# Abstracts

laranja; programação inteira mista; localização de planta industrial

This study discusses the formulation and application of a mathematical location model. The model was used to determine the optimum locations for orange packing houses in the state of São Paulo, Brazil. The proposed model considers orange packing-houses of seven different capacities, seeking to minimize their implementation, processing, and transportation costs. It is based on the theory of location and makes use of a mixed-integer programming structure. For the purposes of the current analysis, 40 Rural Development Offices (EDR) in the state of São Paulo have been adopted as hubs of supply and consumption and as focal points for the installation of orange packing facilities. The main parameters considered in the model include the costs of orange processing/packing and transportation, the costs to implement different capacity orange packing-houses, and each EDR region’s orange supply and user demand. Four distinct scenarios were analyzed, each conditioned by a different mix of specific assumptions: a maximum of one facility per region, equality between supply and demand, and a lack of pre-existent facilities. Results have shown a low volume of inter-regional orange transport and economies of scale in packing-house operations. The model determined intermediate areas as the best packing-house locations and identified areas for future plant construction.

packing-houses; orange; mixed-integer programming; packing-houses; industrial plant location

Spatial distribution of orange packing houses in the state of São Paulo, Brazil: an application of the theory of location

Simone Yuri RamosI; José Vicente Caixeta FilhoII

IAgronomist and Master in Applied Economics by ESALQ/USP. E-mail: syramos2002@yahoo.com.br

IIAssociate Professor at the Department of Agricultural Economics in ESALQ/USP. E-mail: jvcaixet@esalq.usp.br

ABSTRACT

This study discusses the formulation and application of a mathematical location model. The model was used to determine the optimum locations for orange packing houses in the state of São Paulo, Brazil. The proposed model considers orange packing-houses of seven different capacities, seeking to minimize their implementation, processing, and transportation costs. It is based on the theory of location and makes use of a mixed-integer programming structure. For the purposes of the current analysis, 40 Rural Development Offices (EDR) in the state of São Paulo have been adopted as hubs of supply and consumption and as focal points for the installation of orange packing facilities. The main parameters considered in the model include the costs of orange processing/packing and transportation, the costs to implement different capacity orange packing-houses, and each EDR regions orange supply and user demand. Four distinct scenarios were analyzed, each conditioned by a different mix of specific assumptions: a maximum of one facility per region, equality between supply and demand, and a lack of pre-existent facilities. Results have shown a low volume of inter-regional orange transport and economies of scale in packing-house operations. The model determined intermediate areas as the best packing-house locations and identified areas for future plant construction.

Key-words: orange, mixed-integer programming, packing-houses, industrial plant location.

1. Introduction

Implementation of the state of São Paulos concentrated orange juice industry began in the mid 1960s, sparking a profound change in the structure of orange commercialization in Brazil. The states industry is now the Brazilian orange production systems dynamic pole and the countrys major orange juice producer and exporter. The São Paulo market dictates domestic fruit availability according to its own needs and demands while meeting market demand from North America and Europe.

Due to frequent frosts in Florida and high domestic demand, the United States was the major importer of the Brazilian concentrated orange juice in the 1980s, accounting for around 47% of Brazils orange juice exports. At this time, this demand and high orange juice prices in the international market led Brazilian orange producers to rapidly plant new trees in a haphazard fashion.

Floridas orange crop recovered in the 1990s, based on increased planting density and the relocation of production to less frost prone areas. This, allied with the growth of Brazils production, generated a huge increase in international concentrated orange juice supply, a drop in international orange juice prices, and a consequent sharp reduction in the prices offered to orange producers.

In this context, one of the major problems facing orange producers in São Paulo is an excess of oranges for processing. ABECITRUS statistics show that during the 90s orange production in the state of São Paulos grew 2.62% annually whereas industrial orange processing capacity grew 2.14% a year, creating a oversupply of raw material. The solution to this oversupply problem will come from slightly smaller increases in orange production, growth of concentrated orange juice exports, and growth and strengthening of the domestic in natura whole orange market. Should these solutions be implemented, there exists a great opportunity for Brazils citrus agricultural-industrial system to expand its market and cope with the abundant supply of inputs.

