A Performance Measurement And Productivity Assessment Of System Wide Cost Methods

TOPIC: A performance measurement and productivity assessment of system wide cost methods of an industry segment that serves the transportation function in supply chain management. an internal focus of sakunda holdings and total zimbabwe.


The transport sector is playing an increasingly significant role in global energy requirements, accounting for 23 percent of all world energy consumption. A single energy source, petroleum, still accounts for the vast majority 95 percent'of the energy used by the transport sector (IPCC 2007). As a result, the oil price volatility of recent years has created considerable pressures on transport systems, particularly in the developing world. The Zimbabwean retail fuel industry is a highly sophisticated industry built on a solid infrastructure (Research Council, 2010). In this regard, refineries import refined oil from three main sources, namely: Beira; Feruka and South Africa. (Mbendi, 2004b).

The fuel retail sector operates in a highly competitive environment that is characterised by low profit margins and high stock turnover. It is both capital and labor intensive, with approximately 2000 pump attendants employed in the sector (Thomas, 2010). A study conducted by the DME in 2004, found that the average fuel station sold 84 000 litres of fuel per month, with approximately 70% of all fuel stations selling only 62 200 litres (Thomas, 2009). Despite the regulation in the industry, the DME found that only 40% of fuel stations are profitable with regard to selling fuel. Many fuel stations have explored alternative sources of income in order to remain profitable and there is a concern that there are too many fuel stations, resulting in an overtraded market (Thomas, 2005). According to the DME, the retail market may be overtraded by as much as 30% (Visser, 2009).

The reliance of fuel stations on additional sources of income is common place in de-regulated markets. In the USA, fuel is considered the volume driver, whilst convenience store sales drive the bulk of the profits (Reid, 2004). A survey performed by National Petroleum News in 2005, indicated that 66.5% of sales relate to motor fuel, but these sales only contributed 31.7% to the gross profit in the industry. Therefore 68.3% of the gross profit in the US fuel retail industry is derived from convenience store sales. The United Kingdom is no different, and Shell has admitted that they make no profit from UK fuel sales (Harwood, 2006). Profits from European fuel sales are also being eroded, causing companies to search for new revenue streams (Weirauch, 2000). Zimbabwean fuel retailers are already relying heavily on convenience store sales, in an overtraded industry, to remain profitable. With the impending regulation of the industry, it is imperative that retailers understand the variables affecting the profitability of outlets in order to remain in the industry.

Deregulation of the Zimbabwean fuel retail industry has caused a variety of changes to the sector. These changes include the deregulation of the fuel price and import and export controls which were phased out, allowing companies to import the finished fuel (Mbendi, 2010). Deregulation though competitive has had extensive effects on the already overtraded fuel retail market. Lower pump prices, caused by additional competition, have resulted in lower profit
margins being earned by fuel stations (Visser, 2011). The Research Council prophesied deregulation having extensive consequences for existing fuel stations, with the likely demise of marginal outlets and the reduced numbers of low volume rural outlets (Research Council, 2012). The Financial Gazette predicted that approximately 74 of the current 222+ fuel stations could close once the market was liberalised (Pile 2011). A side effect of the termination of these fuel stations was the major job losses that resulted.

Currently, Zimbabwe imports approximately 71% of commercial energy from the total energy used in the country. In 2012, the total use of oil in the entire country was 223.776 million litres. The total consumption of oil by diesel users in transportation, industry, and commercial sectors was 114.126 million litres, which was 51% of the ready-made oil usage. According to Zimbabwe's strategic plan of energy substitution, the Ministry of Energy has stipulated the blending of 5% and 10% composite portions with highly flammable ethanol, called E5 and E10, year ending 2013. This by expectation will replace the usage of diesel by about 5.08 million litres per day, or 1,831 million litres per year.

Mismatching between supply and demand is impacting government policy regarding energy substitution from agricultural products. Additionally, this mismatch is decreasing efficiency in the management of the petroleum supply chain. This research study examined the total system wide cost, which was utilized to measure the efficiency of the supply chain incurred in the fuel energy industry in Zimbabwe. The information gathered was used to consider the total system wide cost of the supply chain network and investigated the location and capacity allocation of petroleum products in order to minimize the total cost. Supply chain in the research study consisted of suppliers, crude-oil plants, depots, refineries, and fuel stations, which are prevalent. Models developed will be useful in decision making for those involved in the strategic planning of energy substitution in Zimbabwe.

