The petroleum industry has a complex, inflexible and challenging supply chain (SC) that impacts both the national economy as well as people’s daily lives with a range of services, including transportation, heating, electricity, lubricants, as well as chemicals and petrochemicals. In the petroleum industry, supply chain management presents several challenges, especially in the logistics sector, that are not found in other industries. In addition, logistical challenges contribute significantly to the cost of oil. Uncertainty regarding customer demand and supply significantly affects SC networks. Hence, SC flexibility can be maintained by addressing uncertainty. On the other hand, in the real world, decision-making challenges are often ambiguous or vague. In some cases, measurements are incorrect owing to measurement errors, instrument faults, etc., which lead to a pentagonal fuzzy number (PFN) which is the extension of a fuzzy number. Therefore, it is necessary to develop quantitative models to optimize logistics operations and supply chain networks. This study proposed a linear programming model under an uncertain environment. The model minimizes the cost along the refineries, depots, multimode transport and demand nodes. Further developed pentagonal fuzzy optimization, an alternative approach is developed to solve the downstream supply chain using the mixed-integer linear programming (MILP) model to obtain a feasible solution to the fuzzy transportation cost problem. In this model, the coefficient of the transportation costs and parameters is assumed to be a pentagonal fuzzy number. Furthermore, defuzzification is performed using an accuracy function. To validate the model and technique and feasibility solution, an illustrative example of the oil and gas SC is considered, providing improved results compared with existing techniques and demonstrating its ability to benefit petroleum companies is the objective of this study.
The manufacturing of products through hand dominated the worldwide economic system as much as in the mid-eighteenth century. However, a good way to meet marketplace needs is to raise manufacturing ranges, which necessitates a transfer from guide labor to steam-powered machines. This marked the beginning of a brand-new generation in global records referred to as the First Industrial Revolution began in England and primarily trusted coal as an essential factor for economic strength and development [
Although coal is still widely used in many regions of the world, it is no longer the main energy source because other more powerful sources have been found. Consequently, oil exploration began at the end of the nineteenth century, after the Second Industrial Revolution. Drake drilled the first oil well in Pennsylvania and built refineries that successfully separate kerosene from crude oil for use in lighting and heating. Automobiles were developed in the early 20th century, requiring the extraction of gasoline. This crude oil product was initially an unwanted byproduct [
Oil supply chains are dynamic, complicated, and have significant revenue and expenses. They are divided into three primary areas: upstream, which deals with production and exploration; midstream, which handles refinery processes; and downstream, which considers the supply of oil products [
Diverse origins, such as measurement errors, limited historical and statistical data, imprecise theory, inadequate knowledge expression, or reliance on human judgement, are uncertainties about facts, numbers, and science. Furthermore, in modelling engineering and science challenges, uncertainty theory plays an important role. Recently, significant changes have occurred in this area. Various theories have been developed to measure uncertainity. Zadeh [
The modern world would not be able to develop without oil and gas. No country can function smoothly without such resources. Following a recent take of events, the Covid pandemic and decreased manufacturing of petroleum products caused the prices and demand of oil to fall dramatically. This situation makes it difficult to predict the upcoming pricing of oil in the international market. This variability and sinking prices of oil products have pushed international companies in fuel markets to reorganize their corporate structures along with their supply chain networks to manage their expenses and costs. Such restructuring, which makes the business more efficient than before in terms of resources and time, is only effective when it remains an on-going process for improvement [
Upstream is an oil supply chain that involves searching for locations that may have hydrocarbons and drilling operations that carry the hydrocarbons to the ground and crude oil transportation. Some authors classify the transportation of crude oil as an upstream activity, whereas others classify it as a midstream activity [
Lima et al. [
Author | Uncertain environment | Multimodal transportation | Objective function | |
---|---|---|---|---|
Cost | Other | |||
Attia et al. [ |
✓ | × | ✓ | × |
Amor et al. [ |
× | × | × | × |
Lima et al. [ |
✓ | × | ✓ | ✓ |
Pudasaini [ |
✓ | × | ✓ | × |
Lima et al. [ |
× | ✓ | ✓ | × |
Wang et al. [ |
✓ | ✓ | ✓ | ✓ |
Fermandes et al. [ |
× | ✓ | × | × |
Kazemi et al. [ |
× | ✓ | ✓ | × |
Zhu et al. [ |
✓ | ✓ | ✓ | ✓ |
According to a literature review, downstream oil and gas supply chain problems contain significant uncertainties. A fuzzy programming strategy has proven highly effective in dealing with a high level of uncertainty in business conditions. This study has the following framework. Section 3 is based on the preliminaries. Section 4 discusses a petroleum supply chain network in a fuzzy environment. The solution methodology used to deal with such a fuzzy environment is discussed in Sections 5 and 6, respectively. To validate this methodology, an illustrative case study is presented in Section 7. Section 8 provides managerial insights and interpretations. Section 9 presents a discussion of the proposed model as well as methodology, and Section 10 presents the conclusions in which the results obtained using the proposed method are presented.