Over the last few decades, the Brazilian in natura whole orange market has remained a second tier industry, a result of the focus on concentrated juice exportation. For the majority of Brazils orange juice producers, the in natura orange market has become residual, seen as an option for times when the price of concentrated juice suffers a significant reduction. Relegation to the second tier has left the in natura orange sector to producers who show a low level of professional skill and whose technological development has lagged. Neves et al. (2001) remarks that the in natura orange market suffers from deficiencies related to fruit standardization, distribution logistics, producer cohesion and professionalism, marketing, and domestic sales focus. In order to overcome these and other difficulties, the system requires a better structure, more professional work habits, and more modern production and distribution techniques. A more efficient in natura orange distribution system would significantly reduce product transportation costs 4% portion of total segment revenues and their 8 to 16% portion of final product prices. Analysis of the spatial distribution of packing-houses in the state of São Paulo can be used to improve in natura orange distribution efficiencies, minimize costs, and enhance that segments competitive position.

The aim of this study is to propose and apply a mathematical model that measures the effect of packing-house location and capacity on whole orange transportation costs, packing plant implementation costs, and whole orange processing costs. The model is applied to hypothetical packing houses of different capacities located in expressive regions of the state of São Paulo.

2. Methodology

2.1 Theory of Location

The theoretic reference used in this study is the theory of industrial plant location, initially developed by Alfred Weber (1909) and improved through the evolution of mathematical and computer techniques.

According to Saboya (2001), the Weberian model considers that the decision of where to locate an industrial plant is determined by three attracting influences, transportation costs, labor costs, and the forces of clustering and non-clustering, with transportation costs having the most affect. In his model, the point of minimum transportation cost is obtained using a location triangle formed by three attracting forces: the location of the consumer market and the location of two raw material sources.

The point of balance of these three forces initially determines a point of minimum total transportation costs for an industrial activity. Having established where this balance lies, adjustments are made upon consideration of the possible advantages gained at other locations, such as less expensive labor, clustered economies, and tax incentives.

The effects of Webers two other attracting forces (labor and clustering) on the industrys location were analyzed using isodapan curves. These curves define a group of points that represent a distance from the minimum transportation cost site at which transportation costs are equally increased. For the analysis of the influence of labor costs on location, Weber used the concept of critical isodapan. The critical isodapan of labor is obtained when the increase in transportation cost equals the cost reduction from the availability of less expensive labor. Lopes (1997) points out that a change of initial plant location would not be interesting if it was within the critical isodapan. On the other hand, if the initial location was outside the critical isodapan, the change is then feasible.

Weber also considered the effect of clustering factors on plant location as economies can arise should enterprises group in a given area. To analyze the effect of industrial clustering, the concept of isodapan was once again used. In the Weberian model, the clustering critical isodapan intersections were where economies arising from industrial clustering equal the additional costs incurred as the industry moves from the point of minimum transportation costs.

The rise of the linear programming in the mid 40s, particularly the transportation model, introduced situations more complex than those Weber initially considered. From this time on, as Lopes (1997) points out, it has been possible to add several regions of demand and raw material offer to the Weberian model.

Lopes (1997) remarked that a great advance in location modeling came from the use of mixed-integer programming, more specifically, from the use of binary variables in the model. The inclusion of binary variables has made it possible to design location models that can test not only for the location that minimizes transportation costs, but also each regions ideal processing capacity. According to the author, the theory of location, in terms of programming, can be constructed as a variation of the transportation model, which, along with integer programming, is a very powerful tool for establishing the best place to locate an industry.

The advent of mixed-integer programming led to projects to determine optimum enterprise location. Among them are works addressed to the Brazilian situation by Almeida (1981), Canziani (1991) and Lopes (1997), which considered the effect of economies of scale on transportation and processing, and studies by Kilmer et al. (1983), Babcock et al. (1985), Brown et al. (1996), Durham et al. (1996) and Snyder et al. (1999) that focus on the more universal situation. Kilmer et al. (1983) used dynamic programming to analyze short-term adjustments, thereby removing one of the limitations of static location models; and Durham et al. (1996) developed a non-linear programming model to examine the influence of pricing on optimum plant location.