Nowadays, supply chain management (SCM) has received a lot of attentions. In APICS Dictionary, SCM is defined as the design, planning, execution, control, and monitoring of supply chain activities with the objective of creating net value, building a competitive infrastructure, leveraging worldwide logistics, synchronizing supply with demand, and measuring performance globally. There are two types of supply chains: forward and reverse supply chains. The forward supply chain (FSC) includes of series of activities in the process of converting raw materials to finished products. The managers try to improve forward supply chain performances in areas such as demand management, procurement, and order fulfilment (Cooper et al., 1997). Reverse supply chain (RSC) is defined as the activities of the collection and recovery of product returns in supply chain management (SCM). Economic features, government directions, and customer pressure are three aspects of reverse logistics (Milo et al., 2009). Generally, there are more supply points than demand points in reverse logistics networks when they are compared with forward networks (Snyder, 2006).

Companies like Sakunda and TOTAL have been forced to overstep their physical frontiers and to visualize the surrounding business environment before planning their activities. Range vision should cover all members that participate direct or indirectly in the work to satisfy a customer necessity. Coordination of this virtual corporation may result in benefits for all members of the chain individually. Beamon (1998) defined such virtual corporation as an integrated process wherein a number of business entities (suppliers, manufacturers, distributors and retailers) worked together in an effort to acquire raw materials, converted them into specified final products and delivered these final products to retailers.

Under another point of view, Tan (2001) stated that there is a definition of supply chain management (SCM), which emerged from transportation and logistics literature of the wholesaling and retailing industry that emphasized the importance of physical distribution and integrated logistics. In the literature, optimization models deal with planning and scheduling of several subsystems of the petroleum supply chain such as oilfield infrastructure, crude oil supply, refinery operations and product transportation. Any enhancement in the existing transportation procedure has the potential for significant cost savings for the Zimbabwean economy.


