Batch Processsor Scheduling - A Class Of Problems In Steel Casting Foundries
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Modern manufacturing systems need new types of scheduling methods. While traditional scheduling methods are primarily concerned with sequencing of jobs, modern manufacturing environments provide the additional possibility to process jobs in batches. This adds to the complexity of scheduling. There are two types of batching namely: (i) serial batching (jobs may be batched if they share the same setup on a machine and one job is processed at a time. The machine which processes jobs in this manner is called as discrete processor) and (ii) parallel batching (several jobs can be processed simultaneously on a machine at a time. The machine which processes jobs in this manner is called as batch processor or batch processing machine). Parallel batching environments have attracted wide attention of the researchers working in the field of scheduling. Particularly, taking inspiration from studies of scheduling batch processors in semiconductor manufacturing [Mathirajan and Sivakumar (2006b) and Venkataramana (2006)] and in steel casting industries [Krishnaswamy et al. (1998), Shekar (1998) and Mathirajan (2002)] in the Management Studies Department of Indian Institute of Science, this thesis addresses a special problem on scheduling batch processor, observed in the steel casting manufacturing. A fundamental feature of the steel casting industry is its extreme flexibility, enabling castings to be produced with almost unlimited freedom in design over an extremely wide range of sizes, quantities and materials suited to practically every environment and application. Furthermore, the steel casting industry is capital intensive and highly competitive. From the viewpoint of throughput and utilization of the important and costly resources in the foundry manufacturing, it was felt that the process-controlled furnace operations for the melting and pouring operations as well as the heat-treatment furnace operations are critical for meeting the overall production schedules. The two furnace operations are batch processes that have distinctive constraints on job-mixes in addition to the usual capacity and technical constraints associated with any industrial processes. The benefits of effective scheduling of these batch processes include higher machine utilization, lower work-in-process (WIP) inventory, shorter cycle time and greater customer satisfaction [Pinedo (1995)]. Very few studies address the production planning and scheduling models for a steel foundry, considering the melting furnace of the pre-casting stage as the core foundry operation [Voorhis et al. (2001), Krishnaswamy et al. (1998) and Shekar (1998)]. Even though the melting and pouring operations may be considered as the core of foundry operations and their scheduling is of central importance, the scheduling of heat-treatment furnaces is also of considerable importance. This is because the processing time required at the heat treatment furnace is often longer compared to other operations in the steel-casting foundry and therefore considerably affects the scheduling, overall flow time and WIP inventory. Further, the heat-treatment operation is critical because it determines the final properties that enable components to perform under demanding service conditions such as large mechanical load, high temperature and anti-corrosive processing. It is also important to note that the heat-treatment operation is the only predominantly long process in the entire steel casting manufacturing process, taking up a large part of total processing time (taking up to a few days as against other processes that typically take only a few hours). Because of these, the heat-treatment operation is a major bottleneck operation in the entire steel casting process. The jobs in the WIP inventory in front of heat-treatment furnace vary widely in sizes (few grams to a ton) and dimensions (from 10 mm to 2000 mm). Furthermore, castings are primarily classified into a number of job families based on the alloy type, such as low alloy castings and high alloy castings. These job families are incompatible as the temperature requirement for low alloy and high alloy vary for similar type of heat-treatment operation required. These job families are further classified into various sub-families based on the type of heat treatment operations they undergo. These sub-families are also incompatible as each of these sub-families requires a different combination of heat-treatment operation. The widely varying job sizes, job dimensions and multiple incompatible job family characteristic introduce a high degree of complexity into scheduling heat-treatment furnace. Scheduling of heat-treatment furnace with multiple incompatible job families can have profound effect on the overall production rate as the processing time at heat-treatment operation is very much longer. Considering the complexity of the process and time consumed by the heat treatment operation, it is imperative that efficient scheduling of this operation is required in order to maximize throughput and to enhance productivity of the entire steel casting manufacturing process. This is of importance to the firm. The concerns of the management in increasing the throughput of the bottleneck machine, thereby increasing productivity, motivated us to adopt the scheduling objective of makespan. In a recent observation of heat-treatment operations in a couple of steel casting industries and the research studies reported in the literature, we noticed that the real-life problem of dynamic scheduling of heat-treatment furnace with multiple incompatible job families, non-identical job sizes, non-identical job dimensions, non-agreeable release times and due dates to maximize the throughput, higher utilization and minimize the work-in-process inventory is not at all addressed. However, there are very few studies [Mathirajan et al. (2001, 2002, 2004a, 2007)] which have addressed the problem of scheduling of heat-treatment furnace with incompatible job families and non-identical job sizes to maximize the utilization of the furnace. Due to the difference between the real-life situation on