Linear Programming Model
Alan Manne in his paper seeks to address the problems of estimating output capabilities for an entire economy. The paper takes one industry experiment, the petroleum refining industry, which essentially relies on engineering data for its purpose. The paper uses linear programming to forecast the industry’s reliability. The purpose is to give numerical answers to questions about the production capability of this industry and take into account the potential substitution between alternative production processes.
In this petroleum model, the question asked was: by using the refining equipment and raw materials that were available then, what would be the product mix alternatives between the output of JP-4 jet fuel and the output of other refinery product, and how would the alternatives be affected by a reduction in the available capacity of refining equipment? These estimates provided the first step in the construction of a linear programming model of the U.S refining and crude oil production. In setting up this model that covered the whole industry, simplifying assumptions were involved and a considerable margin for error in each detailed estimate.
Most importantly, is that the model’s predictions were in line with observable events in two important aspects. Firstly is that the industry could have produced only a slightly higher quantity of the 1952- 53 product mix and secondly, that shadow prices on individual items in this particular product mix correlate fairly well with the actual market prices that prevailed during the 1952-53 period. It’s also important to note that the chief discrepancy between the market price and the shadow prices occurred in the case of product categories that had not been of primary concern the liquefied petroleum gases and number 6 fuel oil.
The study put in some assumptions to enable it to be successful. As would be expected scant attention was placed on the dynamic aspects and the geographical aspect of the problem. The study continues as though the refining equipment and the product were concentrated at a single point in time and space. The study model also neglects the impact of transportation dynamics and the implications of new investments and inventory accumulation.
Linear programming is being used in place of the square Leontief inter-industry flow matrix process. Unlike the latter, the linear programming analysis model provides a more satisfactory allowance for both substitutability and complementarity effects. In the paper, success is dependent on the formulation of meaningful problems, the collection of suitable data, the computation of large scale systems, and the testing of results. This is to be aided by the linear programming model.
The model used is the conventional linear programming whose mathematical model can be described to refer to maximization of linear form, subject to linear inequality restraints. This model provides numerous possibilities for varying product mix.
The research paper carries out linear programming calculation that shows a not so linear relationship. According to the results obtained, the oil industry can neither substitute jet fuel for other products at a constant barrel–for–barrel rate. The model also indicates that the higher the level of jet fuel output, the greater will be the volume of other products that will have to be sacrificed to make an additional barrel of jet fuel.
In conclusion, the most satisfactory check upon the goodness of a model will come from the scrutiny of the structure by refiners themselves. The data in the model is outlined in detailed physical quantities rather than in dollars aggregates that would call for a comparison between the estimates and the data available within individual companies.
Network Model- Minimal Spanning Tree Model
In this model, a minimum spanning tree technology (MST) is used in research whose objective was to optimize the interrelation and hierarchical network design of Indonesian airports. It was also meant to determine the position of Indonesian airports based on the ASEAN. This is so because, for an airport to achieve the optimal role, the airports should be connected. Such interrelations enable to accommodate the growing demand for flights and also be able to maximize the correlation of economic potential of each region in Indonesia. Furthermore, strong interrelation among regions will become a competitive advantage when facing connectivity issues at a regional level and an international level.
The research was conducted as mentioned earlier, using the minimum spanning tree (MST) technique. The research was based on secondary data, that is, flight frequencies, the distance between the airports in a network, and the values of GDRP in each province in Indonesia. The research was purposively done to design and analyze the interrelation and hierarchical network that connected all the airports in Indonesia and thirdly, to identify the impact of the ASEAN Open sky policy.
These airports include Sultan Iskandar Muda (BTJ), Polonia (MES), Minangkabau (PDG), Sultan Syarif Kasim II (PKU), Sultan Thaha (DJB), S.M. Badaruddin II (PLM), Fatmawati Soekarno (BKS), Radin Inten II (TKG), Depati Amir (PGK), Hang Nadim (BTH), Halim Perdanakusuma (HLP), Husein Sastranegara (BDO), Adi Sumarmo (SOC), Adi Sutjipto (JOG), Juanda (SUB), Soekarno Hatta (CGK), Ngurah Rai (DPS), Supadio (PNK), Tjilik Riwut (PKY), Syamsuddin Noor (BDJ), Sepinggan (BPN), Sam Ratulangi (MDC), Mutiara (PLW), SultanHasanuddin (UPG), Wolter Monginsidi (KDI), Djalaluddin (GTO), Tampa Padang (MJU), Lombok Baru (LOP), Eltari (KOE), Pattimura (AMQ), Sultan Babullah (TTE), Rendani (MKW), and Sentani (DJJ).