The petroleum supply chain is illustrated in Petroleum exploration is at the highest level of the chain. Decisions regarding petroleum exploration include design and planning of oil field infrastructure. Petroleum may be also supplied from international sources. Oil tankers transport petroleum to oil terminals, which are connected to refineries through a pipeline network. Decisions at this level incorporate transportation modes and supply planning and scheduling. A trend has been that a company is focusing on cost one year and the next year they focus on performance. Christopher and Towill (2000) described the trends for Supply Chain Management from the beginning of the eighties to end of the nineties. In the beginning of the eighties the focus was on cost effective Supply chains. During the coming years quality was in focus and then in the end of eighties the focus went back to cost. In the beginning of the nineties it was high availability that gave market shares. The strategy was to combine cost effectiveness to the breakeven point between forecast driven flow and customer order drive flow. In the end of the nineties many companies had reached high availability and then shorter lead-time came in focus. The same factors quality, cost, availability and lead-time were considered, but the priority differed.
The underlying principles for the basis of determination of the Basic Fuels Price (BFP) were to represent the realistic, market-related costs of importing a substantial portion of Zimbabwe's liquid fuels requirements, and it was therefore deemed that such supplies are sourced from external refining centres capable of meeting our requirements in terms of both product quality and sustained supply considerations. The petrol price in Zimbabwe is therefore directly linked to the price of petrol quoted in US dollars at refined petroleum export orientated refining centres be it at Beira, in the Mediterranean area, the Arab Gulf or Singapore. This means that the domestic prices of fuels are influenced by (a) international crude oil prices, (b) international supply and demand balances for petroleum products and (c) the Rand/US Dollar exchange rate. The import parity (BFP) principle is an elegant, arms-length method of basic fuels price determination to ensure that local retailers compete with their international counterparts. This promotes cost efficiency and astute fuel acquisition strategies to ensure survival in a volatile and competitive international environment, thus eliminating domestic inflationary pressures.
At the core of the development of every modern nation is petroleum and its products (Sakunda, 2005). Currently, petroleum is among our most important natural resources in Africa (African Union, 2012). We use oil-related products such as gasoline, jet fuel, and diesel fuel to run cars, trucks, aircraft, ships, and other vehicles. The benefits that are gained from using crude oil through the channels of production are numerous and there are no alternatives that can match all the benefits. However, there are ongoing researches into other sources of energy such as wind and solar. This important natural resource should be managed efficiently that is, its processing, distribution and disposal. Planning and scheduling activities related to product distribution have been receiving growing attention for the past decade. Every company's focal point should be on attending to all its client requirements at the lowest possible cost. As a matter of fact, transportation costs had already surpassed 400 billion dollars in the early eighties (Bodin et al., 1983).
Every decision maker must deal with unforeseen events. He or she must plan for these events as well as respond to them. As a mainstay of transportation analysis, network modelling is an interesting methodology around which to build decision aids for planning unforeseen events. And yet, because unforeseen events in transportation are so diverse, any single methodological approach is best suited only for certain of these decisions (Magnanti, 1983). Linear Programming (LP) is a mathematical programming technique which involves creating and solving optimization problems with linear objective functions and linear constraints (Ragsdale, 2004). Mathematical Programming is a field of management science that finds the optimal or most efficient way of using limited resources to achieve the objectives of an individual or a business (Ragsdale, 2004). Other MP techniques include Integer Linear Programming, Mixed-Integer Programming and Mixed-Integer Quadratic Programming.
LP has been around since the 1940s and has now reached a very high level of advancement with the dramatic rise in computing power (M.K.Sahdev, K.K.Jain, & Srivastava, 2008). LP has a wide range of practical applications including business, economics, scheduling, agriculture, medicine, natural science, social science, transportation, and even nutrition. Bok, Grossmann, and Park (2000) present an application to the optimization of continuous flexible process networks. This paper was concerned with developing an LP model for Sakunda Holdings and Total that could improve the performance of their existing procedure whereby petroleum products would distributed on a first-come, first-served basis additional to their internal distributions.
Sakunda Holdings is a leading player in the fuel sector in Africa's Southern Region, creating a better future with better fuelling. Founded in 2005, following the deregulation of the sector in the early 2000's Sakunda Energy as known by others has now grown to become one of the leading importers and suppliers of fuel into Zimbabwe and across our boundaries near and as far as Zambia, Malawi and DRC. It seeks to leverage on local and international opportunities to create value chains that enable customers to get dynamic products of higher quality and service that feels like home. With an empire of over 50 plus service stations with one of its latest state of the art Civic Centre in Mutare which opened its doors on the 9th of June 2013 which is a first of its kind, gas and lubricant ventures, some of its premises are rented from the BP and Shell Franchise under the wings of local business tycoon Shingi Mtasa. It is one of the few indigenous fuel companies that have remained on its feet where majorities, including EXOR, COMOIL and Country Petroleum have floundered.
TOTAL is renowned for producing some of the best high-quality lubricants available on the market today. They offer a wide range of lubricants all over Zimbabwe through their distribution network. With a market share of 28%, Total is the leader on the oil & gas market in Zimbabwe and is still growing, the only exotic dealer of such magnitude. From 2014, its network of 96 service stations throughout the country will be revamped with a brand new design while the mandatory E-10 gas-ethanol blend fuel will be available in all its stations. The knowledge and experience vested at TOTAL helps to advise customers on which products are best suited for their equipments and needs. TOTAL Zimbabwe is able to provide its current and potential customers with a big basket of lubricants that comply with the latest technological requirements. Organization's main fuel offering cover petrol and eco-diesel as well as illuminating paraffin.
With the recent mandatory blending bio fuel initiative by government, changes are becoming permanent within the fuel sector and adjustments inevitable. To the advantage of Sakunda it had already launched its bio-unleaded fuel product E10 by 23 March 2013 in all its Harare service stations, also available in some sites in Bulawayo with expectations of spreading it countrywide. For Total such changes were novel. With Zimbabwe's daily demand in excess of 2million litres, with the supply of the cheaper pipeline falling short at 1.2illion and the road transportation a paltry 0.5million, furthermore Chisumbanje Ethanol Plant is the only ethanol producer. The questions that were still to be answered were whether it will be able to sustain the much needed demand without an escalation of overall transactional, time and deadline costs fuelled by NOCZIM being the distributor of the recently made precious Ethanol.
Besides the transportations costs associated with loading out fuel from near and as far as Beira, Msasa and Feruka for local transportation. Emerging challenges of fuel siphoning, political meddling and mushrooming of unsanctioned illegally operating retailers distorted the market prices by selling fuel at prices lower than the normal price by $0.12c which threatened the pricing and competitiveness of the established industry. With the country's lack of a market adjustable and controlled price and margin mechanism, increased consumer knowledge of suppliers, optimisation was no longer about prices which in the 1970s were driven by price wars and fuel shortages.
The country's volume of importers stands at 32 and 222 plus retailers, the pot is just but getting hotter. Fuel prices globally did not give retailers a piece of mind or freedom from anxiety; they became volatile and hit a record low in the recent months. Industries joined singing the blues of the down the valley hymn, relegated from business by the unmerciful Zimbabwean economy, the demand then was not stationary. It responded like America at the possibility of invasion. Profitability though still achievable the profits became uncertain and unguaranteed thereby bringing into existence a dire need for organisations, Total and Sakunda in particular to revise their internal and outlook policy and opt for optimisation policy frameworks if they are to beat their rivals who are already selling their trucks in exchange for a loaf of bread.


