Minimizing Total Tardiness and Earliness Problem with Controllable Processing Times Using an Effective Heuristic Iraj Mahdavi, Vahid Kayvanfar, G.M.Komaki Department of Industrial Engineering Mazandaran Uni. Of Sci. and Tech. Babol, Iran irajarash@rediffmail.com, vkayvanf@ustmb.ac.ir, mohammad.komaki@gmail.com Abstract—This research addresses the single machine scheduling problems with controllable processing times. In this area, it is often assumed that the possible processing time of a job can be continuously controlled, i.e. it can be any number in a given interval. When the processing times of jobs are controllable, selected processing times affect both the manufacturing cost and the scheduling performance. In this study, our objective is determining a set of compression/expansion of processing times as well as a sequence of jobs simultaneously, so that total tardiness and earliness on a single machine are minimized. In this way, we first propose a mathematical model for the considered problem and then a net benefit compression-net benefit expansion (NBC-NBE) heuristic is presented for obtaining a set of amounts of compression and expansion of jobs processing times in a given sequence. Also, a simulated annealing approach is used to solve medium to large size problems as an effective local search method. The addressed problem is NP-hard since the single machine total tardiness problem (SMTTP) is already NP- hard. The computational results show that our proposed heuristic is an efficient solution method for such Just-In-Time (JIT) problem. Keywords-tardiness and earliness; controllable processing times; single machine; Just-in-time approach; heuristic algorithm. I. INTRODUCTION The importance of JIT scheduling has led to a wide range investigation of scheduling problems that include both earliness and tardiness penalty. Actually, JIT philosophy seeks to identify and eliminate waste components as over production, waiting time, transportation, processing, inventory, movement and defective products [1]. Since, neither earliness nor tardiness is desirable, because of one can represent manufacturer concerns and the other one may represent the customer concerns, it motivated us to present a model which both earliness and tardiness are minimized. It is assumed that the normal processing time of jobs can be reduced or increased to predefined limit. The controllable processing time means that each job can process in a shorter or longer time depends on its efficacy on objective function by reducing or increasing the available resources such as equipment or human resources. Scheduling problems with controllable processing time can be seen in some contexts such as metallurgy and chemical industries. For instance, in chemical industry, the processing time of job is reduced by using catalyzer or increase by an inhibitor. An inhibitor is any agent that interferes with the activity of an enzyme. Enzyme inhibitors are molecules that bind to enzymes and decrease their activity. As another example for increasing the processing time so as to minimize the earliness in the real life is project planning that project manager increase the processing time of some activities that are not in critical path to smooth the usage of facilities. Scheduling problems with controllable processing times have received increasing attention during the last decade. Most of the earlier studies on controllable processing times address the single machine environment because of complexity of working on other machine environment. Vickson [2] has studied one of the first researches on controllable processing time scheduling problems, with goal of minimizing the total flow time and the total processing cost incurred due to job processing time compression. Researches on scheduling problem with controllable processing times and linear cost functions up to 1990 are surveyed by Nowicki and Zdrzalka [3]. Panwalkar and Rajagopalan [4] considered the static single machine sequencing problem with a common due date for all jobs in which job processing times are controllable with linear costs. Zdrzalka [5] deals with the problem of scheduling jobs on a single machine in which each job has a release date, a delivery time and a controllable processing time, having its own associated linearly varying cost and propose an approximation algorithm for minimizing the overall schedule cost. Also, Cheng et al. [6] regarded the single machine scheduling problem in which job processing times as well as release dates are controllable parameters and they may vary within given intervals. There are some researches on other environments with controllable processing times. For instance, Gupta et al. [7] worked on hybrid flow shop environment with controllable processing time as well as assignable due dates. Also, Gurel and Akturk [8] surveyed the identical parallel CNC machines with controllable processing time which a time/cost trade-off consideration is conducted. In this study, our objective is determining a set of amount of