MODELLING AND ANALYSIS OF INTEGRATED PRODUCTION - INVENTORY - DISTRIBUTION SYSTEMS. A. NOORUL HAQ Department of Mechanical Engineering

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1 MODELLING AND ANALYSIS OF INTEGRATED PRODUCTION - INVENTORY - DISTRIBUTION SYSTEMS 0 00 By A. NOORUL HAQ Department of Mechanical Engineering z-l1l2 THESIS SUBMITTED IN FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY b 1LS% to the INDIAN INSTITUTE OF TECHNOLOGY, DELHI September, 1990

2 CERTIFICATE The thesis entitled "Modelling and Analysis of Integrated Production-Inventory-Distribution Systems" being submitted by Mr. A.Noorul Haq to the Indian Institute of Technology, New Delhi, for the award of the degree of Doctor of Philosophy, is a record of bonafide research work carried out by him. He has worked under our guidance and supervision, and has fulfilled the requirements for the submission of this thesis, which has attained the standard required for a Ph.D. degree of the Institute. The results presented in this thesis have not been submitted elsewhere for the award of any degree or diploma. Prof. PREM VRAT Prof. of Industrial Engineering Department of Mechanical Engineering Indian Institute of Technology New Delhi Dr. ARUN KANDA Asst. Prof. of Industrial Engineering Department of Mechanical Engineering Indian Institute of Technology New Delhi

3 ACKNOWLEDGEMENT I take this opportunity to express my deepest sense of gratitude to Prof.Prem Vrat and Dr.Arun Kanda of Department of Mechanical Engineering, Indian Institute of Technology, New Delhi for their able guidance, encouragement and suggestions through out the period of research work reported in this thesis. At every stage of my work I have freely encroached upon their time, and, but for their keen interest, invaluable guidance and intellectual stimulation, this study would not have taken its present shape. I thank the authorities of Regional Engineering College, Tiruchirapalli (Tamilnadu) for sponsoring me under Q.I.P. for the Doctoral Programme. I wish to express my thanks to Dr.C.R.Kandaswamy, Prof. and Head of the Department of Production Engineering, Regional Engineering College, Tiruchirapalli for his support and motivation to do the Doctoral Programme under Q.I.P. Thanks are due to my colleagues, Mr.R.Narayanasamy and Mr.T.Selvaraj for looking after my official as well as personal matters at Regional Engineering College, Tiruchirapalli during the period of my stay at 1.I.T. Delhi for the Doctoral Programme. I am extremely fortunate in having friends like Mr.D.N.Rao, Mr.V.Shankar, Mr.P.M.Jawahar, Mr.G.Padmanabhan, Mr.G.Kanagaraj and Mr.S.Bhaskar who gave me constant encouragement and moral support throughout my stay at IIT Delhi. I wish to appreciate and thank my wife Raziya and daughters Shaheen and Shahanaz, for their patience, understanding and co-operation, but for which this work could not have been completed in time. Finally, I wish to thank Mr. Balachandran for his painstaking efforts and excellent typing. C K,1 WN G.)

4 ABSTRACT The main objective of this thesis is to model and analyze integrated productioninventory-distribution systems incorporating many of the realistic conditions found in practice such as, multiple production stages, multiple levels (plant-warehouse-retailer), multiple periods, multiple modes of transfer, multiple objectives, set-up costs, lead times, losses during production and distribution, recycling of production losses, inflationary trend of the cost parameters and deterioration of the product. The thesis consists of ten chapters. Initially, the study introduces the subject, presents an overview of the problem and brings out the importance of the integration concepts. A consolidated review of the literature is presented with pictorial and tabular schemes. Two alternative formulations, a linear programming (without set-up cost) and a network flow based model (with set-up cost) are proposed for the integrated production-inventory-distribution systems. The effects of production losses, in the form of defectives, and distribution losses in the form of damages during production and distribution stages of the integrated system are then explored. The recycling concept is also considered in which the defectives occurring at any stage of production are sent for rework at the same stage and after reprocessing, these are sent to the next stage of production. A network model with side constraints and a mixed integer programming model are also developed, incorporating a constant rate of inflation, deterioration of inventory (I)

5 and lost sales. In one of the models, a mixture of lost sales and backlogging is considered. Multiple modes of distribution which vary with respect to time and cost in a distribution network of integrated systems are included in generalizing the network model developed earlier. An attempt is then made to consider multiple objectives in production-inventorydistribution systems. A goal programming approach is used to model and analyze the system. A real life case study pertaining to a large public sector organisation manufacturing fertilizers is presented on the application of the integrated productioninventory-distribution model. Finally a summary of research and the contributions of the research study are highlighted. The limitations and the possible extensions for future research are also suggested. An extensive bibliography on the subject is included. A substantial part of the research reported in this thesis is presented in various journals/conferences. A list of papers presented based on the work reported is given at the end.

