Increased recognition is being placed, both in industry and in academia, on effective supply chain management. The term supply chain management presupposes that there exists a supply chain to be managed. Supply chain management has become a universal approach to cost effectiveness, timely delivery and the creation of growth oriented exchange system in goods and services.

With a focus on supply chain management in which cost, inventory and time are the key challenges, this paper develops a model to aid the improvement of performance of supply chain system. The model is developed based on existing supply chain management knowledge and the results of an assessment of logistics and supply chain management on manufacturing industries in Ethiopia.

In order to make the paper more practical and realistic, an actual case study was conducted on an existing brewing factory in Ethiopia, Meta Abo. The factory’s current performances were compared with the supply chain model developed and some areas of improvements were identified. Finally, general procedures were developed in order to facilitate the application of the model for practical purpose.

1. Introduction

Logistics and supply chain have great importance to a national economy. The cost of moving products from the factory to the market place is estimated to account for about 20% of the Gross National Product in the developed world [9]. It is projected to be a greater proportion in the developing world like Ethiopia, where a large amount of capital is tied up in inventories and in transportation systems for moving materials. In order to survive and compete effectively today, industries must abandon the functional model of management and operations, and move toward an enterprise and “virtual supply chain” view. Figure 1 shows an ideal supply chain network for a typical manufacturing system.

In Ethiopia, the issue of supply chain system is a major area of economic activities that concerns, directly or indirectly, private and public institutions, investors, contractors, national and international organizations as well as the diplomatic community. In order to alleviate the problem of being unable to be competent in market and technology, the concept of logistics and supply chain management is important for the firms. Excellent industries (where “excellence” translates into market success) approach their competitive environment through truly enterprise wide and integrated business process.

Logistics and supply chain process is the key cross- sectional process of management of materials and information flow from supplier to customer and vice versa. Logistics joins sales and sales generation, design, and transformation as fundamental process of a business.

There are several issues associated to supply chain management in Ethiopia. Some of the problems associated with logistics and supply chain management in Ethiopia are:
• Low competitiveness with local and global industries
• Low customer service level
• Longer lead times
• Poor strategic alliance

2. Literature Review

The concept of supply chain management has its roots in the 1960s concept of logistics management – a planning tool that seeks to develop a system–wide, integrated view of the firm. Subsequently, supply chain management extends the concept of logistics management to external integration of the firm. It is conceived as “a series of linked suppliers and customers” [8].

Supply chain system comprises an interlinked network of supplies, manufacturers, distributors and customers whereby material flows from the supplier through manufacturers and distributors to the customers.

To balance customers' demands with the need for profitable growth, many companies have moved aggressively to improve supply chain management. Their efforts reflect seven principles of supply chain management that can enhance revenue, cost control, and asset utilization as well as customer satisfaction. The seven principles of supply chain managements are: [4]

- Customer segmentation
- Customizing logistics networks
- Demand planning
- Product differentiation
- Sourcing suppliers strategically
- Integration of technology
- Performance measures

Generally, multi-stage models for supply chain design and analysis can be divided into four categories, by modeling approach [1]. The four categories are:
- Deterministic Analytical Models, in which the variables are known and specified,
- Stochastic Analytical Models, where at least one of the variables is unknown, and is assumed to follow a particular probability distribution,
- Economic Models and
- Simulation Models.

3. Model Development for Supply Chain Management System

Because of the inherent complexity of decision making in supply chains, there is a growing need for modeling supply chain system with different methodologies. Developing a supply chain management system requires the analysis of the flow of materials from the initial sourcing to the final end customers.

3.1 Development of Material Flow System

Every manufacturing system has its own material flow system (MFS) in order to collect raw materials from geographically dispersed vendors and distribute finished products to customers at a widely dispersed geographical location. Materials, in the process of passing through an MFS are either in transit through various transportation modes, or are waiting in areas, which may be called stores. Even processing at production work centers is akin to storage for a period of processing. Therefore the materials within a material flow system is in either transit or storage mode. [7]

Figure 3 shows an MFS model for manufacturing firm. The MFS can therefore be conceptualized as network of storage nodes (or points), interconnected by a number of movement pathways.

