ABSTRACT

In the Nigerian Bottling Company, Production planning has a fundamental role to play. In this study, the particular scenario considered concerns the Nigerian Bottling Company (NBC) with many production facilities and multi-products production systems. The Products are being distributed to a number of depots at which the demand for each product is known. The problem of interest involves determining what products should be made, how much of each product should be produced, and where production should take place. The objectives of the company are to minimize the total cost of operations as well as maximizing the total sales revenue based on the set of decisions, including demands, capacity restriction and budget constraints. The model, which consists of eighty-eight (88) variables and fifty-four (54) constraints is solved using a linear programming software known as Linear Programming Solver. The results show that production without the optimization principle gives a profit margin of five billion, forty two million, four hundred and thirty one thousand, two hundred naira (-N-5,042,431,200.00K) while production with the optimization principle gives a profit margin of five billion, sixty six million, eight hundred and ninety thousand naira (-N-5,066,890,000.00K). The model improved the profit of the company under study by -N-24,458,800 and reduced the Production, Inventory and Distribution (PID).

TABLE OF CONTENTS

Title Page i Declaration ii Certification iii Acknowledgement iv Abstract v Table of content xi List of figures xii List of Tables xiii List of appendices xiv CHAPTER ONE 1
1.0 INTRODUCTION 1
1.1 Background of the Study 1 1.2 Statement of the Problem 2 1.3 The Present Research 5
1.4 Aim and Objectives of the Study 5
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1.5 Significance of the Study 6 1.6 Justification of the Study 6 1.7 Scope of the Study 7 1.8 Company Profile 7 CHAPTER TWO 9
2.0 LITERATURE REVIEW 9
2.1 Introduction 9 2.2 A Supply Chain Model 10 2.3 Optimization 12 2.4 Stochastic Linear Programming 13 2.5 Components of the Linear Programming Model 15 2.6 Conditions for using the Linear Programming 15 2.7 Applications of Linear Programming Techniques 16 2.8 Alternatives to Linear Programming Techniques 17 2.9 The General Linear Programming Model 17 2.10 Modeling 18 2.11 Review of Past Work 19
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CHAPTER THREE 23
3.0 METHODOLOGY AND MODELING 23
3.1 Methodology 23 3.2 Location of Study Areas 23 3.3 Sources of Data 23 3.4 Method of Data Collection 24 3.5 Software Application 25 3.5.1 The working principles of the linear programming solver, LiPs 25 3.5.2 Model editor 26 3.5.3 Model solver 26 3.5.4 Sensitivity analysis 27 3.6 Linear Programming Modeling 27 3.6.1 Assumptions 29 3.6.2 Constraints 29 3.6.3 Model development 30
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CHAPTER FOUR 32
4.0 DATA PRESENTATION AND ANALYSIS 32
4.1.1 Profit analysis of year 2013 (without optimization Principle) 47 4.1.2 Profit analysis of year 2013 (with optimization Principle) 48 CHAPTER FIVE 50
5.0 RESULTS AND DISCUSSION 50
5.1 Interpretations and Discussion of Results 50 5.1.1 The optimum solution 50 5.1.2 Sensitivity analysis 51 5.1.3 Slacks/surplus 51 5.1.4 Duality/dual price (shadow price) 52 5.1.5 Reduced cost 52 CHAPTER SIX 53
6.0 SUMMARY, CONCLUSION AND RECOMMENDATIONS 53
6.1 Summary 53 6.2 Conclusion 53
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6.3 Recommendations 55 REFERENCES 56 APPENDICES 60