6 CONTENTS Page.No: ABSTRACT LIST OF FIGURES LIST OF TABLES NOMENCLATURE (i) (xii) (xiiv) (xviii) CHAPTER I INTRODUCTION 1.1 Multi-stage production-inventory-system Important aspects of multi-stage production-inventory systems Design of multi-stage production-inventory system Planning and control of multi-stage production-inventory system Inventory control in a multi-stage production-inventory system Multi-echelon distribution-inventory systems Important aspects of multi-echelon distribution-inventory systems Design of a multi-echelon distributioninventory system Planning and control of a multi- echelon distribution-inventory system Inventory control in a multi-echelon distribution-inventory system Concept of integration Parameters relevant to productioninventory-distribution systems Scope of the present research Over-view of the thesis 18

7 CHAPTER II LITERATURE REVIEW 2.1 Introduction Proposed classification scheme Review of the literature on general production-inventory and distributioninventory systems Pictorial scheme for the review Tabular scheme for the review A Review of models based on nature of demand A.1 Deterministic models A.la Models with static demand A.lb Models with dynamic demand A.2 Stochastic model B Review of models based on the planning horizon Review of models based on the number of products D E Review of models based on the number of production stages 33 Review of models based on the system configuration E.1 Models on production-inventory systems E.2 Models on distribution-inventory systems E.3 Models on integrated systems F Review of papers based on the system parameters G Review of papers based on the objectives Review of literature on integrated systems 41

8 2.5 Review of literature incorporating various parameters of relevance to production-inventory and distributioninventory systems Models with lead time considerations Models with losses Models with recycling Models with inflation Models with deterioration Models with multiple modes of distribution Current state of the art Limitations of the existing models Need for further research and focus of this study Conclusions 58 CHAPTER III INTEGRATED PRODUCTION-INVENTORY-DISTRIBUTION MODEL 3.1 Introduction Linear cost model - a linear programming formulation Assumptions Production-inventory model Distribution-inventory model Production-inventory-distribution model Illustrative examples Results and analysis Fixed cost model with deterministic lead times - a network formulation Assumptions Network model 71 (v)

9 Production stage nodes Warehouse nodes Retailer nodes Production arcs Inventory arcs Distribution arcs Demand arcs Mathematical formulation Solution methodology An illustrative example Conclusions 80 CHAPTER IV EFFECT OF LOSSES IN INTEGRATED PRODUCTION- INVENTORY-DISTRIBUTION SYSTEMS 4.1 Introduction Assumptions Mathematical formulation An illustrative example Sensitivity analysis Effect of change in production and distribution loss parameters on total system cost Effect of under-estimation and overestimation of production and distribution loss parameter on total system cost Conclusions 102 CHAPTER V RECYCLING OF LOSSES IN A INTEGRATED PRODUCTION- INVENTORY-DISTRIBUTION SYSTEM 5.1 Introduction Model with recycling of all the production losses without backlogging 104

10 Assumptions Problem formulation An illustrative example Results and analysis Model with recycling of a fraction of production losses with backlogging Assumptions Mathematical formulation Results and analysis Effect of changes in recycling parameter on total system cost Effect of production loss and recycling parameter on total system cost Conclusions 119 CHAPTER VI EFFECT OF INFLATION, DETERIORATION AND LOST SALES IN INTEGRATED PRODUCTION-INVENTORY- DISTRIBUTION SYSTEMS 6.1 Introduction Network model with side constraints without backlogging Assumptions Network model Production stage nodes Recycling nodes Warehouse nodes Retailer nodes Dummy nodes Production arcs Production loss arcs Production recycling arcs 125

11 Inventory arcs Inventory loss arcs Beginning inventory arcs Distribution arcs Distribution loss arcs Demand arcs Lost sales arcs Mathematical formulation An illustrative example Discussion of results Mixed integer programming model with a mixture of backlogging and lost sales Assumptions Mathematical formulation An illustrative example Sensitivity analysis Variation in the estimated cost of production Variation in the estimated cost of carrying inventory Variation in the estimated cost of distribution ConclusiOns 142 CHAPTER VII MULTIPLE MODES OF DISTRIBUTION IN PRODUCTION- INVENTORY DISTRIBUTION SYSTEMS 7.1 Introduction Assumptions Network model Production stage nodes )

12 7.3.2 Recycling nodes Warehouse nodes Retailer nodes Dummy nodes Production arcs Production loss arcs Production recycling arcs, Inventory arcs Inventory loss arcs Beginning inventory arcs Distribution arcs Distribution loss arcs Demand arcs Backlogging arcs Lost sales arcs Mathematical formulation Illustrative example Discussion of results Conclusions 157 CHAPTER VIII MULTIPLE OBJECTIVE CONSIDERATIONS IN PRODUCTION-INVENTORY-DISTRIBUTION SYSTEMS 8.1 Introduction Assumptions System and goal constraints Inventory balance at production stages, warehouses and at retailers Capacity restrictions of production stages and distribution modes 162

13 8.3.3 Satisfying atleast a fraction of demand of a retailer Lost sales minimization Back order minimization Total system cost minimization Goal priorities Goal programming achievement function An illustrative example Sensitivity, analysis Sensitivity to changes in goal priority structures Sensitivity to variations in the capacities of production stages and distribution modes Sensitivity to changes in the demands at retailers Conclusions 177 CHAPTER IX APPLICATION OF THE PRODUCTION-INVENTORY- DISTRIBUTION MODEL TO A REAL LIFE PROBLEM 9.1 Introduction The organization Production system Distribution system Application of the model Results and analysis Sensitivity analysis Conclusions 194

14 CHAPTER X SUMMARY OF FINDINGS AND CONCLUSIONS 10.1 Introduction Summary of the research and findings Significant developments and contributions of the research study Limitations of the research study Suggestions for future research Concluding remarks 205 BIBLIOGRAPHY 206 APPENDIX 232 LIST OF PAPERS PRESENTED 235 CURRICULUM VITAE 236