The MFS can be divided into two subsystems- supply system (SS) and distribution system (DS) (Figure 2). In addition to these two physical sub-systems, the MFS has a third intangible sub-system called the planning system (PS), whose task is the programming and scheduling of the two physical sub-systems.

Figure 2: Coupling of Systems

3.2 Analysis of the Model

Supply chain management is primarily concerned with the utilization of three resources, i.e. costs, inventory and time.

Terminologies in Model analysis

The following terms were important in analysis of the model.
a) Nodes
These are essentially storage areas.
There are five different types of nodes which constitute a supply chain.
• Source Nodes (SN)
• Exit Nodes (EN)
• Mother Node (MN)
• Master Node (MaN)
• Storage Node (StN)

b) Flow paths

These are route/mode combinations between two nodes through which the material moves (figure 4). Generally there are two types of flow paths:

• Normal Flow Paths: These are flow paths along which the movement or flow of material is not impeded by barriers, which have extra cost and time implications, in addition to the usual freight and insurance costs.
• Barrier Flow Paths: These are flow paths across which barriers exist, to impede flow and have additional cost and time implications.

c) Chain link
A chain link is two nodes connected by a flow path. The supply chain will usually consist of one or more chain links. A complete nodal representation of typical manufacturing system is shown in figure 5.

Figure 4: Chain Link

Figure 5: Nodal Representation of Typical Manufacturing Firm.

Figure 3: Model of Material Flow System of Typical Manufacturing Firm in Ethiopia

3.3 Principles of Model Analysis

Supply chain has three specific techniques for each of these resources.

i) Supply Chain Costs Analysis (SCCA)

The primary process of material flow through the MFS involves the expenditure of costs at each and every node and flow paths of the supply chain. At each node/flow path, costs incurred due to materials flow fall into one or more of the following categories.

• Input Node Cost (INC)
• Flow costs (FC)
• Barrier costs (BC)
• Node Activity Costs (NAC)
Once the different cost components have been determined, they are arranged in matrix form in order to simplify the analysis as shown in table 1.
Table 1: Matrix for Supply Chain Analysis
Node

SCC
For each unique supply chain, a unique supply chain cost can be defined as:

where ;
= number of input nodes
= number of flow paths
= number of barrier flow paths
= number of intermediate nodes
= number of nodes/ flow paths where is occurred
= input node cost
= flow cost
= barrier cost
= node activity cost
= capital tie- up cost

Note that capital tie-up costs are costs incurred if material spends more time in the supply chain than the credit period offered. It is defined as:

where:
= capital tie-up cost at the jth node/ flow path

= the amount of capital (usually the price to vendor plus any non-credit costs incurred)
= rate of capital cost
= time period at the jth node after credit period has expired

The concept of supply chain cost measures the total ultimate cost of material to a subject firm arising due to the particular supply chain in question. It is obvious that the structure of the supply chain will determine supply chain cost and any modification of supply chain structure will affect the supply chain cost.

If represents the cost of the jth supply chain, then the total supply system cost can be defined as ;

ii) Supply Chain Inventory Analysis (SCIA)

The basic objective of SCIA is to design supply chains in consonance with a target level of customer service and system and supply chain inventories. The optimization of node/ flow path inventory levels will ensure smooth operations.

Supply chain inventory for supply chain, can be defined as;

Where;
= inventory at node of the supply chain
= inventory at flow path of the supply chain
= the number of nodes and the number of flow paths respectively

Similarly, the total system inventory is defined as:

where the supply system consist of supply chains.

iii) Supply Chain Time Analysis (SCTA)

The supply system has two dimensions for time associated with each node, flow path and the total system. Each node and flow path have a characteristic task performance cycle time associated with them called the node cycle time for the node and flow path cycle time for the flow path.

Therefore, the supply chain cycle time is defined as the sum total of time a batch of material takes to move through the supply chain as follows:

where a supply chain has nodes and flow paths.