CHAPTER ONE

INTRODUCTION 1.1 BACKGROUND OF THE STUDY
For nearly three decades, multi-echelon supply chains have constituted a focal research area. As a result, models for the control of supply chain of several forms and operating disciplines are now available. Due to the shear volume and variety of these models, surveys of varying scope or focus often appear (Inderfurth, 1994; Van Houtum et al., 1996; Diks et al., 1996; de Kok and Fransoo, 2003 ; Mula et al., 2006). Manufacturing and Production companies are profit-oriented; as a result, a well-defined mathematical model should be established and formulated, so that solving this model can generate an optimal strategy. In recent years, the mathematical theory of production, inventory and distribution has been extended to cover many of the situations that arise in practice. Mathematical programming has been applied frequently and successfully to a wide variety of production, inventory and distribution problems for a variety of industries. For example, Camm and Moni (1997) used integer programming and network to improve Procter and Gamble‟s distribution system; Arntzen and Luka (1995) used mixed integer linear programming to determine Digital Equipment Corporation‟s distribution strategy: Martin et al (1993) used linear programming to assist in distribution operations for Libbey-Owens-Ford; Robinson et al (1993) used optimization in designing a distribution decision support system for Dow Brands, Inc; Mehring and Gutterman (1990) used
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linear programming to plan distribution at Almoco (U.K.) Limited. Most consumer products flow through a pipeline that begins with production at a plant, finished products moved down to the warehouse located at the plant site (if there is any), followed by transportation/distribution to a depot or customer outlets. Most companies manage these three functions independently with little or no integration among production, inventory and distribution planning. Companies will need to make the necessary organizational changes that will facilitate coordination of these major functions and develop an ability to make more decisions within the structure. Many research works have dealt with the coordination of production, inventory and distribution Pyke (1987) studied integrated production/distribution systems under stochastic demand. He developed an analytical model of a simple three-node system (factory, finished goods stockpile and single retailer) and examined the properties of the cost functions arising from this model for a single product case. 1.2 STATEMENT OF THE PROBLEM This project work will integrate the coordination of production, inventory and distribution of multi-products, multi-facilities in the Nigerian Bottling Company (NBC), with several plant locations that produce a number of products over time. Finished goods (or products) are maintained at each plant warehouse, followed by the distribution of these products by
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a fleet of trucks to a number of depots/customers. The demand for each product at each depot is known for each period horizon and such products are subsequently distributed. There are about 13 bottling plants and 59 depots across Nigeria namely: Abuja, Apapa, Asejire, Benin, Challawa, Enugu, Ikeja, Ilorin, Jos, Kaduna, Maiduguri Owerri and PortHarcourt. For example, Kaduna plant has two production lines namely: line 1 which produces 35cl with filler capacity cases of 1,083 cases per day and also 50clwith filler capacity cases of 833 cases per day while line 3 produces only 50cl with filler capacity cases of 1000 cases per day. Conservatively, the plant sales volume ranges from an average of 22,000 – 24,000 cases per day. The unit production time of products at any production line is 8 hours per day while the maximum available time at each plant is 20 hours per day. The Capacity restriction on production is 540 cases averagely while the maximum storage capacity at warehouse ranges from 100,000 units – 150,000 units. Similarly, Challawa plant has two production lines namely, line 1 which produces 35cl with filler capacity cases of 1,123 cases per day and also 50cl withfiller capacity cases of 944 cases per day while line 2 produces only 50cl with filler capacity cases of 1024 cases per day. The sales volume range for Challawa plant ranges from an average of 23,500-24,500 cases per day. The unit production time of products at any production line is 9 hours per day while the maximum available time at each plant is 22 hours per day. The capacity restriction on production is 600 cases averagely while the maximum storage capacity at warehouse ranges from 150,000 – 200,000 units. According
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to the Nigerian Bottling Company balance sheet Management and Assessment (2013), the company‟s profit stood at about ₦5,024,242,323.74K in 2013. Based on the dynamic nature of the Nigerian Bottling Company (NBC), the following problems are identified: There is a seasonal demand for the NBC products which create a chain of intricate and far reaching effects that could not be responded to so adequately.
There is a serious erosion or reduction of the NBC profit as a result of a steeply escalating production, inventory and distribution costs.
There is a web of interacting influences which spanned through the NBC principal activities – production, inventory and distribution which require an integrated computer-based planning system to uncover the appropriate decisions.
There is a need for optimal product mix where NBC produces different products each competing for the available scarce resources.
There is period capacity restriction on production of NBC products.
