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).

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 Gambleâs distribution system; Arntzen and Luka (1995) used mixed integer linear programming to determine Digital Equipment Corporationâs 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).