Here, review some fundamental definitions and results of fuzzy numbers.
A fuzzy set
Here,
A fuzzy number Membership value of
Owing to the various applications of the fuzzy number, two forms of fuzzy numbers, namely, triangular and trapezoidal fuzzy numbers, are introduced in the field of fuzzy algebra.
The triangular fuzzy number
The trapezoidal fuzzy number
The pentagonal fuzzy number
Some basic arithmetic operations are defined as below:
Addition
Let Subtraction
Let Scalar multiplication
Let
Consider the pentagonal fuzzy number
Accuracy function
Here
The goal of this section is to construct a single-objective optimization model. To minimize the costs of single-objective, which are primarily transportation-related, it is necessary to consider customer demand, product yield, and storage and transportation capacity constraints.
This study addressed an
The model includes product
In the MILP model, binary and continuous decision variables were addressed. A binary variable is an integer with a value of 0 or 1. In this case,
The objective function
A set of constraints that expresses the problem parameters is presented in the following subsections.
expression
Constraint
Each new depot must have a capacity greater than the number of products that pass through it. Adding a factor of
Balance constraint
Consider single-objective optimization problem
Only the cost coefficient is converted into a PFN by taking the remaining parameters and decision variables as crisp values. Transform the cost coefficient, remaining parameters and decision variables into a pentagonal fuzzy number Change the cost coefficient and the remaining crisp parameters into a pentagonal fuzzy number.
Here, only one model is discussed: the cost coefficient and the remaining crisp parameters are converted into pentagonal fuzzy numbers to achieve the desired goal. Then, the crisp linear model is converted into pentagonal fuzzy linear programming model using the second model.
Most decision-making challenges in the real world are ambiguous or uncertain. The use of fuzzy numbers is prevalent in many areas, including fuzzy process modelling and decision making. The management of product supply chains is a critical aspect of today’s dynamic market so that businesses can offer their customers competitive rates. Because of market uncertainty, supply chain management has become more challenging. When dealing with a fuzzy unknown parameter in a supply chain, it seems natural to use a pentagonal fuzzy number instead of a fuzzy number for efficient and improved results. Because the mathematical model effectively addresses uncertainty, the pentagonal fuzzy optimization model can deal with ambiguous data more accurately. A flowchart of thr optimization technique is shown in
In this study, the downstream petroleum supply chain according to Pakistan’s region is considered. The under discussed multimode optimization model was further redesigned according to the fuzzy environment. Our natural environment is fuzzy in nature and there are many unpredictable changes that appear on a daily basis in Pakistan due to political, economic or environmental triggers. The fuel prices in Pakistan change abruptly within a month, as shown in
Product name | Effective price from 01 Feb 2022 | Effective Price from 16 Feb 2022 |