According to Lasschuit and Thijssen (2003), there was great appeal that the supply chain of oil and chemical industry involve the horizontal integration across departmental divisions and coupled coordination of the layers of strategic, planning, scheduling and operational execution (vertical integration). This whole context has been usually described by massive amount of operational data and decision making processes that comprise feedstock, manufacturing, and exchange and blending across supply, distribution, terminals and depots, and into demand, channel segmentation. It was clearly verified, in the next section, that the case study which was addressed in this work clearly pointed towards the stated requirements.

The margins for many companies are becoming smaller and smaller due to increasing demand from the customers on lower prices. Solvang (2001) wrote that one of the biggest challenges for manufacturing supply chains was to continuously improve their performance so that their competitiveness could be sustained in long term. To be able to survive on the market the companies have to cut cost in all areas and focus on SCM. Tummala et al. (2006) stated that to make changes to the Supply chain helps to lower cost and enables a company to more easily compete based on the price. Many concepts for Supply chain design and Supply chain modelling have been presented during the last couple of years with different focus according to Svensson (2003). An interesting question related to this was what should a company aim for when designing a Supply chain and what optimization methods are superlative. The traditional management cost sytems or emerging Financial Engineering performance systems?

The objective of this study was to ascertain the superlative productivity system wide cost method of industry segment that serves the transportation function in supply chain management

' Determine the efficiency of the methods measured in the supply chain and does it exist as a simple model or index for measuring efficiency in the distribution of products.
' Determine the optimal amount to distribute between companies in one specific provinceand their service areas to minimize the total Supply Chain Cost and to meet the given demand.
' To suggest a quantitative method to evaluate how efficient a Supply chain is and combining the cost concept with the performance concept.
' Perform a sensitivity analysis of the optimal petroleum allocation in Zimbabwe. The purpose of the analysis, and its perspective, was to determine whether they consider only short-run marginal costs, long-run costs, and or total social costs.

The research questions were:
' What is the most superlative system wide cost method, the traditional industry based or the emerging sources of innovation like optimization methods? Is they need for further realignment or they are top-notch?
' How efficient are these established techniques and are they simple index measures of performance?
' What is the optimal amount that can be allocated and the capacity for the most efficient method which minimizes costs?
' How long will the actual allocation program remain the optimal solution?
' How possible double-counting is addressed, such as whether taxes are counted as costs or economic transfers, and whether congestion costs are summed with travel time costs.
' Whether cost estimates are point values or ranges.
' What is the impact of the imminent Government expected continual revision of the mandatory blending policy on the overall transportation cost?

H0 The optimization methods were superlative.
H1 The optimization methods were playing second fiddle to the traditional system wide cost methods.
H0 The techniques were efficient performance measures and indices for profitability.
H1 The techniques were not efficient performance measures and indices for profitability.
H0 The optimal values for allocation were determined by optimization.
H1 The optimal values where determined by traditional cost system.
H0 The research optimal allocation program will remain optimal solution longer than the company's allocation program.
H1 The research's optimal allocation will not remain optimal solution longer than the company's allocation program.
H0 Double counting was possibly addressed.
H1 Double counting was not possibly addressed.
H0 There was a significant impact of the government policy on the overall transportation cost.
H1 There was no significant impact of the government policy on the overall transportation cost.


