A Stochastic Linear Programming Approach for the Production, Distribution and Inventory Systems of the Nigerian Bottling Company (NBC) : A Case Study of the North- Western Zone of Nigeria
Chapter One
AIM AND OBJECTIVES OF THE STUDY
The overall aim of the study is to optimize the production, inventory and distribution of the Nigerian Bottling Company products so as to maximize profit.
The objectives of the study include the following:
- To carry out an assessment of the NBC production, inventory and distribution systems.
- To identify the decision variables, parameters and constraints necessary for formulating a model of the NBC production, inventory and distribution operations
- To fit a linear programming model relating to the production, inventory and distribution of the NBC
- To evaluate the profit margin in the production plant of the
- To identify production activities that will achieve high efficiency in the production processes of the NBC.
Chapter Two
LITERATURE REVIEW
INTRODUCTION
Supply chain management (SCM) is an emerging field that has commanded attention and support from the industrial community. Demand forecasting and taking inventory into consideration is an important issue in SCM. There are many diverse inventory systems, in theory or practice, which are operated by entities (companies) in a supply chain. In order to increase supply chain effectiveness, minimize total cost, and reduce the bullwhip effect, integration and coordination of these different systems in the supply chain (SC) will be required using information technology and effective communication. This research will develop a multi-agent system to simulate a supply chain, where agents operate these entities with different inventory systems. Agents are coordinated to control inventory and minimize the total cost of a supply chain by sharing information and forecasting knowledge. The demand will be forcasted with a genetic algorithm (GA) and the ordering quantity is offered at each echelon incorporating the perspective of “systems thinking”. By using this agent-based system, the result will show that the total cost decreases and the ordering variation curve becomes smooth. According to New and Payne (1995), Supply chain is defined as the chain linking each entity of the manufacturing and supply process from raw materials through to the end user. In the words of Yung and Yang (1999), a supply chain comprises many systems, including various manufacturing, storage, transportation, and retail systems. Gavirneni et al. (1999) showed that managing any one of these systems involves a series of complex trade-offs between different business function costs. For example, to efficiently run a manufacturing operation, the cost must compromise with the costs of inventory and raw materials Chen et al. (2000). According to Lee et al. (1992), to integrate different supply chain systems, entities must be coordinated incorporating the “system thinking” perspective.
A SUPPLY CHAIN MODEL
A supply chain model may be considered as an integrated process in which a group of several organizations, such as suppliers, producers, distributors and retailers, work together to acquire raw materials with a view to converting them into end products which they distribute to retailers (Beamon,1998). Simultaneously considering supply chain production and transport planning problems greatly advances the efficiency of both processes. The literature in the field is vast, so an extensive review of existing research on the topic is presented in an attempt to gain a better understanding of the mathematical modeling methods used in supply chain production and transport planning so as to provide a basis for future research. Given the globalization of operations, new models and tools for improving the forecasting, replenishment and production plans along supply chains, manufacturing companies increasingly need to integrate production and transport planning in order to optimize both these processes simultaneously. Multi echelons including suppliers, manufacturers, distributors and retailers are allowed to use different inventory systems as shown below in figures 1.1 and 1.2 respectively.
Chapter Three
METHODOLOGY AND MODELING
METHODOLOGY
Having highlighted the importance of optimization techniques in the previous chapter, the comprehensive model for Nigerian Bottling Company, (NBC) will be developed and all parameters substituted as required.
LOCATION OF STUDY AREAS
The data used in this project work was collected from Nigerian Bottling Company (NBC) Kaduna plant in Kaduna and Challawa plant in Kano. All in the North-western Zone of the country.
SOURCES OF DATA
Data for this project work was collected from Nigerian Bottling Company (NBC). This data includes: estimated demand for products at depot in a given time interval, maximum shipping weight of truck, unit weight of each product depending on bottle type, unit production time of products at plant, maximum available time for production of products at plant, fixed set up cost of production facilities, transportation cost from plant to depot, unit cost of production of products at plant in a given time interval, inventory level at their warehouse and depot, maximum storage capacity for each product at warehouse, fixed vehicle cost, etc.
Chapter Four
DATA PRESENTATION AND ANALYSIS
For ease of identification and Simplification, the variables used are redefined as follows Table 4.1: Quantity of product „j‟ produced at plant „i‟ in period „t‟ in year 2013.
Chapter Five
RESULTS AND DISCUSSION
The result of the linear model is as shown in Appendix C.
INTERPRETATION AND DISCUSSION OFRESULTS
The following summarizes the information from the results of the formulated model:
The Optimum solution
The Objective function gives a maximum profit value of ₦ 5,066,890,000.00K (target year – 2013) and the inventory level is kept at minimum as against the existing profit margin of ₦ 5,042,431,000.00K without Optimization principle. Hence, the Optimization method employed in the profit analysis of year 2013 has yielded a significant extra profit increment of ₦ 24,458,800.00K as against the profit margin recorded in year 2013 without Optimization principle.
Chapter Six
SUMMARY, CONCLUSION AND RECOMMENDATIONS
SUMMARY
This Project work studied a manufacturing Company (case Study – Nigeria Bottling Company), with many production facilities and multi-products production system. In the system, products are distributed to a number of depots at which the demand for each product is known. Chapter one gives the introduction of the project work where the study objectives, statement of the problem, justification of study, limitation and sources of data are all stated. Chapter two deals mainly with the literature review; where past related work and the contributions of other previous researchers are carefully studied. Chapter three comprises the method of work, data collection, software application, and model development while the data is presented and analyzed in chapter four and the results are discussed in chapter five.
CONCLUSION
The Production, inventory and distribution systems of the NBC have been assessed and the potentials for using Linear Programming model in managing a large scale Production, inventory and distribution problems subsequently identified. The decision variables, parameters and constraints necessary for formulating a model of the company‟s Production, inventory and distribution operations so identified have been solved using the linear Programming Solver, Lips. A linear Programming model which consists of eighty-eight (88) variables and fifty-four (54) constraints has been fitted and subsequently formulated. The Optimal Production, inventory and distribution of NBC products has been analyzed and the model improved the profit of the company under study by about ₦ 24,458,800 and also enhanced the Production, inventory and distribution (PID) strategy used by the company. The model developed resulted insignificant profit margin of about ₦ 24,458,800 with the Optimization principle (a profit margin of
₦ 5,066,890,000.00K – year 2013) in contrast with the existing profit of
₦ 5,042,431,200.00K without the Optimization principle in year 2013 and a profit increment of ₦ 42,647,676.26K without the Optimization principle in year 2012. The result of the work has shown that optimization of different NBC products can be achieved using LiPs software (linear programming) and is highly sensitive to changes putting into considerations the constraints that limit what is achievable. It is therefore highly recommended that the Optimization software should be adopted and used for effective planning and profit maximization.
RECOMMENDATIONS
There are some limitations in using the linear programming for planning operations in the NBC. There are also some fluctuations in market demand and price. A possible remedy to linear programming problems is to update model continuously based on plant data . There are many other software packages such as ASPEN PLUS (ASPEN FIMS), HYSIS etc, that can also be used to achieve similar results. Further work can still be done on this project work especially on the review of multi-objective optimization for the decision model and the effects of the addition of new constraints should also be studied. The addition of a new economic activity (introduction of a new variable) provided it is profitable (that is, if it improves the optimal value of the objective function) should be studied.
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