---|---|---|
Gasoline | 125.83 | 134.49 |
Diesel | 144.62 | 154.15 |
JP | 129.20 | 140.65 |
As the downstream petroleum supply chain in Pakistan is the main target, the model is formulated accordingly. The main hub for crude oil is Port Qasim Sindh, from which several retailers consume demand through pipelines, ships and roads. Pipelines and ships are cost-effective methods. The Punjab and Khyber Pakhtoon Khawa provinces of Pakistan are not directly connected by any sea port and the cheapest oil transportation mode for these regions is pipeline. The Pak Arab refinery limited (PARCO) transfers crude oil directly from Karachi to Multan’s refinery by an 870 km pipeline, further another 362 km long pipeline transfers that product to nearby Lahore stations. Pakistan’s oil pipeline is based on 16309 km network, 47% of which is shared by different refineries, while 57% is owned by PARCO. For model formulation, the main refineries and oil depots from a specific region were considered to analyze the validity of this study. Two of the six refineries were from Balochistan, Karachi, Multan and Rawalpindi. Petroleum products were further transferred to four distribution centers through different means (see
Based on hypothetical data according to present time this petroleum supply chain network under study is operating six refineries (Cnergyico Pakistan limited (CPL), PARCO, National refiney limited (NRL), ENAR petroleum refining facility (EPRF), Attock refinery limited (ARL) and Pakistan refinery limited (PRL)) four potential depots and further main three customers for each distributor namely as industries, domestic sector and railways. From refinery to distributor and further from distributor to customer dual transportation means are specifically considered as shown in
To make the optimization model flexible, it is necessary to consider its fuzzy nature. For this purpose, the considered multi-mode model is further converted into a pentagonal fuzzy multi-mode model by converting the parameters into pentagonal fuzzy numbers (see
Depots | Fixed cost |
---|---|
Karachi | (850, 900, 1000, 1100, 1225) |
Lahore | (1290, 1400, 1500, 1600, 1875) |
Islamabad | (1435, 1600, 1700, 1800, 2100) |
Multan | (1649, 1800, 1900, 2000, 2380) |
Products | Industrial sector | Domestic sector | Railway |
---|---|---|---|
Diesel | (1670, 1820, 1920, 2020, 2190) | (2160, 2310, 2410, 2510, 2580) | (870, 1020, 1120, 1220, 1390) |
Gasoline | (1650, 1800, 1900, 2000, 2160) | (970, 1120, 1220, 1320, 1490) | (760, 910, 1010, 1220, 1360) |
Jet fuel | (770, 920, 1020, 1120, 1300) | (960, 1110, 1210, 1310, 1430) | (1850, 1000, 1100, 1200, 1370) |
Refinery | Capacity |
---|---|
CPL | (6.0, 6.5, 7.0, 7.5, 8.5) |
PARCO | (3.5, 4.0, 4.5, 5.0, 6.0) |
NRL | (1.83, 2.33, 2.83, 3.33, 4.33) |
EPRF | (1.44, 1.70, 2.44, 2.94, 3.94) |
ARL | (2.30, 2.39, 3.30, 3.80, 5.807) |
PRL | (1.1, 2.50, 2.1, 2.6, 4.6006) |
Product | Refinery | Depots | |||||||
---|---|---|---|---|---|---|---|---|---|
Karachi | Lahore | Islamabad | Multan | ||||||
Diesel | CPL | (1913, 1980, 2080, 2180, 2580) | (748, 800, 900, 1000, 1400) | (1973, 2040, 2140, 2240, 2640) | (968, 1020, 1120, 1220, 1620) | (1953, 2020, 2120, 2220, 2620) | (958, 1010, 1100, 1210, 1610) | (943, 1010, 1110, 1210, 2610) | (838, 890, 990, 1090, 1490) |