This problem was of great economic significance to Zimbabwe and the fuel sector following the recent introduction of ethanol production and the fact that most industries and companies are driven by oil-related products in their operations. Hence, the efficient distribution of oil-related products would not only minimize cost of distribution for the organizations in study but also that the industries and companies would get access to oil-related products when needed. This research project was initiated to fulfil an aim for more knowledge about
models for measuring the cost and performance of the Supply chain using the transportation optimization problem.

Zimbabwe's economic performance has been a cause for concern in the recent years being described as unsatisfactory resulting in an almost stagnant growth of a number of sectors. This research aimed to bring to the light of stakeholders the relative futuristic importance of reorganising internal activities and searching for home grown solutions to improve operating efficiency rather than the look east shun the other direction where financial winds blow similarly.

While to Harare Institute of Technology, the research would add value to the degree program of financial engineering making it recognized through its innovativeness to research the fundamental problems in the economy, the fuel industry in particular as well as providing a vast arrays of financial solutions which if implemented would see the organizations realizing all their goals.

' Time. Our research was confined to one academic year which was not sufficient enough for us to collect all the necessary information, analyze it and produce a sound documentation.
' Accessibility of data and budgetary constraints.
' Supply Chain Management has a wide scope and includes a lot of theories about how to set up the chain. The thesis did not going into details regarding everything included in the term Supply Chain Management. The aim for this report was to give a view of methods that can be used to evaluate if a Supply chain is efficient or not, and in the end suggest a model or index that combine different measurements.

' The information we acquired was accurate and reliable
Given that all of the above set of research objectives were fully met and executed, a well-articulated research on the optimisation of the fuel sector will facilitate the country's economic growth providing a critical centre upon which economic policies pertaining to the resuscitation of the economy will be based. Furthermore our research concerns were fully addressed; a sound economic evaluation will expound the magnitude of the driving economic force of energy sector performance posed on economic growth.


This chapter explored literature relevant to the topic.

Sear (1993) was probably the first to address the supply chain management in the context of an oil company. The author developed a linear programming network model for planning the logistics of a downstream oil company. The model involved crude oil purchase and transportation, processing of products and transportation, and depot operation. Escudero, Quintana, and Salmeron (1999) proposed an LP model that handled the supply, transportation and distribution of an oil company that accounted for uncertainties in supply costs, demands and product prices. Dempster, Pedron, Medova, Scott, and Sembos (2000) applied a stochastic programming approach to planning problems for a consortium of oil companies. First, a deterministic multi-period linear programming model was developed for supply, production and distribution. The deterministic model was then used as a basis for implementing a stochastic programming formulation with uncertainty in product demands and spot supply costs. More recently, Lasschuit and Thijssen (2003) pointed out how the petrochemical supply chain was organized and stressed important issues that must be taken into account when formulating a model for the oil and chemical industry.

Ponnambalam, Vannelli, and Woo (1992) developed an approach that combined the simplex method for linear programming with an interior point method for solving a multi-period planning model in the oil refinery industry. Still at the production planning level, Liu and Sahinidis (1997) presented a fuzzy programming approach for solving a petrochemical complex problem involving uncertainty in model parameters. Bok, Lee, and Park (1998) addressed the problem of long-range capacity expansion planning for a petrochemical industry. Ross (2000) formulated a planning supply network model on the petroleum distribution downstream segment. Resource allocation such as distribution centres (new and existing) and vehicles was managed in order to maximize profit. Delivery costs were determined depending on the geographic zone, trip cost, order frequency and travel distance for each customer.