Although the performance measurements for supply chain are cost, inventory and time, under this paper, more emphasis is given to cost. Concentrating on cost minimization have direct impact on the other performance measures for supply chain i.e. inventory turn over rate and supply chain response time.

3.4 Supply Chain Model Optimization

The model of supply chain can be simplified with supply chain flow structure as show in figure 6.

Figure 6: Supply Chain Network Structure

i) Sourcing / Suppliers selection

The selection of suppliers with proper allocation helps the manufacturing firm for proper management of suppliers. There are a number of factors that have to be considered for suppliers selections.

 Number of vendor per raw materials
 Vendor location
 Capacity allocation
 Local regulation and tax implementation
 Local market implication
 Local labor and material costs

There are different models and methodologies used in supply chain decision making. In this paper, linear programming(LP) techniques are applied in order to aid decision in supply chain management.

The selection of suppliers and capacity allocation can be modeled as transportation problem which can be solved by LP techniques [2].

The mathematical model for transportation problem can be represented as follows.

Let
Sources of raw materials
Capacity to deliver from source
Raw materials warehouse
Demand of each warehouse
Cost of transporting a unit of raw material from to
Amount delivered from to
the number of sources of raw materials and the number of raw materials warehouse, respectively
The LP model can be formulated to minimize the overall transportation cost.

Objective function:

Constraints:
Suppliers constraint

If the objective functions and the constraints are properly modeled, one can easily determine the optimum solution. As a result, the number of raw materials warehouse required with their proper capacity can also be determined. Tools like management science and LINDO are available in order to aid the determination of optimal solution for the problem like supplier selection and other related problems.

ii) Inbound and Outbound Logistics

One convenient way to view a supply chain for a single manufacturing firm is to divide its logistics system into inbound and outbound logistics. Inbound logistics is a process material flow from suppliers to manufacturers and outbound logistics is the distribution of finished products to end users.

There are a number of factors that have to be considered in inbound and outbound logistics. The following are key factors where proper decision is important in order to achieve a good profit margin and to reduce unnecessary expenses.
 Warehouse location
 Number of warehouse
 Warehouse size and capacity
 In- house fleet vs contract carriers
 Number of carriers
 Local regulations and tax implementation

Warehouse location, number of warehouse and warehouse size & capacity can be modeled using mathematical model as follows.

• Inbound logistics

Let
raw material warehouse
the number of raw material warehouse
the capacity of raw material warehouse
the cost of transporting a unit of raw materials from warehouse to the manufacturing firm.
the demand of the manufacturing firm
The relationship between raw material warehouse and manufacturing system can be modeled as linear programming model as follows.

Objective function

Constraints:

iii) Manufacturing System

This is the area where raw materials coming from suppliers are converted into useful products. The key factors that have to be considered in relation to the manufacturing firm are: plant location, plant capacity, local labor, material costs, local economy, and political situations.

4. Evaluation and Application of the Model

The model can be applied for either the development of the new supply chain system or for an improvement of the existing system. As an application for the existing system, the model is used to evaluate the performance of the existing system and tries to identify the areas of improvement. On the other hand, the model can also be applicable for the development of new supply chain system from scratch by generating different alternatives.

Figure 7 is a flow diagram showing the procedures that are important in order to apply the model either for the existing system or for developing a new system.

4.1 Case Study: Meta Brewery

The main purpose of the case study is to apply the model and to illustrate the merits and demerits of the model. To select industries for the application of the model, a survey of industries like sugar industries, leather and beverage industries has been undertaken.

4.2 Existing Material Flow Model

Materials used to produce beer are generally categorized as direct materials and indirect materials. The direct materials (table 2) are ingredients which are converted to product through various conversion processes, while the indirect materials are added in order to facilitate the various reactions. Under this paper, more attention is given to direct materials due to their higher impact on the cost of supply chain system..