PARCO | (1889, 1956, 2056, 2156, 2556) | (748, 800, 900, 1000, 1400) | (949, 1016, 1116, 1216, 1616) | (948, 1000, 1100, 1200, 1600) | (1963, 2030, 2130, 2230, 2630) | (958, 1010, 1110, 1210, 1610 ) | (903, 970, 1070, 1170, 1570) | (828, 880, 980, 1080, 1480) | |
NRL | (1893, 1960, 2060, 2160, 2560) | (0, 0, 0, 100, 500) | (953, 1020, 1120, 1220, 1620) | (958, 1010, 1110, 1210, 1610) | (1973, 2040, 2140, 2240, 2640) | (948, 1000, 1100, 1200, 1600) | (1923, 1990, 2090, 2190, 2590) | (838, 890, 990, 1090, 1490) | |
EPRF | (1973, 2040, 2140, 2240, 2640) | (0, 0, 0, 100, 500) | (1903, 1970, 2070, 2170, 2570) | (958, 1000, 1100, 1200, 1600) | (1893, 1960, 2060, 2160, 2560) | (968, 1020, 1120, 1220, 1620) | (913, 1980, 1080, 1180, 1580) | (848, 880, 980, 1080, 1480) | |
ARL | (909, 976, 1076, 1176, 1576) | (1048, 110, 1200, 1300, 1700) | (1989, 2056, 2156, 2256, 2656) | (648, 700, 800, 900, 1300) | (1023, 1090, 1190, 1290, 1690) | (0, 0, 0, 100, 500) | (933, 1000, 1100, 1200, 1600) | (848, 900, 1000, 1100, 1500) | |
PRL | (1933, 2000, 2100, 2200, 2600) | (638, 690, 790, 890, 1290) | (1903, 1970, 2070, 2170, 2570) | (838, 890, 990, 1090, 1490) | (913, 980, 1080, 1180, 1580) | (648, 700, 800, 900, 1300) | (1833, 1950, 2050, 2150, 2550) | (0, 0, 0, 100, 500) | |
Gasoline | CPL | (631, 721, 820, 920, 1320) | (806, 900, 1000, 1100, 1500) | (1711, 1800, 1900, 2000, 2400) | (946, 1040, 1140, 1240, 1640) | (1701, 1790, 1890, 1990, 2390) | (906, 1000, 1100, 1200, 1600) | (1691, 1780, 1880, 1980, 2380) | (796, 890, 990, 1090, 1490) |
PARCO | (1611, 1700, 1800, 1900, 2300) | (786, 880, 980, 1080, 1480) | (1671, 1760, 1860, 1960, 2360) | (926, 1020, 1120, 1220, 1620) | (1691, 1780, 1880, 1980, 2380) | (936, 1030, 1130, 1230, 1630) | (1631, 1720, 1820, 1920, 2300) | (796, 890, 990, 1090, 1490) | |
NRL | (611, 1700, 1800, 1900, 2300) | (0, 0, 0, 100, 500) | (1691, 1780, 1880, 1980, 2380) | (1006, 1100, 1200, 1300, 1700) | (1711, 1800, 1900, 2000, 2400) | (1046, 1140, 1240, 1340, 1740) | (1651, 1740, 1840, 1940, 2340) | (906, 1000, 1100, 1200, 1600) | |
EPRF | (611, 1700, 1800, 1900, 2300) | (0, 0, 0, 100, 500) | (1691, 1780, 1880, 1980, 2380) | (1006, 1100, 1200, 1300, 1700) | (1711, 1800, 1900, 2100, 2400) | (1046, 1040, 1240, 1340, 1740) | (1651, 1740, 1840, 1940, 2340) | (906, 1000, 1100, 1200, 1600) | |
ARL | (1691, 1780, 1880, 1980, 2380) | (1206, 1300, 1400, 1500, 1900) | (1631, 1720, 1820, 1920, 2320) | (1006, 1100, 1200, 1300, 1700) | (1611, 1700, 1800, 1900, 2300) | (0, 0, 0, 100, 500) | (1631, 1720, 1820, 1920, 2300) | (1056, 1150, 1250, 1350, 1750) | |
PRL | (1611, 1750, 1850, 1950, 2350) | (806, 900, 1000, 1100, 1500) | (1631, 1720, 1820, 1920, 2320) | (826, 920, 1020, 1120, 1520) | (1641, 1730, 1830, 1930, 2330 ) | (856, 950, 1050, 1150, 1550) | (1611, 1700, 1800, 1900, 2300) | (0, 0, 0, 100, 500) | |
Jet Fuel | CPL | (1338, 1400, 1500, 1600, 2000 ) | (738, 850, 950, 1050, 1450) | (1438, 1500, 1600, 1700, 2100 ) | (778, 890, 990, 1090, 1490) | (1418, 1480, 1580, 1680, 2080 ) | (768, 880, 980, 1080, 1480) | (1398, 1460, 1560, 1660, 2060) | (758, 870, 970, 1070, 1470) |
PARCO | (1338, 1400, 1500, 1600, 2000) | (738, 850, 950, 1050, 1459) | (1398, 1460, 1560, 1660, 2060) | (898, 1010, 1110, 1210, 1610) | (1418, 1480, 1580, 1680, 2080) | (908, 1020, 1120, 1220, 1620) | (1358, 1420, 1580, 1680, 2020) | (773, 885, 985, 1085, 1485) | |