Dowing (1992) advocated that the Lagrangian method should be used for any optimization subject to a single inequality constraint, the Graphic approach for optimization subject to only two inequality constraints, and the linear programming model for optimization subject to many inequality constraints. Supporting this view, Dwivedi (2008) posited that linear programming was of great use in making business decision because it helped in measuring complex economic relations and thereby, provided an optimum solution to the problem of resource allocation. According to him, linear programming technique thus, bridged the gap between abstract economic theories and managerial decision-making. Furthermore, he stressed that any linear programming equation should have three specifications, namely: objective function specification, constraint equation specification, and non-negativity requirement. Corroborating this view, several authors (Dowling, 1992, Dwivedi, 2008, Koutsoyiannis, 1979, Henderson and Quandt, 2003, etc) gave the general specification of the linear programming model.
Turban and Meredith (1991) agreeing with Dwivedi (2008), stated that linear programming was one of the best known tools to management science. Management science methods according to them were composed of three components; the decision (uncontrolled) variables, the environment (uncontrolled) parameters and results (dependent) variables. The linear programming model was composed of the same components but they assume different names; the decision variables which we sought to determine, the objective function which we aimed to optimize and the constraints we needed to satisfy. But Koutsoyiannis (1979) insisted that linear programming could be considered as providing an operation method for dealing with economic relationship which involves discontinuities. She however maintained that neither economic theory nor linear programming say anything about the implementation of the optimal plan or solution. They simply derived the optimal solution in any particular problem.

Cooper (1972) defined a problem type, called the transportation-location problem that could be considered a generalization of the Hitchcock - Koopmans transportation problem in which, in addition to seeking the amounts to be shipped from origins to destinations, the optimal locations of these sources with respect to a fixed and known set of destinations were also found concurrently. This new problem was characterized mathematically, and exact and approximate methods were presented for its solution.
Keeler, et al (1975), The Full Costs of Urban Transport; Intermodal Comparisons, Institute of Urban and Regional Development (Berkeley). This report compared commuting costs of automobile, bus and rail in the San Francisco Bay area. It included marginal congestion costs, public services, noise, air pollution, facilities, accidents, parking, and user costs. This is the oldest study of its type. The analysis is still highly regarded.

FRA (1993), Environmental Externalities and Social Costs of Transportation Systems - Measurement, Mitigation and Costing, Federal Railroad Administration, Office of Policy (Washington DC). This study described various motor vehicle social costs. It included two charts that described taxonomy of costs and mitigation strategies, summarized in Table 2.2-6.
Christopher Zegras with Todd Litman (1997), An Analysis of the Full Costs and Impacts of Transportation in Santiago de Chile, International Institute for Energy Conservation (www.iiec.org). This was one of the first comprehensive transport cost studies in the developing world. Included vehicles, roadway, parking, congestion, crash, and environmental costs. Although automobile ownership is relatively low compared with developed countries, rapid (10% annual) growth in vehicle ownership imposes considerable medium-term costs in terms of increased congestion, facility needs, pollution, etc. Because Chile imports most vehicles and fuel, increased auto mobility also imposed macroeconomic costs by capturing a major portion of foreign exchange and potential investment funds.
David Forkenbrock (1999 & 2001), 'External Costs of Intercity Truck Freight Transportation,' Transportation Research A, Vol. 33, No. 7/8 (www.elsevier.com/locate/tra), Sept./Nov. 1999, pp. 505-526; David Forkenbrock, 'Comparison of External Costs of Rail and Truck Freight Transport,' Transportation Research A, Vol. 35, No. 4, May 2001, pp. 321-337. These articles summarized existing intercity truck internal costs. Internal costs were estimated at $1.25 per vehicle-mile, or 8.42?? per ton-mile in 1994 (these values are disaggregated by cost category and trip length). Rail external costs were much smaller in magnitude but larger as a portion of internal (private) costs. Estimates of external costs were as indicated in Table 2.3-3. Concluded that heavy truck road user charges would need to approximately triple to internalize these costs.

Yan (1988) presented a heuristic method for scheduling of trucks from many warehouses to many delivery points subject to constraints on truck capacity, travelling time, and loading and unloading time. He considered the truck scheduling problem faced by STARLINK, a warehousing and distribution Company based in Hong Kong. This heuristic method was used to build a complete schedule. The author reported the success of this method for the STARLINK Company with 8.8% average cost improvement over the previously used manual method.
Charnes and Cooper (1954) explored transportation-type problems and models in detail. Transportation-type problems have certain features which make it possible to devise special computational techniques which are extremely simple to understand and apply. An illustrative example was presented in his paper which explained the "stepping stone" method for solving these kinds of problems.
Kataoka (1963) proposed a stochastic programming model which considered the distribution of an objective function and probabilistic constraints. He derived a nonlinear programming problem with linear inequalities constraints by applying the model to a transportation type problem, and showed that it could be solved by iteration of linear programming.

