The single machine weighted mean squared deviation problem

This paper studies a single machine problem related to the Just-In-Time (JIT) production objective in which the goal is to minimize the sum of weighted mean squared deviation of the completion times with respect to a common due date. In order to solve the problem, several structural and dominance properties of the optimal solution are investigated. These properties are then integrated within a branch-and-cut approach to solve a time-indexed formulation of the problem. The results of a computational experiment with the proposed algorithm show that the method is able to optimally solve instances with up to 300 jobs within reduced running times, improving other integer programming approaches.

[1]  Maurice Queyranne,et al.  Polyhedral Approaches to Machine Scheduling , 2008 .

[2]  Adam Janiak,et al.  A survey on scheduling problems with due windows , 2015, Eur. J. Oper. Res..

[3]  Joanna Józefowska,et al.  Just-in-Time Scheduling : Models and Algorithms for Computer and Manufacturing Systems , 2007 .

[4]  Hemant V. Kher,et al.  The Production of Several Items in a Single Facility with Linearly Changing Demand Rates , 2002, Decis. Sci..

[5]  William E. Weihl,et al.  Lottery scheduling: flexible proportional-share resource management , 1994, OSDI '94.

[6]  J. J. Kanet.  Minimizing the average deviation of job completion times about a common due date , 1981 .

[7]  E.L. Lawler,et al.  Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[8]  Gary D. Scudder,et al.  Sequencing with Earliness and Tardiness Penalties , 1989 .

[9]  Tobias Jacobs,et al.  An Experimental and Analytical Study of Order Constraints for Single Machine Scheduling with Quadratic Cost , 2012, ALENEX.

[10]  Wieslaw Kubiak,et al.  A half-product based approximation scheme for agreeably weighted completion time variance , 2005, Eur. J. Oper. Res..

[11]  Gerhard J. Woeginger.  An Approximation Scheme for Minimizing Agreeably Weighted Variance on a Single Machine , 1999, INFORMS J. Comput..

[12]  Jordi Pereira,et al.  Exact and heuristic procedures for single machine scheduling with quadratic earliness and tardiness penalties , 2013, Comput. Oper. Res..

[13]  Michael Pinedo,et al.  Scheduling: Theory, Algorithms, and Systems , 1994 .

[14]  Yih-Long Chang,et al.  Minimizing Mean Squared Deviation of Completion Times About a Common Due Date , 1987 .

[15]  Martin E. Dyer,et al.  Formulating the single machine sequencing problem with release dates as a mixed integer program , 1990, Discret. Appl. Math..

[16]  Óscar C. Vásquez.  For the airplane refueling problem local precedence implies global precedence , 2015, Optim. Lett..

[17]  Chengbin Chu,et al.  A lower bound for weighted completion time variance , 2010, Eur. J. Oper. Res..

[18]  Wieslaw Kubiak,et al.  Completion time variance minimization on a single machine is difficult , 1993, Oper. Res. Lett..

[19]  Débora P. Ronconi,et al.  Minimizing earliness and tardiness penalties in a single-machine problem with a common due date , 2005, Eur. J. Oper. Res..

[20]  M. Lübbecke.  Column Generation , 2010 .

[21]  Nikhil Bansal,et al.  The local–global conjecture for scheduling with non-linear cost , 2017, J. Sched..

[22]  Jose A. Ventura,et al.  Scheduling about a given common due date to minimize mean squared deviation of completion times , 1996 .

[23]  Kuo-Ching Ying,et al.  Minimizing earliness-tardiness penalties for common due date single-machine scheduling problems by a recovering beam search algorithm , 2008, Comput. Ind. Eng..

[24]  Ching-Jong Liao,et al.  A variable neighborhood search for minimizing single machine weighted earliness and tardiness with common due date , 2007, Comput. Ind. Eng..

[25]  Alan G. Merten,et al.  Variance Minimization in Single Machine Sequencing Problems , 1972 .

[26]  Yih-Long Chang,et al.  Minimizing absolute and squared deviations of completion times with different earliness and tardiness penalties and a common due date , 1987 .

[27]  Sakib A. Mondal.  Minimization of squared deviation of completion times about a common due date , 2002, Comput. Oper. Res..

[28]  B. Srirangacharyulu,et al.  An exact algorithm to minimize mean squared deviation of job completion times about a common due date , 2013, Eur. J. Oper. Res..

[29]  Ahmet B. Keha,et al.  Mixed integer programming formulations for single machine scheduling problems , 2009, Comput. Ind. Eng..

[30]  Andreas C. Nearchou,et al.  A differential evolution approach for the common due date early/tardy job scheduling problem , 2008, Comput. Oper. Res..

[31]  Gary D. Scudder,et al.  Sequencing with Earliness and Tardiness Penalties: A Review , 1990, Oper. Res..

[32]  Francis Sourd,et al.  New Exact Algorithms for One-Machine Earliness-Tardiness Scheduling , 2009, INFORMS J. Comput..

[33]  Cheng Wu,et al.  Single machine scheduling with sequence-dependent family setups to minimize maximum lateness , 2010, J. Oper. Res. Soc..

[34]  Endre Boros,et al.  Minimization of Half-Products , 1998, Math. Oper. Res..

[35]  Gilles Savard,et al.  Time-Indexed Formulations and the Total Weighted Tardiness Problem , 2005, INFORMS J. Comput..

[36]  Martin Feldmann,et al.  Single-machine scheduling for minimizing earliness and tardiness penalties by meta-heuristic approaches , 2003 .

[37]  Xiaoqiang Cai,et al.  Minimization of agreeably weighted variance in single machine systems , 1995 .

[38]  Laurence A. Wolsey,et al.  A time indexed formulation of non-preemptive single machine scheduling problems , 1992, Math. Program..

[39]  Jose A. Ventura,et al.  Minimizing single-machine completion time variance , 1995 .