In response to the more competitive market of the airline industry in Indonesia, the airline companies need to be able to optimize their operations activities without sacrificing the criteria of the interrelation and hierarchy among the airports in the country. This is only achievable by optimizing the network design of Indonesian airports, where the optimal network should not only be seen from the aspect of demand but from total distance to connect all the airports and the correlation of economic potential of each region in Indonesia. It is also observed that the economic potential of a region affects the connectivity between the two regions.
This is shown by Gross Domestic Regional Product (GDRP). It is observed that the stronger the correlation between two regions is, the stronger the connectivity between two regions the greater the connectivity. The connectivity is therefore critical, and it should be built properly. This local connectivity will alleviate the economic transactions and resource movement from one region to another in a more effective way. Besides that, regionally, this connectivity will support the realization of the ASEAN community and economic integration in near future. The connectivity within this network is expected to reduce business transaction cost, time, and travel cost and to connect the core and the periphery in the ASEAN region.
The result of the research shows that networks of airports were obtained based on the presence of commercial flights from one airport to another. The result also showed the network of the airport recently used by airlines in Indonesia. In the obtained network it shows that airports had been connected except a few which had no commercial flight to/ from that airport. Meanwhile, other airports were functioning as the main and the busiest hubs in the network.
The total distance to connect all the airports using the network was 84, 108.58 km. The MST network flight frequency showed that only five airports had the biggest flight services. If all the airports were connected by maximizing the flight frequencies from one airport to the other, the interrelation and hierarchical network would become more efficient and inclusive.
In conclusion, the outcome of the research resulted in several points. That the current network of airports in Indonesia does not represent the optimal network. A new system was suggested. This system was to be put in place such that airports and regions regarded as the hub and those regarded as spokes formed a network of their own.
Multiple Linear Regression Model
Multiple linear regression study objective was based on malaria distribution. The research was aimed at developing a distribution map on the spread of malaria. The study took advantage of techniques such as the GIS and sensing remote data techniques. This model was built to enable the determination of malaria levels in different sectors. In this model, malaria reported cases served as dependent variables whereas the independent variables were Population density, Rainfall, distance to rivers, water pods and health facilities, temperature, land use/ land cover, distance to road, and normalized difference vegetation index.
The study was conducted on a vast 1454.11sq. Km in the Varanasi district, UP. The GIS software was used in generating thematic maps that relate to the occurrence of malaria. Multiple linear regression models used in this study were based on the variables of 50×50 networks which occur in form of the matrix 38622×9. This matrix is transferred from the GIS. The application of this model also helped to develop a malaria vector breeding source.
Different parameters that relate to the occurrence of malaria were used in coming up with thematic maps or data layers in GIS. These parameters were based on such things as distance to water pods, hospital, the rainfall distribution, temperature, and the population of the community. In the study, Lewis Version -3.4 and the Ach Gis Version 9. The GIS and ERDAS software’s were important in the production of susceptibility malaria layer maps. The topography map whose scale was represented as 1:50,000 were essential in the digitalization of the host district and also helped to develop its boundary.. The GPS technology was also an important tool. It was used for the reference point to malaria-prone areas. The technology was used to survey the existing care facilities.
The regression coefficients of this model were given, rainfall, temperature, population density, and the others that have already been mentioned.
The model is summarized as follows:-
M=1593.04+(0.62*Pd)+((-0.663)*Rf)+((-0.0012)*Dri)+((0.0019)*Dpo)+(0.0003*Dhf)+(63.44*Temp.)+(0.119*Lu/Lu) + (-0.0002)*Dro) +(0.901*NDVI)
- M – Occurrence of malaria,
- Pd- population density,
- Rf- rainfall,
- Dri –distance to river or stream,
- Dhf is the distance to a health facility,
- Temp – temperature,
- Lu/Lc Land use / Land cover, Dro – distance to road and NDVI is normalized difference vegetation index.