There is facility restriction on production of NBC products.
There is storage capacity restriction of NBC products.
(Extracted from the NBC Balance Sheet Management And Assessment Records).
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1.3 THE PRESENT RESEARCH To improve the production and supply chain‟s performance under demand uncertainty (which happens by chance) in the Nigerian Bottling Company (NBC), a review of mathematical programming models for supply chain production and transport planning is inevitable. The purpose of this review is to identify current and future researches in this field and to propose a taxanomy framework based on the following elements: supply chain structure, decision level, modeling approach, purpose, shared information, limitations, novelty and application. 1.4 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:
a) To carry out an assessment of the NBC production, inventory and distribution systems.
b) To identify the decision variables, parameters and constraints necessary for formulating a model of the NBC production, inventory and distribution operations
c) To fit a linear programming model relating to the production, inventory and distribution of the NBC products.
d) To evaluate the profit margin in the production plant of the NBC.
e) To identify production activities that will achieve high efficiency in the production processes of the NBC.
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1.5 SIGNIFICANCE OF THE STUDY In this work, a solution was developed to forecast the ordering quantity in a given period of time, where every entity was allowed to use different inventory systems. A constraint network was proposed and incorporated with agent technology to coordinate the supply chain. Based on experimental results, this approach showed great promise in searching for a desired demand ordering quantity and globally optimized the total cost of the supply chain. According to Lucey (1996), the inventory model will help companies. 1.6 JUSTIFICATION OF THE STUDY
The seasonal demand for beverages is creating a chain of intricate and far reaching effects that could not be responded to adequately. As a result, the company‟s profit was being seriously eroded by steeply escalating production, inventory and distribution such as the NBC to reduce the variation in demand and production of their products by disposing goods at each finite time intervals to cushion the effect of excess demand which could be taken care of by an initial quantity of goods in the warehouse. Furthermore, it will give the NBC the leverage to take advantage of bulk purchasing discount by enjoying some price reductions on account of quantity order of raw materials. It will also help the NBC to meet up with possible shortages in future so as to enable production processes flow smoothly and efficiently. Finally, it will help the NBC to
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cushion the effects of serious reduction of the company‟s profit by formulating a linear programming model that will determine the best combination of products quantities that would minimize cost or maximize profit. 1.7 SCOPE OF THE STUDY For the sake of clarity and ease of validation, the model presented in this work is limited to 2-plants: Kaduna and Challawa plants, 2-products: Coke and Fanta, 3-depots: Zaria, Katsina and Dutse depots and 4-periods: Period 1, Period 3 and Period 4. However, the model can extend to any length of time depending on the capacity of the software. costs. The web of interacting influences which spanned the company‟s principal activities – Production, inventory and distribution, required an integrated computer-base planning system to uncover the appropriate decisions. The integrated framework allows the system to consider the relevant impacts of all decisions simultaneously, thereby equipping it to provide analyses for planning and operational decisions. 1.8 COMPANY PROFILE
This thesis work was carried out in Nigerian Bottling Company (NBC). Coca-cola was first made on 18th May, 1886 by Dr. John Pembeton in his home town Atlanta, Georgia in USA. Coca-cola first came to Nigeria in the year 1953, when the Nigerian bottling Company opened its first plant in Lagos. Nigerian bottling Company PLC was then
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incorporated in November 1951 as a subsidiary of the A.G Leventis group with the franchise to bottle and sell products of the Coca-cola company in Nigeria. Two years later in 1953, the production of Coca-cola began at a bottling facility in Ebute-metta, Lagos state. In the same year, the company opened its first plant in Apapa and its second bottling facility at Ibadan, Oyo state. There is also a Quality Assurance department whose responsibility is to ensure that only quality products that meet the requirements are forwarded to the warehouse as finished products. Finished products are distributed/transported to the depots using a fleet of trailers. Not all the products are produced in all the plants, e.g. the production of the bottled coke and other beverages is at Kaduna plant, the production of the plastic coke is at the Lagos plant only, while the production of Five alive is at the Benin plant only. The finished products such as coke, Fanta, Sprite, Lemon Five-alive, Eva water, etc are transferred to the warehouse located at each plant site. A fleet of trucks are stationed at each plant site to deliver products from the plant to a number of depot/customer locations. The demand for each product at each depot is known. The goal of the company is to coordinate production, inventory and distribution to maximize profit without violating other environmental restrictions.
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