According to certain definitions of Supply chains there has to be more than one
company involved in the chain in order for it to be defined as a Supply chain.
Holmberg (1997) claimed that at least two organisations are required to form a
Supply chain. Shapiro (2001) said that a Supply chain comprised geographically
dispersed facilities where raw material, intermediate products or finished
products were acquired, transformed, stored or sold and transportation links that
connected facilities along with products flow. The facilities could be operated by the own company or by vendors, customers, third party providers or with other companies with which the company has business arrangements. The definition Supply chain may not be dependend on the number of companies involved in the chain, but rather on what functions were involved.

Christopher (1998) wrote that many discussions in the literature focused on the
Supply chain from the chain perspective meaning that the whole Supply chain
Was to be optimised and that you could not focus on just one company. This was from the perspective that you had to consider the whole Supply chain when you managed it to get the best result, but it is always the profit of the own company that was the most important. Decisions regarding the location and capacity allocation of a facility represented an important aspect of strategic planning for supply chain management. These decisions were instrumental in the determination of the sets of locations and allocation of capacity for a facility. This review focused on the application of mathematical programming models in the strategic design and improvement of global logistics systems.

Jeff Ferrio and John Wassick (2008) explained that chemical supply chain network optimization with the objective of cost reduction functions through the redesign of the flow of materials from producers to customers. A mixed integer linear program (MILP) was capable of optimizing a multi-product supply chain network made up of production sites, an arbitrary number of echelons of distribution centres, and customer sites. Didier Vila et al. (2006) present generic methodology for designing the production-distribution network of divergent process industry companies in a multinational context. A mathematical programming model was used to map the industry manufacturing process to potential production-distribution facility locations and capacity options.

Francisca H.E. Wouda et al. (2002) proposed the optimization of the supply network of Nutricia Hungary using a mixed'integer linear programming model. The objective of the study was to evaluate these strategies through identification of the optimal number of plants, locations, and allocations of the product portfolios, while minimizing the sum of production and transportation costs. Marc Goetschalckx et al. (2002) suggested that logistics systems design problems were comprised of the following as follows: potential suppliers, potential manufacturing facilities, distribution centres with multiple possible configurations, and customers with demands that determine the configuration of the production'distribution system and transfer prices between various subsidiaries of a corporation. This included seasonal customer demands and service requirements that were met after tax profits are maximized. After tax profits were the difference between the sale revenues minus the total system costs and taxes. The total cost was defined as the sum of supplies, production, transportation, inventory, and facility costs.

Network flow problems were linear programming problems in which the objective was to minimize the cost, penalty or distance from a source to a destination. These problems shared a common characteristic ' they can be described or displayed in a graphical form called a network. The network consisted of nodes connected by arcs, each arc having a given direction and a limited capacity. Hsu and Cheng (2002) developed a generalized network flow optimization model for long-term supply-demand analysis for basin-wide water resources planning. A set of nodes and arcs were used to form the network, and the decision variables were reservoir storage and water supply for public and agricultural uses. The objective function to be minimized was formed by summing the products of the decision variables and their corresponding cost coefficients. The constraints of the model included continuity equations, reservoir operation rule curves, reduced water supply due to water shortage, and evaporation losses from reservoirs. The formulated network model was solved by an efficient embedded generalized network solver (EMNET).
Ford Jr. et al. (1956) gave a simplified description of a new computing procedure for the Hitchcock- Koopmans transportation problem (the case study used), together with a step by step solution of an illustrative example. Cooper (1972) defined a problem type, called the transportation-location problem that could be considered a generalization of the Hitchcock - Koopmans transportation problem in which, in addition to seeking the amounts to be shipped from origins to destinations, the optimal locations of these sources with respect to a fixed and known set of destinations were also found concurrently. Yan (1988) presented a heuristic method for scheduling of trucks from many warehouses to many delivery points subject to constraints on truck capacity, travelling time, and loading and unloading time. Bowman (1956) states that; with fluctuating sales, a manufacturer must have fluctuating production, or fluctuating inventory, or both. Penalties are associated with either type of fluctuation.
Lee et al. (1996) addressed the problem of inventory management of a refinery that imports several types of crude oil which are delivered by different vessels. A mixed-integer optimization model was developed which relies on time discrimination. Warner and Prawda (1972) defined The Nursing Personnel Scheduling Problem as the identification of that staffing pattern which (1) specifies the number of nursing personnel of each skill class to be scheduled among the wards and nursing shifts of a scheduling period, (2) satisfies total nursing personnel capacity, integral assignment, and other relevant constraints, and (3) minimizes a "shortage cost" of nursing care services provided for the scheduling period. Lawrie (1969) described an approach based on larger items of departments, group of pupils (generally year groups), and layouts. The problem was given an integer linear programming formulation, and computational methods used in obtaining solutions were discussed.
Maio and Roveda (1971) considered a special class of transportation problems. These problems had a set of sources producing the same material with a fixed maximum capacity, and a set of users whose 13 demands for the material are known. A cost is associated with the transportation of the material from each source to each user. Al-Yakoob (1997) explored mathematical programming optimization models and algorithms for routing and scheduling ships in a maritime transportation system. The case study for the research was the Kuwait Petroleum Corporation (KPC) Problem. A mixed-integer programming model for the KPC problem was developed. Klingman et al. (1974) described the development, implementation, and availability of a computer program for generating a variety of feasible network problems together with a set of benchmarked problems derived from it.