dynamic scheduling of heat-treatment furnace of the steel casting manufacturing and the research reported on the same problem, we identified three new class of batch processor problems, which are applicable to a real-life situation based on the type of heat-treatment operation(s) being carried out and the type of steel casting industry (small, medium and large scale steel casting industry) and this thesis addresses these new class of research problems on scheduling of batch processor. The first part of the thesis addresses our new Research Problem (called Research Problem 1) of minimizing makespan (Cmax) on a batch processor (BP) with single job family (SJF), non-identical job sizes (NIJS), and non-identical job dimensions (NIJD). This problem is of interest to small scale steel casting industries performing only one type of heat treatment operation such as surface hardening. Generally, there would be only a few steel casting industries which offer such type of special heat-treatment operation and thus the customer is willing to accept delay in the completion of his orders. So, the due date issues are not important for these types of industries. We formulate the problem as Mixed Integer Linear Programming (MILP) model and validate the proposed MILP model through a numerical example. In order to understand the computational intractability issue, we carry out a small computational experiment. The results of this experiment indicate that the computational time required, as a function of problem size, for solving the MILP model is non-deterministic and non-polynomial. Due to the computational intractability of the proposed MILP model, we propose five variants of a greedy heuristic algorithm and a genetic algorithm for addressing the Research Problem 1. We carry out computational experiments to obtain the performance of heuristic algorithms based on two perspectives: (i) comparison with optimal solution on small scale instances and (ii) comparison with lower bound for large scale instances. We choose five important problem parameters for the computational experiment and propose a suitable experimental design to generate pseudo problem instances. As there is no lower bound (LB) procedure for the Research Problem1, in this thesis, we develop an LB procedure that provides LB on makespan by considering both NIJS and NIJD characteristics together. Before using the proposed LB procedure for evaluating heuristic algorithms, we conduct a computational experiment to obtain the quality of the LB on makespan in comparison with optimal makespan on number of small scale instances. The results of this experiment indicate that the proposed LB procedure is efficient and could be used to obtain LB on makespan for any large scale problem. In the first perspective of the evaluation of the performance of the heuristic algorithms proposed for Research Problem 1, the proposed heuristic algorithms are run through small scale problem instances and we record the makespan values. We solve the MILP model to obtain optimal solutions for these small scale instances. For comparing the proposed heuristic algorithms we use the performance measures: (a) number of times the proposed heuristic algorithm solution equal to optimal solution and (b) average loss with respect to optimal solution in percentage. In the second perspective of the evaluation of the performance of the heuristic algorithms, the proposed heuristic algorithms are run through large scale problem instances and we record the makespan values. The LB procedure is also run through these problem instances to obtain LB on makespan. For comparing the performance of heuristic algorithms with respect to LB on makespan, we use the performance measures: (a) number of times the proposed heuristic algorithm solution equal to LB on makespan (b) average loss with respect to LB on makespan in percentage, (c) average relative percentage deviation and (d) maximum relative percentage deviation. We extend the Research Problem 1 by including additional job characteristics: job arrival time to WIP inventory area of heat-treatment furnace, due date and additional constraint on non-agreeable release time and due date (NARD). Due date considerations and the constraint on non-agreeable release times and due date (called Research Problem 2) are imperative to small scale steel casting foundries performing traditional but only one type of heat treatment operation such as annealing where due date compliance is important as many steel casting industries offer such type of heat treatment operations. The mathematical model, LB procedure, greedy heuristic algorithm and genetic algorithm proposed for Research Problem 1, including the computational experiments, are appropriately modified and\or extended for addressing Research Problem 2. Finally, we extend the Research Problem 2 is by including an additional real life dimension: multiple incompatible job families (MIJF). This new Research Problem (called Research Problem 3) is more relevant to medium and large scale steel casting foundries performing more than one type of heat treatment operations such as homogenizing and tempering, normalizing and tempering. The solution methodologies, the LB procedure and the computational experiments proposed for Research Problem 2 are further modified and enriched to address the Research Problem 3. From the detailed computational experiments conducted for each of the research problems defined in this study, we observe that: (a) the problem parameters considered in this study have influence on the performance of the heuristic algorithms, (b) the proposed LB procedure is found to be efficient, (c) the proposed genetic algorithm outperforms among the proposed heuristic algorithms (but the computational time required for genetic algorithm increases as problem size keeps increasing), and (d) in case the decision maker wants to choose an heuristic algorithm which is computationally most efficient algorithm among the proposed algorithms, the variants of greedy heuristic algorithms : SWB, SWB(NARD), SWB(NARD&MIJF) is relatively the best algorithm for Research Problem 1, Research Problem 2 and Research Problem 3 respectively.
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