Just-in-Time Scheduling with Machining Economics for Single-Machine Turning Process

Traditional machining economics looks into the optimal set of machining conditions under which the production cost or time per part is minimized. No due dates are included in the consideration. Job sequencing searches for the optimal order of jobs so that lateness and/or earliness is minimized. The optimization assumes that processing times are fixed. In practice, processing times are variable within a certain range by adjusting the combination of machining conditions. This paper presents the modeling of a machining sequencing problem that is integrated with the lower-level machining process optimization problem of a turning process in a justin-time delivery environment. A combination of dynamic programming and an enumerative procedure is used to solve the optimization problem. Keyword$ : Just-in-Time, Sequencing, Economics, Due Window Scheduling Machining Introduction The widespread adoption of the just-in-time (JIT) philosophy has led manufacturers to develop scheduling policies with the goal of producing products at the necessary time, that is, simultaneously minimizing both earliness and tardiness costs. There are a number of papers on scheduling problems involving tardiness and earliness costs. For a recent comprehensive review, see Baker and Scudder. ~ However, the literature is scanty on earliness/tardiness problems with controllable job processing times. Actually, processing time can be easily adjusted by changing the machine parameters such as cutting speed and feeding rate. Work on controllable job processing times was initialized by Vickson. z'3 Van Wassenhove and Baker, 4 Nowicki and Zdrzalka, s and Panwalker and Rajagopalan 6 have also contributed notably to this topic. Their considerations are more in the traditional production environment where JIT is not practiced. For a good summary of the known results of the problems concerning controllable processing times, the reader is referred to the survey paper by Nowicki and Zdrzalka. 7 Solutions to machine economics problems seek the optimal machining conditions that minimize the production cost or production cycle time. There are also many papers on this topic, for example, Wysk, 8 Hati and Rao, 9 Challa and Berra, 10 Subbarao and Jacobs," Hayes, Davis, and Wysk, Iz Chang et al., 13 Arsecularatne, Hinduja, and Barrow, 14 Zhou and Wysk, ~ Linn and Mishra, ~6 and Yeo? 7 Generally speaking, these studies sought the optimal cutting speed, feed rate, and/or depth of cut for either minimal production time or cost to produce a batch of the same parts. The due dates were not considered in the problems. In practice, job sequencing and machining process parameters should be determined simultaneously to achieve best performance. This study integrates machining process optimization with the job sequencing problem of a single turning process. Considered is a single-machine problem with due windows and controllable job processing times by changing machining parameters. The objective is to minimize the total sum of earliness, tardiness, and machining costs. Problem Description Consider a single-machine scheduling problem in which there is a set of n parts, N -{ 1, 2, 3 ..... n }, to be processed on the machine without preemption. The processing time pj o fpa r t j is a variable and can be adjusted by altering the machining conditions. Let S denote the set of all permutations of all parts 1, 2, ..., n, let s be a sequence of the parts while s E S, let t be the vector of the starting time of the parts