Based on the ingredients used to produce beer, the materials flow system for Meta Brewery can be developed as shown in the figure 8
Table 2: Raw Materials and the Source of Raw Materials for the Meta Brewery

4.3 Cost Analysis Using Supply Chain Model

The existing costing method at Meta Brewery is a traditional accounting system which has some drawback such as double counting and being unable to detect some hidden costs. Furthermore the traditional costing system works effectively on the monthly or yearly basis and it is a time dependent costing method.

Although traditional cost accounting is the easiest and least complicated of the cost analysis method, this method of cost analysis typically ignores future liability costs and considers all indirect costs as overhead or omits them altogether. These overhead costs, if considered, are randomly allocated to a process or product based on some measurable, yet arbitrary parameter (e.g., labor hours, capital equipment costs). This method is the most common accounting method used throughout industry.

The stage by stage analysis necessitate by supply chain cost analysis system models the materials flow or supply chain process, and reveals hidden material and supply chain costs which may not be obvious and may be misallocated by traditional cost accounting system . Supply chain cost analysis introduces a transparency or clarity which may not be available to mangers operating under information generated standard accounting system. During the analysis of cost using supply chain models, it is better to normalize to a single unit of measures. Suggested units of measurement are cost/unit of materials or cost/batch of materials. Since the production of beer is batch type in nature, a cost/batch of materials has been selected as a single unit of cost measurement.

The cost component for supply chain system includes INC, NAC, FC, and BC. In order to use supply chain model for cost analysis, the existing MFS should have to be modified to the developed model format as shown in figure 9.

The cost components within the supply chain system in Meta Brewery can be indicated as shown in figure 10. In order to simplify the analysis further, the material flow system should have to be converted in the form of nodal representation as shown in figure 11. As a result, total supply chain cost for a single batch can be obtained by summing up the total cost of INC, NAC, BC, and FC. Thus , SCC

4.4 Searching for Improvement

In order to minimize the effort made on the raw materials, major raw materials which have more impact on cost of materials can be identified with the aid of principles of Pareto (ABC analysis). This system can also be applied for the distribution system.
i) Improvement at Supply System

From the direct raw materials, the cost of malt is very high as compared to hops and various chemicals; therefore, concentrating on malt will have major impact on cost of supply chain system. Currently, the only local supplier of malt for the factory is Assela Malt Factory (AMF). The Brewery allocated its own trucks for the purpose of transporting malt from AMF to Meta Brewery which adds some unnecessary cost over the factory.

If the delivery of malt to the factory is contracted to liable third party logistic providers (Transport Enterprises), the factory can reduce the administration cost of trucks. Comparing the various costs, if the transport is done with its own trucks and leased to liable third party logistics provider, the brewery can have an improvement of 43.83 % in inbound logistics.

ii) Distribution System

In the case of Meta Brewery, the products of the factory are bottled beer and draught. Bottled beer has high percentage of share compared to draught.

Here, further analysis should have to be made to determine potential distribution region. Concentrating on few regions like Addis Ababa, Tigray and Amhara have major impact for the improvement of cost of distribution. The other point that is observed from the distribution system is that, the factory should have to work more in order to improve the percentage of distribution of some regions like Oromia, Southern Nations, Nationalities, and People's (SNNP) and others.

5. Conclusion

A supply chain model used to analyze cost, inventory and time was developed on the basis of material flow system of manufacturing firms in Ethiopia. To reduce the overall supply chain cost, proper integration of supply chain partners and high customer service level with shorter lead times is essential.

The case study under this paper reveals that the developed supply chain model can be applicable in practice. This model can be used by manufacturing firms in Ethiopia to improve their performance in supply chain management and can also be used for firms’ self-assessment.
In order to achieve proper integration within the supply chain management system, there are a number of factors to be considered. The basic principle in supply chain management system is the creation of collaboration and trust in supply chain partners. To facilitate this collaboration process effectively, the integration of information technology within the supply chain partners is essential.

Sharing benefits among supply chain partners is an important success factor for organization. It is not good practice to scarify other benefits for gaining more. Therefore, the benefits should be equally shared within the supply chain members, in order to have continuous relationship.

Figure 8: Existing Material Flow System for Meta Brewery

Figure 10 : Supply Chain Cost Component for Meta Brewery

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