NRL | (1338, 1400, 1500, 1600, 2000) | (0, 0, 0, 100, 500) | (1398, 1460, 1560, 1660, 2060) | (928, 1040, 1140, 1240, 1640) | (1418, 1480, 1580, 1680, 2080) | (948, 1060, 1160, 1260, 1660) | (1358, 1420, 1520, 1620, 2020) | (888, 1000, 1100, 1200, 1600) | |
EPRF | (1338, 1400, 1500, 1600, 2000) | (0, 0, 0, 100, 500) | (1398, 1460, 1560, 1660, 2060 ) | (928, 1040, 1140, 1240, 1640) | (1418, 1480, 1580, 1680, 2080 ) | (948, 1060, 1160, 1260, 1660) | (1358, 1420, 1520, 1620, 2020) | (888, 1000, 1100, 1200, 1600) | |
ARL | (1518, 1580, 1680, 1780, 2180) | (1088, 12001300, 1400, 1800) | (1458, 1520, 1250, 1720, 2120 ) | (1038, 1150, 1250, 1350, 1750) | (1438, 1500, 1600, 1700, 2100) | (0, 0, 0, 100, 500) | (1468, 1530, 1630, 1730, 2130 | (988, 1100, 1200, 1300, 1700) | |
PRL | (1388, 1450, 1550, 1650, 2050) | (608, 720, 820, 920, 1320) | (1358, 1420, 1520, 1620, 2020) | (618, 730, 830, 930, 1330) | (1368, 1430, 1530, 1630, 2030) | (638, 750, 850, 950, 1350) | (1338, 1400, 1500, 1600, 2000 ) | (0, 0, 0, 100, 500) |
Products | Depots | Customer | |||||
---|---|---|---|---|---|---|---|
Industrial sector | Domestic sector | Railway | |||||
Diesel | Karachi | (1004, 1100, 1200, 1300, 1700) | (1894, 1990, 2090, 2190, 2510) | (904, 1000, 1100, 1200, 1600) | (1604, 1700, 1800, 1900, 2300) | (1104, 1200, 1300, 1400, 1800) | (1254, 1350, 1450, 1550, 1950) |
Lahore | (1033, 1129, 1229, 1329, 1729) | (804, 900, 1000, 1100, 1500) | (849, 990, 1090, 1190, 1590) | (1004, 1100, 1200, 1300, 1700) | (1104, 1200, 1300, 1400, 1820) | (1151, 1247, 1347, 1447, 1847) | |
Islamabad | (1044, 1140, 1240, 1340, 1690) | (1304, 1400, 1500, 1600, 2000) | (894, 990, 1090, 1190, 1610) | (1364, 1460, 1560, 1660, 2060) | (1124, 1220, 1320, 1420, 1820) | (1260, 1356, 1456, 1556, 1956) | |
Multan | (994, 1090, 1190, 1290, 1690) | (1504, 1600, 1700, 1800, 2200) | (914, 1010, 1110, 1210, 1610) | (1493, 1589, 1689, 1789, 2189) | (1114, 1210, 1310, 1410, 1810) | (1474, 1570, 1670, 1770, 2170) | |
Gasoline | Karachi | (1204, 1300, 1400, 1500, 1900) | (864, 990, 1090, 1190, 1590) | (924, 1020, 1120, 1220, 1620) | (1054, 1150, 1250, 1350, 1750) | (1154, 1250, 1350, 1450, 1850) | (1504, 1600, 1700, 1800, 2200) |
Lahore | (1214, 1310, 1410, 1510, 1910) | (854, 950, 1050, 1150, 1550) | (914, 1010, 1110, 1210, 1610) | (1154, 1250, 1350, 1450, 1550) | (1144, 1240, 1340, 1440, 1840) | (1254, 1350, 1450, 1550, 1950) | |
Islamabad | (1194, 1290, 1390, 1490, 1890) | (1004, 1100, 1200, 1300, 1700) | (924, 1020, 1120, 1220, 1620) | (1064, 1160, 1260, 1360, 1760) | (1164, 1260, 1360, 1460, 1860) | (904, 1000, 1100, 1200, 1600) | |
Multan | (1184, 1280, 1380, 1480, 1880) | (904, 1000, 1100, 1200, 1600) | (934, 1030, 1130, 1230, 1630) | (1593, 1689, 1789, 1889, 2289) | (1144, 1240, 1340, 1440, 1840) | (1694, 1790, 1890, 1990, 2390) | |
Jet Fuel | Karachi | (1404, 1500, 1600, 1700, 2100) | (1094, 1190, 1290, 1390, 1790) | (804, 900, 1000, 1100, 1500) | (804, 900, 1000, 1100, 1500) | (1304, 1400, 1500, 1600, 200) | (1204, 1390, 1490, 1590, 1990) |
Lahore | (1414, 1510, 1610, 1710, 2110) | (1479, 1575, 1675, 1775, 2175) | (784, 880, 980, 1080, 1480) | (1304, 1400, 1500, 1600, 2000) | (1284, 1380, 1510, 1610, 1980) | (1164, 1260, 1360, 1460, 1860) | |
