Purushothaman Damodaran

Minimizing makespan for single machine batch processing with non-identical job sizes using simulated annealing

Abstract This research proposes a simulated annealing (SA) approach to minimize makespan for a single batch-processing machine. Each job has a corresponding processing time and size. The machine can process the jobs in batches as long as the machine capacity is not exceeded. The processing time of a batch is equal to the longest processing time among all jobs in the batch. Random instances were generated to test our approach with respect to solution quality and run time. The results of the SA approach were compared to CPLEX. Our approach outperforms CPLEX on all the instances.

Minimizing makespan on parallel batch processing machines

A simulated annealing approach to minimize makespan for identical parallel batch-processing machines is presented. Each job has a corresponding processing time and size. The machine can process the jobs in batches as long as the total size of all the jobs in a batch does not exceed the machine capacity. The processing time of a batch is equal to the longest processing time among all the jobs in the batch. Random instances were generated to test the approach with respect to solution quality and run time. The results of the simulated annealing approach were compared with CPLEX. The approach outperforms CPLEX on most of the instances.

A simulated annealing algorithm to minimize makespan of parallel batch processing machines with unequal job ready times

A simulated annealing (SA) algorithm to minimize the makespan on a group of identical batch processing machines arranged in parallel is presented. We consider the case where each job has an arbitrary processing time, non-identical size, and non-zero ready time. Each machine can process simultaneously several jobs as a batch as long as the machine capacity is not exceeded. The batch processing time is equal to the largest processing time among those jobs in the batch. Similarly, the batch ready time is equal to the largest ready time among all the jobs in the batch. Random instances were used to compare the results of the SA approach against a lower bound, a mathematical model, and two heuristics published in the literature: the Modified Delay (MD) heuristic and a Greedy Randomized Adaptive Search Procedure (GRASP). Computational experiments showed that the SA approach is comparable to GRASP with respect to solution quality, and less computationally costly. Both SA and GRASP comfortably outperformed the MD heuristic.

Mixed integer formulation to minimize makespan in a flow shop with batch processing machines

Batch processing machines are commonly used in wafer fabrication, kilns, and chambers used for environmental stress screening (ESS). This paper proposes two models to schedule batches of jobs on two machines in a flow shop. A set of jobs with known processing times and sizes has to be grouped, to form batches, in order to be processed on the batch processing machines. The jobs are nonidentical in size. The processing time of a batch is the longest processing time of all the jobs in that batch. Mixed integer formulations are proposed for the flow shop problem when the buffer capacity is unlimited or zero. Numerical examples are presented to demonstrate the application of our model.

Scheduling identical parallel batch processing machines to minimise makespan using genetic algorithms

This paper aims to minimise the makespan of a set of identical batch processing machines in parallel. The batch processing machine can process a batch of jobs as long as the total size of all the jobs in the batch does not exceed its capacity. The processing time of the job and its size are given. Batch processing time is equal to the longest processing job in the batch. Two interdependent decisions are required, namely grouping jobs into batches, and scheduling the batches on the machines. The problem under study is NP-hard and hence a Genetic Algorithm (GA) approach is proposed. The effectiveness of the GA approach to solve randomly generated problems was compared with a Simulated Annealing (SA) approach, a Random Keys Genetic Algorithm (RKGA), a Hybrid Genetic Heuristic (HGH) and a commercial solver. The proposed GA approach was found to be very effective in finding a good solution in a short time as opposed to SA, RKGA and a commercial solver. Both GA and HGH are marginally better than each other on different problem instances. [Submitted 17 August 2007; Revised 10 October 2007; Revised 30 May 2008; Revised 29 July 2008; Accepted 15 September 2008]

A GRASP approach for makespan minimization on parallel batch processing machines

In this paper we consider the problem of scheduling a set of identical batch processing machines arranged in parallel. A Greedy Randomized Adaptive Search Procedure (GRASP) approach is proposed to minimize the makespan under the assumption of non-zero job ready times, arbitrary job sizes and arbitrary processing times. Each machine can process simultaneously several jobs as a batch as long as the machine capacity is not violated. The batch processing time is equal to the largest processing time among those jobs in the batch. Similarly, the batch ready time is equal to the largest ready time among those jobs in the batch. The performance of the proposed GRASP approach was evaluated by comparing its results to a lower bound and heuristics published in the literature. Experimental study suggests that the solution obtained from the GRASP approach is superior compared to other heuristics.

A branch and price solution approach for order acceptance and capacity planning in make-to-order operations

Make-to-order (MTO) operations have to effectively manage their capacity to make long-term sustainable profits. This objective can be met by selectively accepting available customer orders and simultaneously planning for capacity. We model a MTO operation of a job-shop with multiple resources having regular and non-regular capacity. The MTO firm has a set of customer orders at time zero with fixed due-dates. The process route, processing times, and sales price for each order are given. Since orders compete for limited resources, the firm can only accept some orders. In this paper a Mixed-Integer Linear Program (MILP) is proposed to aid an operational manager to decide which orders to accept and how to allocate resources such that the overall profit is maximized. A branch-and-price (B&P) algorithm is devised to solve the MILP effectively. The MILP is first decomposed into a master problem and several sub-problems using Dantzig-Wolfe decomposition. Each sub-problem is represented as a network flow problem and an exact procedure is proposed to solve the sub-problems efficiently. We also propose an approximate B&P scheme, Lagrangian bounds, and approximations to fathom nodes in the branch-and-bound tree. Computational analysis shows that the proposed B&P algorithm can solve large problem instances with relatively short time.

Prescribing the Content and Timing of Product Upgrades

Demand for a family of high-technology products such as notebook computers erodes over time as competitors introduce new products that incorporate improved technologies. A manufacturer may compensate for this by applying the model formulated in this paper to prescribe the content and timing of upgrades to maximize total profit over the life cycle of the product family. The model deals with economies of scale that might be achieved by the upgrading process. It provides decision support by integrating decisions of relevant organizations in the enterprise: marketing (e.g., marketing strategy, pricing), product design engineering, process design engineering, and supply chain management (e.g., suppliers, production, outsourcing, inventory, backorders, and distribution). The paper presents a branch-and-price solution approach that employs an effective, new method for solving associated subproblems. Computations evaluate the efficacy of the solution approach and examples demonstrate contexts in which managers might apply the model to advantage.

The capacity planning problem in make-to-order enterprises

This paper addresses the short-term capacity planning problem in a make-to-order (MTO) operation environment. A mathematical model is presented to aid an operations manager in an MTO environment to select a set of potential customer orders to maximize the operational profit such that all the selected orders are fulfilled by their deadline. With a given capacity limit on each source for each resource type, solving this model leads to an optimal capacity plan as required for the selected orders over a given (finite) planning horizon. The proposed model considers regular time, overtime, and outsourcing as the sources for each resource type. By applying this model to a small MTO operation, this paper demonstrates a contrast between maximal capacity utilization and optimal operational profit.

A model to optimize placement operations on dual-head placement machines

Dual-head placement machines are important in the assembly of circuit cards because they offer the capability to place large components accurately. This paper presents a novel column-generation approach for optimizing the placement operations of a dual-head placement machine with the ultimate goal of improving the efficiency of assembly operations. Research objectives are a model that reflects relevant, practical considerations; a solution method that can solve instances within reasonable run times; and tests to establish computational benchmarks. Test results demonstrate the efficacy of our optimization approach on problems of realistic size and scope.