In this chapter, a linear programming model was developed. Many transportation and logistics problems faced by the businesses fell into a category of problems known as network flow problems. A common scenario of a network flow problem arose in industrial logistics concerning the distribution of a single homogeneous product from plants (origins) to consumer markets (destinations). The total number of units produced at each plant and the total number of units required at each market are known. The product needed not be sent directly from source to destination, but was routed through intermediary points reflecting warehouses or distribution centres. Further, there were capacity restrictions that limited some of the shipping links. The objective of the network flow problem was mainly to minimize the variable cost of producing and shipping the products to meet the consumer demand.
Models of the elements presented in the previous section took part in the set of constraints that composed the optimization problem of the whole complex. The optimization problem was then given as stated in problem. The objective function was defined in equations below where the maximization of the revenue obtained by the product sales minus costs related to raw material, operation, inventory and transportation was determined. The operating cost was represented by a non-linear term that depended on the unit operating mode. Those units which operated at their design condition incurred a fixed cost. Otherwise, a proportional cost was incurred, which depended on the deviation variable Vu,v,t

The distribution of oil-related products by Sakunda and Total fell within the scenario given above. For the purpose of this study, the following scenario was considered;


A network is set of points, called nodes, and set of curves, called arcs, which connect certain pairs of nodes. An example network on Fig. 3 consists of five nodes, labelled 1 through 5, and six arcs: (1,2), (1,3), (2,3), (1,4), (3,4) and (4,5). An arc is oriented if it has a direction associated with it. Schematically, arrows indicate directions. The arrow on arc (1, 2) in Fig. 3 signifies that this arc is directed from node 1 to node 2. Any movement along this arc must originate at node 1 and terminate at node 2. Movement from node 2 to node 1 is not permitted along that arc; such a movement should be possible if the other arc exists between those two nodes with opposite direction. If all arcs are directed, the network is oriented.


The Decision variables for Sakunda and Total Problem
Sakunda and Total needed to determine the least cost of transporting petroleum products from the various depots to the various requirement areas. A graphical representation of the problem was drawn from the data collected. The circles (or nodes) in the figure representation were for the depots and DCs and retails in the problem. The arrows (or arcs) connecting the various depots and DCs and retail outlets represented different transportation routes. The decision problem faced by these companies determined how many tankers to transport on each of these routes. Hence, each of the arcs in the LP model represented a decision variable.

If the total supply is equal to total demand, then the given transportation problem is a balanced one.

A sensitivity analysis was developed with the purpose of determining two objectives. The first identified the possible alternative routes in the optimal allocation program and the impact of their use over the total cost. The second identified how long the actual allocation program could remain the optimal solution. According to the analysis, if the conditions remained constant, the allocation generated in this project will be still optimal until the year 2014.

Proposal submission Week 1
Proposal presentation Week 2
Supply networks Week 4
Distribution Truck Week 5
Demand Points Week 6
Retail Points Week 7
Collection of secondary data Week 8
Presentation of research findings Week 10

The results of study will improve the body of knowledge upon which future studies can be carried as well as increasing body of literature upon which references can be made to researches that are aimed at explaining the challenged faced in the fuel sector.

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