2.2 Proposed Model

Using mixed-integer programming, a model was formulated to determine the optimum locations for orange packing-houses in the state of São Paulo. The generic structure of the model is as follows:

A) Objective Function:

where,

Xij = amount of raw material transported from producing region ( i ) to packing-houses in region ( j );

Cij = cost of transporting raw material from the producing region ( i ) to packing-houses in region ( j );

Hj = total operational costs of packing-houses located in region ( j );

Bjm = cost of in natura orange transportation from packing-houses in region ( j ) to the consumer market in region ( m );

Yjm = amount of in natura oranges transported from packing-houses located in region ( j ) to the consuming market located in region ( m );

B) Constraints:

• The orange output of region ( i ) should not exceed the regions production capacity:

• where,

= amount of oranges transported from producing region ( i ) to the packing-houses established in various regions ( j );

Si = total amount of oranges available in the producing area ( i ).

• Orange demand by processing centers:

• where,

= amount of oranges received from all the producing regions ( i ) that meets the total demand of packing-houses of size ( t ) established in facility ( j );

= total amount demanded by all packing-houses of size ( t ) established in facility ( j );

= binary variable ( zero & one ) associated to the establishment or non-establishment of a packing-houses of size ( t ) in facility ( j ).

• Orange output of packing-houses:

• = amount of oranges transported from packing-houses established in facility ( j ) that will supply the market in region ( m );

= amount of oranges received from all producing regions ( i ) to meet the total demand of packing-houses established in facility ( j );

• In natura orange consuming market demand:

• where,

= amount of oranges transported by the various packing-houses established in facilities ( j ) that will supply the market in region ( m );

Dm = in natura orange demand by consuming market in region ( m ).

• Balance between the consuming centers demand and facility output:

• where,

= total orange demand in region ( m );

= total amount of oranges offered by all packing-houses of size ( t ) in facility ( j ).

• In order to arrive at the total cost for packing-house implementation and product processing at each facility ( j ), the following equation was inserted into the model:

• where,

COj = operational cost (implementation & processing) of packing-houses located in processing region ( j ).

The proposed model is limited to the in natura orange market in the state of São Paulo; it does not consider the industrys installed capacity or oranges exported to other Brazilian states and foreign countries.

In equations (1) and (7), the respective upper limits for i, j, m and t were 40 (number of producing regions), 40 (number of producing regions as prospective packing-house locations), 40 (number of consuming markets) and 7 (number of packing-house sizes). Notice that the regions where the center cities housing EDR offices were situated were considered producing, processing, and consuming regions. The mathematical structure presented (expressions 1 to 6) was coded and processed using the GAMS optimization system (Brooke et al., 1982).

2.3 Scenarios

Four scenarios were created to determine optimum packing-house locations in the state of São Paulo. They considered variations in the EDR regions in natura orange supply and demand, the costs of orange transportation and packing-house implementation, and packing-house processing capacity. All scenarios assume that there are no pre-existing orange packing-houses in the state. Scenarios 2 and 4 were also conditioned by restrictions to the maximum number of packing-houses that could be established in each region and Scenarios 3 and 4 by assumptions regarding regional supply and demand conditions.

Scenario 1 modeled the state of São Paulo conditioned only by the assumption that there are no pre-existing orange packing-houses in the state, a condition applied to all four scenarios. This scenario was designed to determine the optimum number, location, and processing capacity of packing houses in each EDRs region for comparison with the actual situation. Scenario 2 differed from Scenario 1 in that the number of packing-houses that could be established in any EDR region was restricted to one. The effect of this restriction on the optimum packing-house locations determined in Scenario 1 was then analyzed. The results from Scenarios 1 and 2 showed that the ideal number of packing-houses needed to meet the state São Paulos in natura orange demand is much smaller than the actual number of packing-houses operating in the state.

