PRODUCTION PLANNING AND SCHEDULING IN  
                MULTI-STAGE BATCH PRODUCTION ENVIRONMENT 
           
           
           
           
           
                                A THESIS 
            SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS 
                 FOR THE FELLOW PROGRAMME IN MANAGEMENT 
                     INDIAN INSTITUTE OF MANAGEMENT 
                              AHMEDABAD 
           
           
           
                                  By 
                                    
                                    
                                    
                                    
                             PEEYUSH MEHTA 
                            Date: March 15, 2004 
                                    
                                    
                                    
                          Thesis Advisory Committee 
                      __________________________[Chair] 
                            [PANKAJ CHANDRA]  
                     __________________________[Co-Chair] 
                           [DEVANATH TIRUPATI] 
                     __________________________[Member] 
                           [ARABINDA TRIPATHY] 
           
           
           
           
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                 Production Planning and Scheduling in  
                Multi-Stage Batch Production Environment 
                           By 
                        Peeyush Mehta 
                            
                         ABSTRACT 
           We address the problem of jointly determining production planning and scheduling 
        decisions in a complex multi-stage, multi-product, multi-machine, and batch-production 
        environment. Large numbers of process and discrete parts manufacturing industries are 
        characterized by increasing product variety, low product volumes, demand variability and 
        reduced strategic planning cycle. Multi-stage batch-processing industries like chemicals, 
        food, glass,  pharmaceuticals, tire, etc. are some examples that face this environment. Lack of 
        efficient production planning and scheduling decisions in this environment often results in 
        high inventory costs and low capacity utilization.  
            
           In this research, we consider the production environment that produces intermediate 
        products, by-products and finished goods at a production stage. By-products are recycled to 
        recover reusable raw materials. Inputs to a production stage are raw materials, intermediate 
        products and reusable raw materials. Complexities in the production process arise due to the 
        desired coordination of various production stages and the recycling process. We consider 
        flexible production resources where equipments are shared amongst products. This often 
        leads to conflict in the capacity requirements at an aggregate level and at the detailed 
        scheduling level.  The environment is characterized by dynamic and deterministic demands 
        of finished goods over a finite planning horizon, high set-up times, transfer lot sizes and 
        perishability of products. The decisions in the problem are to determine the production 
        quantities and inventory levels of products, aggregate capacity of the resources required and 
        to derive detailed schedules at minimum cost.  
            
           We determine production planning and scheduling decisions through a sequence of 
        mathematical models. First, we develop a mixed-integer programming (MIP) model to 
        determine production quantities of products in each time period of the planning horizon. The 
        objective of the model is to minimize inventory and set-up costs of intermediate products and 
        finished goods, inventory costs of by-products and reusable raw materials, and cost of fresh 
        raw materials.  This model also determines the aggregate capacity of the resources required 
        to implement the production plan. We develop a variant of the planning model for jointly 
        planning sales and production. This model has additional market constraints of lower and 
        upper bounds on the demand. Next, we develop an MIP scheduling model to execute the 
        aggregate sales and productions plans obtained from the planning model. The scheduling 
        model derives detailed equipment wise schedules of products. The objective of the 
        scheduling model is to minimize earliness and tardiness (E/T) penalties.  
            
           We use branch and bound procedure to solve the production-planning problem. 
        Demand of finished goods for each period over the planning horizon is an input to the model. 
        The planning model is implemented on a rolling horizon basis.  
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             We consider flowshop setting for the finished goods in the production environment. 
         The due dates of finished goods are based on the customer orders. We report some new 
         results for  scheduling decisions in a permutation flowshop with E/T penalties about a 
         common due date. This class of problems can be sub-divided into three groups- one, where 
         the common due date is such that all jobs are necessarily tardy; the second, where the due 
         date is such that the problem is unrestricted; and third is a group of problems where the due 
         date is between the above two. We develop analytical results and heuristics for flow shop E/T 
         problems arising in each of these three classes. We also report computational performance on 
         these heuristics. The intermediate products follow a general job shop production process with 
         re-entrant flows. We develop heuristics to determine equipment wise schedule of 
         intermediate products at each level of the product structure. The due date of an intermediate 
         product is based on the schedule of its higher-level product.  
              
             The models developed are tested on data for a chemical company in India. The results 
         of cost minimization model in a particular instance indicated savings of 61.20 percent in 
         inventory costs of intermediate products, 38.46 percent in set-up costs, 8.58 percent in 
         inventory costs of by-products and reusable raw materials, and 20.50 percent in fresh raw 
         material costs over the actual production plan followed by the company. The results of the 
         contribution maximization model indicate 42.54 percent increase in contribution. We also 
         perform sensitivity analysis on results of the production planning and scheduling problem. 
              
             The contribution of this research is the new complexities addressed in the production 
         planning and scheduling problem. Traditional models on  multi-stage production planning and 
         scheduling are primarily based on assembly and fabrication types of product structures and 
         do not consider the issues involved in recycling process. Scheduling theory with E/T 
         penalties is largely limited to single machine environment. We expect that models developed 
         in this research would form basis for production planning and scheduling decisions in multi-
         stage, multi-machine batch processing systems. The sensitivity analysis of the models would 
         provide an opportunity to the managers to evaluate the alternate production plans and to 
         respond to the problem complexities in a better way. 
          
          
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                       Acknowledgements 
           I wish to express my deepest gratitude to my thesis advisor Professor Pankaj Chandra. 
        He has been a tremendous source  of learning for me during my stay at IIMA. Professor 
        Chandra has been a great motivator, and has a significant share in my academic grooming. 
        Much of the credit for this work goes to Professor Devanath Tirupati, co-chair of my thesis 
        committee. He has been very patient with me and has provided very useful research training. I 
        would also like to thank Professor Arabinda Tripathy, member of my thesis committee for 
        providing very useful feedback throughout my work.  
           I am grateful to Professor Diptesh Ghosh, Professor P. R. Shukla, Professor Ashok 
        Srinivasan and Professor Goutam Dutta for their useful feedback on my thesis. I am also 
        thankful to Professor Shiv Srinivasan for giving some pointers on the drafting of this 
        document.  
           I wish to especially thank my wife Ritu, as this thesis would not have been possible 
        without her support. She has a major share in raising our daughter Riti, and her break from her 
        professional career helped me to stay focused on my work Riti always provided the much-
        needed break from the thesis work. I dedicate this work to my parents. They have eagerly 
        waited to see me accomplish this work. Dhiraj, my brother, has been, as always, a source of 
        encouragement.  
           I would like to thank my colleagues Bharat, Rohit, Satyendra and all those with whom 
        I have interacted at various stages of my thesis. The staff members of FPM office, computer 
        center and library have obliged me in more ways than one. 
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