KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY DEPARTMENT OF MATHEMATICS TOPIC: THE OPTIMAL PRODUCTION-TRANSPORTATION PROBLEM OF LATEX FOAM GHANA LTD. BY COLLINS KWADWO KRAH (B.Sc. Mathematics and Economics) A THESIS SUBMITTED TO THE DEPARTMENT OF MATHEMATICS, KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY IN PARTIAL FUFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF M.PHIL APPLIED MATHEMATICS APRIL, 2012. DECLARATION I hereby declare that this submission is my own work towards the M.Phil degree and that, to the best of knowledge, it contains no material previously published by another person nor material which has been accepted for the award of any other degree of the University, except where due acknowledgement has been made in the text. COLLINS KWADWO KRAH (PG 5070810). ….................................... ................... Student Name & ID Signature Date Certified by: DR. S. K. AMPONSAH ….................................... ................... Supervisor’s Signature Date MR. F .K. ADARKWA ….................................... ................... Head of Department Signature Date ii ACKNOWLEDGEMENT Thanks … To God, the Father, the giver and maker of vision. Thanks for a dream come true. To my thesis supervisor, Dr. S. K. Amponsah for his supervision throughout the study. To the Management of Latex Foam Rubber Products Limited-Kumasi (especially Mr. Afful and mr.Estmond), for providing the data for the study. Last but not least, I would like to express my gratitude to my family and friends for their support which enabled me to accomplish the study. iii DEDICATION To the family of Mr. Joseph and Madam Anna (Anna Store) D/SO II. I REALLY APPRECIATE YOUR KINDNESS iv ABSTRACT Manufacturing firms are tasked to produce to meet market demand at a minimum cost. Production and transportation are the major components of total cost to such firms. Coordinating production and distribution functions of such firms is seen as a step towards cost optimization. Latex Foam Ghana. Ltd. was incorporated in March, 1969 to produce quality foam products for the bedding and furniture Industry. In this thesis, we assume that the customers' monthly demand for high density mattress as well as the monthly production capacities of each plant is known. We consider the problem of finding an optimal monthly production program for each plant as well as the optimal monthly transportation of products to customers for which the sum of the production and transportation costs is minimized. We solve the production and transportation planning problems sequentially each by the transportation model for the available data from Latex Foam Ghana Ltd for the 2012 operation year. As a result we get a complete solution consisting of production and transportation plans. The study revealed that with the introduction this model, management could reduce production and transportation cost by 43% and 38% respectively. The model is useful for annual budget planning and financial planning. The proposed model solution has demonstrated improvement in cost optimization as compared to the rule-of-thumb based planning. v TABLE OF CONTENT DECLARATION ........................................................................................................II ACKNOWLEDGEMENT ....................................................................................... III DEDICATION ......................................................................................................... IV ABSTRACT................................................................................................................ V TABLE OF CONTENT ........................................................................................... VI LIST OF TABLE ..................................................................................................... IX LIST OF FIGURE ..................................................................................................... X LIST OF ABBREVIATIONS .................................................................................. XI CHAPTER 1 ................................................................................................................ 1 INTRODUCTION ....................................................................................................... 1 1.1.BACKGROUND OF THE STUDY...................................................................... 2 1.1.1 PROFILE OF THE STUDY AREA ................................................................... 2 1.1.2THE PRODUCTION SYSTEM ......................................................................... 3 1.1.3 THE TRANSPORTATION PROBLEM ............................................................ 6 1.1.4THE PRE-INDUSTRIAL PRODUCTION-TRANSPORTATION ERA ............. 6 1.1.5 THE INDUSTRIAL REVOLUTION ................................................................. 7 1.1.6 PRODUCTION AND TRANSPORTATION TODAY ...................................... 8 1.2 STATEMENT OF THE PROBLEM ..................................................................... 9 1.3 OBJECTIVES OF THE STUDY ........................................................................ 10 1.4 RESEARCH METHODOLOGY ........................................................................ 10 1.5 JUSTIFICATION .............................................................................................. 11 1.6 SCOPE OF THE PROBLEM.............................................................................. 11 1.7 THE MANUFACTURING ENVIRONMENT AND MEANS OF TRANSPORTATION IN GHANA .......................................................................... 12 1.7.1 ROAD TRANSPORT IN GHANA .................................................................. 13 1.7.2 RAIL TRANSPORT IN GHANA .................................................................... 13 1.7.3 AIR TRANSPORT IN GHANA ...................................................................... 14 1.7.4 WATER TRANSPORT IN GHANA ............................................................... 14 1.8 LIMITATION OF THE STUDY ........................................................................ 15 1.9 THESIS ORGANISATION................................................................................ 15 vi CHAPTER 2 .............................................................................................................. 16 LITERATURE REVIEW ......................................................................................... 16 2.0 INTRODUCTION ............................................................................................. 16 2.1 PRODUCTION SCHEDULING, A FUNCTION OF PRODUCTION PLANNING AND CONTROL ..................................................................................................... 16 2.2 THE TRANSPORTATION PROBLEM ............................................................. 24 2.3 INTEGRATING PRODUCTION AND TRANSPORTATION PROBLEMS ..... 25 2.4 SUMMARY ...................................................................................................... 33 CHAPTER 3 .............................................................................................................. 34 METHODOLOGY .................................................................................................... 34 3.0 INTRODUCTION ............................................................................................. 34 3.1 THE PRODUCTION PROBLEM ...................................................................... 34 3.2 GRAPHICAL REPRESENTATION OF TRANSPORTATION MODEL ........... 34 3.3 MATHEMATICAL MODEL OF TRANSPORTATION PROBLEM ................. 35 3.4 FORMULATING THE TRANSPORATATION PROBLEM AS A LINEAR PROGRAMMING MODEL 36 3.5 THE BALANCED TRANSPORTATION PROBLEM ....................................... 38 3.6 BALANCING AN UNBALANCED TRANSPORTATION PROBLEM ............ 41 3.6.1 IF THE TOTAL SUPPLY EXCEEDS TOTAL DEMAND .............................. 41 3.6.2 IF TOTAL DEMAND EXCEEDS TOTAL SUPPLY....................................... 42 3.7 METHODS OF SOLVING TRANSPORTATION PROBLEMS ........................ 43 3.7.1 FINDING INITIAL BASIC FEASIBLE SOLUTION OF BALANCED TRANSPORTION PROBLEMS (IBFS). ................................................................. 44 3.7.1.1 THE NORTHWEST CORNER RULE ......................................................... 44 3.7.1.2 THE LEAST COST METHOD ..................................................................... 46 3.7.1.3 THE VOGEL‘S APPROXIMATION METHOD (VAM) .............................. 46 3.7.2 METHODS FOR SOLVING TRANSPORTATION PROBLEMS TO OPTIMALITY……………………………………………………………………….47 3.7.2.1 THE STEPPINGSTONE METHOD ............................................................. 47 3.7.2.2 THE MODIFIED DISTRIBUTION METHOD (MODI) ............................... 49 3.8 SUMMARY ...................................................................................................... 50 vii CHAPTER 4 .............................................................................................................. 51 DATA COLLECTION AND ANALYSIS ................................................................ 51 4.0 INTRODUCTION ............................................................................................. 51 4.1 PROBLEM DESCRIPTION .............................................................................. 51 4.2 PRODUCTION LEVELS .................................................................................. 52 4.3 FORMULATING THE PRODUCTION PLANNING PROBLEM BY THE TRANSPORTATION MODEL ..............................................................................