In Scenario 3, each EDR regions in natura orange supply and demand were considered to be in balance, a significant distortion of reality. This scenario was created to determine the ideal number and location of packing houses if the states in natura orange consumption increased to equal state production. In Scenario 4, it was again assumed that there was equality between orange supply and demand in each EDR region but that no more than one packing-house could be established in any region.

2.4 Data specifications

2.4.1 Sub division of study area

To simplify the analyses related to in natura orange supply and demand flows and the determination of transportation and facility implementation costs, 40 existing EDRs, as defined by the State of São Paulos Secretary of Agriculture, were selected to represent specific regions in the state of São Paulo. Each of the 40 EDRs selected is located in close proximity to one specific regions most important city; each EDR represents a center of supply and consumption; and the location of each EDR is a possible location of one or more packing-houses (see: Figure 1). This choice to use the location of EDRs serves as a reference and does not presuppose that facilities would be established in a regions most important city, rather, that any facilities established would be distributed within the citys region.

2.4.2 Orange supply and demand

Each regions annual in natura orange supply was considered to be twenty-two percent of the regions total orange supply. This percentage was adopted because it was the states contribution to the countrys total production of oranges destined for the domestic in natura orange market in the 90s, a time when excess orange supply became one of the major problems for São Paulos citrus industry. The demand for in natura oranges within each EDR region was obtained by considering per capita consumption of oranges in the years 1995/96 (12.8 Kilos/year) and the population in each region. This per capita consumption level was taken from the most recent data from the Brazilian Institute of Geography and Statistics (IBGE). It is important to point out that the most adequate way of measuring each regions orange output and demand would be from forecasts of the respective supply and demand functions  which goes beyond the scope of this study. The supply and demand values adopted in this study can be considered simplifications of reality.

2.4.3 Packing-house potential locations and processing capacities

To reduce model processing time, the number of variables, and the need for even more detailed data, we opted to analyze only those 40 regions with an EDR. The seven most common processing capacities in the state were adopted as the orange packing-house sizes used in the simulations: 50 thousand, 100 thousand, 250 thousand, 500 thousand, 1 million, 2 million and 3 million boxes of oranges packed per year.

2.4.4 Processing, implementation, and transports costs

The cost of implementation was determined by adding the prices of packing-house equipment, obtained from a field study, to the cost of facility construction. For the value of construction, R$150.00 per square meter of facility constructed was adopted. According to the field study, packing-houses that process up to 250 thousand boxes per year make use of an area of approximately one thousand square meters. Facilities with greater processing capacity were considered to use two thousand square meters of space. The costs of transportation between the 40 raw material supplying regions, the 40 possible processing regions, and the 40 consuming centers were calculated using the table of road freight prices provided by companies working in the sector and the distance the materials needed to be transported. Packing-house processing costs were obtained through a field study. 3. Results and discussion In Scenario 1, the model suggested the implementation of 12 facilities to process the state of São Paulos in natura orange demand. The packing houses were established within the EDRs of Araraquara (1 unit), Campinas (5 units), Dracena (1 unit), Itapetininga (1 unit), Limeira (1 unit), São José do Rio Preto (1 unit) and São Paulo (1 unit). The model suggested the establishment of greater capacity facilities (40,800 t/year). The only low capacity unit (2,040 t/year) was established in the Dracena region. The minimum cost to implement all the packing houses and their annual expenses for operations and product transportation was R$14,372,200.

Our models results and FUNDECITRUSs 1998 study show that the number of facilities existing in the state of São Paulo, around 400, is far higher than the number needed to meet the states in natura orange demand. However, São Paulo is an exporter of in natura oranges to other Brazilian states and the countrys major orange juice production center. These two factors are not considered by our proposed model, which may explain the great difference noticed between the models results and the actual number of packing houses existing in the state.

As for the spatial distribution of facilities, it was noticed that the study prioritized the establishment of units in areas close to consuming markets, as shown by the number and location plants in the EDR regions centered on the cities of Campinas [a city adjacent to the city of São Paulo] and São Paulo. The packing plants hypothetically located in these two regions would supply almost 54% of the states demand. This differs significantly from current plant distribution, which locates plants in close proximity to the main orange producing centers. It was also found that regions that are in close proximity to both producing and consuming centers appeared as potential areas for the establishment of packing-houses, the cases of the EDR regions centered on Itapetininga, Limeira and Piracicaba1 1 For further details about this study, see Ramos (2001). .

