0.72
|
Minter City
|
1
|
53
|
159.00
|
0.72
|
Drew
|
3
|
55
|
165.00
|
0.75
|
Goodman
|
1
|
55
|
165.00
|
0.75
|
Stoneville
|
2
|
56
|
168.00
|
0.76
|
West
|
1
|
60
|
180.00
|
0.82
|
Greenwood
|
4
|
60
|
180.00
|
0.82
|
Winterville
|
1
|
63
|
189.00
|
0.86
|
Rome
|
1
|
66
|
198.00
|
0.90
|
Source: National Agricultural Statistics Service (NASS), Mississippi.
| ||||
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