Islamabad | (1384, 1480, 1580, 1680, 2080) | (814, 910, 1010, 1110, 1510) | (784, 880, 980, 1080, 1480) | (864, 960, 1060, 1160, 1560) | 1314, 1410, 1510, 1610, 2010) | (958, 1054, 1154, 1254, 1654) | |
Multan | (1384, 1480, 1580, 1680, 2080) | (1274, 1370, 1470, 1570, 1970) | (814, 910, 1010, 1110, 1510) | (1404, 1500, 1600, 1700, 2100) | (1294, 1590, 1490, 1590, 1990) | (1204, 1300, 1400, 1500, 1900) |
The literature examined in this study is categorized as shown in
A key conclusion of this study is that pentagonal fuzzy numbers can be used to deal with many uncertain scenarios.
Optimization technique | Cost function value |
---|---|
Crisp linear programming | |
Pentagonal fuzzy linear programming |
Pentagonal fuzzy optimization yields the optimum value for each decision variable. As long as the optimization method is effective, the constraints are met while attaining the target. The demand of customer 12910 million tons/year and product supply from the depot to the customer are the same (see
Depots | Capacity |
---|---|
Karachi | 0 |
Lahore | 0 |
Islamabad | 4807 |
Multan | 9431 |
Product | Refinery | Depots | |||||||
---|---|---|---|---|---|---|---|---|---|
Karachi | Lahore | Islamabad | Multan | ||||||
Diesel | CPL | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
PARCO | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
NRL | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
EPRF | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
ARL | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
PRL | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 5446 | |
Gasoline | CPL | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
PARCO | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
NRL | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
EPRF | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
ARL | 0 | 0 | 0 | 0 | 0 | 1042 | 0 | 0 | |
PRL | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3123 | |
Jet Fuel | CPL | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
PARCO | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
NRL | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
EPRF | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
ARL | 0 | 0 | 0 | 0 | 0 | 3328 | 0 | 0 | |
PRL | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 4 |
Products | Depots | Customer | |||||
---|---|---|---|---|---|---|---|
Industrial sector | Domestic sector | Railway | |||||
Diesel | Karachi | 0 | 0 | 0 | 0 | 0 | 0 |
Lahore | 0 | 0 | 0 | 0 | 0 | 0 | |
Islamabad | 0 | 0 | 0 | 0 | 0 | 0 | |
Multan | 1922 | 0 | 2402 | 0 | 1122 | 0 | |
Gasoline | Karachi | 0 | 0 | 0 | 0 | 0 | 0 |
Lahore | 0 | 0 | 0 | 0 | 0 | 0 | |
Islamabad | 0 | 0 | 0 | 0 | 0 | 1030 | |
Multan | 0 | 1901 | 1222 | 0 | 0 | 0 | |
Jet Fuel | Karachi | 0 | 0 | 0 | 0 | 0 | 0 |
Lahore | 0 | 0 | 0 | 0 | 0 | 0 | |
Islamabad | 0 | 1013 | 1203 | 0 | 0 | 1091 | |
Multan | 0 | 0 | 4.0 | 0 | 0 | 0 |
Numerical example data were hypothesized because data on oil and gas downstream supply chains (OGDSC) are not accessible. The refineries and distribution centers shown in
This study aims to address the gap in the literature review by considering a single objective optimization model for tactical planning decisions of petroleum supply chains products. The model based on the method proposed by Kazemi et al. [