According to our results, eight facilities would plainly meet the demand of all the EDRs in the state. It is important to point out that the demand from all the EDR regions with the exception of Assis, Pindamonhangaba, Dracena, Campinas, and Ribeirão Preto could be met by only one facility.

The analysis of marginal transportation costs reflects possible changes in the cost of transporting raw material from the producing region to the packing-house if the route must were to be altered. In general terms, the increase in cost is represented by the difference between the cost of transportation using the new route and the cost of transportation using the old, disabled route.

It was noticed that the supply of oranges from the Limeira region could meet the orange demand of the EDRs in Campinas and Piracicaba in all scenarios; and if these two EDR regions were to be supplied from Limeira, the increase in transportation costs would be nil. This is explained through the fact that Limeira is adjacent to Campinas and Piracicaba. In the case of the region centered on the city of São Paulos EDR, the main supplying regions would be Bragança Paulista, Campinas and Mogi das Cruzes.

In Scenario 2, the minimum cost to implement all the packing houses combined with their annual expenses for operations and product transportation was the same as that obtained in Scenario 1: R$14,372,200. Scenario 2 called for the establishment of 12 packing plants, also the same as in Scenario 1. However, due to Scenario 2s restriction that each region would house only one facility, packing-houses were established in regions close to the Campinas region, aiming to supply a region that, according to Scenario 1, required 5 packing plants to optimally meet demand. The following were other results of note from Scenario 2: inter-regional transport would be of minor importance; packing-house economies of scale were observed, as plants with greater processing capacity predominated in the Scenario (11 plants with a capacity of 40,800 t/year [1,000,000 boxes] and 1 plant with a capacity of 2,040 t/year [500,000 boxes]); and facilities were generally located in intermediate areas, close to both producing and consuming centers. In Scenario 3, eighty-one packing plants were established in 39 EDRs at a total cost of R$ 111,157,300. It was noticed that while packing plants would be established in the EDRs of most large orange producing regions, more plants were established adjacent to the consuming centers. In this scenario, 40% of the plants would be established in regions closer to consuming centers than to producing centers, 32% in intermediate areas, and 28% closer to the major orange producing regions.

In Scenario 4, the total cost of plant implementation, annual transportation, and processing was R\$ 140,182,800, with one packing-house established in each of the 40 EDR regions (an adopted maximum/region). In both Scenarios 3 and 4, inter-regional transport would be reduced from existing levels, as packing-house demands are met by 4 producing regions at most; and there was predominance of packing houses with higher processing capacities, which could result in economies of packing-house scale.

4. Conclusions

The results from the proposed optimization model call for prioritizing the implementation of large capacity packing-houses (491,176 to 1,000,000 boxes/yr or 20,040 to 40,800 t/yr) to provide reasonable economies of scale. The model gave a preference to packing houses located in intermediate areas. However, it was found that the intermediate regions do not belong to the "citrus business belt," rather they are actually quite close to the states most expressive consuming centers. This allows a conclusion that the solution presented by the optimization model emphasized plant locations in the proximity of centers of demand. It was also observed that packing-houses that presented a raw material deficit showed the greatest need for inter-regional transportation services.

In Scenarios 1 and 2, it was found that only 12 packing-houses could process enough oranges to meet the states entire in natura orange demand. In Scenarios 3 and 4, it was observed that 81 and 103 packing-houses were implemented respectively. From these findings, it is concluded that the approximately 400 packing houses now existing in the state greatly exceeds the number of packing-houses needed to meet actual in natura orange demand.

Location models can be considered as an important tool to assist in entrepreneurial and public policy decision making, permitting the agents to evaluate the location and processing capacity of future industries. Location models are able to provide the optimum number, size, productive capacity, and location of new industrial concerns, suggest the most efficient way to structure economic activities, and thereby secure for these industries a competitive advantage.

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