Proportionate flow-shop scheduling with rejection

In many heavily loaded manufacturing systems, managers routinely make use of outsourcing options in order to maintain reasonable Quality of Service for customers. Thus, there is a strong need to provide tools for managers to economically coordinate sourcing and scheduling decisions. Our main aim is to provide such tools for an important set of flow-shop scheduling problems where rejection (outsourcing) is allowed and processing times are machine-independent. Our scheduling problems are essentially bicriteria problems, which combine a scheduling objective and the total outsourcing cost. We study several problems which differ according to the scheduling criterion considered. Moreover, each problem is divided into four different variations depending on the way the two criteria are dealt with. For example, in one variation the two criteria are aggregated into a single objective function; in two other variations the aim consists of minimizing one criterion subject to ensuring that the value of the other criterion will not exceed a predefined threshold. From a theoretical point of view, a computational complexity classification is provided for all variations of the problems under consideration. Moreover, optimization algorithms have been constructed to solve all problem variations, and approximation schemes have been developed for solving hard variations. Those schemes enable managers to solve large instances of hard variations while controlling the maximal gap between the obtained solution and the (unknown) optimal solution.

[1]  Byung-Cheon Choi,et al.  Two-stage production scheduling with an outsourcing option , 2011, Eur. J. Oper. Res..

[2]  Gerhard J. Woeginger,et al.  When Does a Dynamic Programming Formulation Guarantee the Existence of a Fully Polynomial Time Approximation Scheme (FPTAS)? , 2000, INFORMS J. Comput..

[3]  Yuzhong Zhang,et al.  On Several Scheduling Problems with Rejection or Discretely Compressible Processing Times , 2006, TAMC.

[4]  Leen Stougie,et al.  Multiprocessor scheduling with rejection , 1996, SODA '96.

[5]  Zhigang Cao,et al.  A PTAS for parallel batch scheduling with rejection and dynamic job arrivals , 2009, Theor. Comput. Sci..

[6]  T.C.E. Cheng,et al.  A modified artificial bee colony algorithm for order acceptance in two-machine flow shops , 2013 .

[7]  Deming Lei,et al.  A parallel neighborhood search for order acceptance and scheduling in flow shop environment , 2015 .

[8]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[9]  Dvir Shabtay,et al.  Two-machine flow-shop scheduling with rejection , 2012, Comput. Oper. Res..

[10]  Chuanli Zhao,et al.  Single Machine Scheduling with an Availability Constraint and Rejection , 2014, Asia Pac. J. Oper. Res..

[11]  Susan A. Slotnick,et al.  Order acceptance and scheduling: A taxonomy and review , 2011, Eur. J. Oper. Res..

[12]  John A. Quelch,et al.  Externalizar el márketing , 2005 .

[13]  Yuzhong Zhang,et al.  Scheduling with Rejection to Minimize the Makespan , 2009, COCOA.

[14]  Sudipta Sengupta,et al.  Algorithms and Approximation Schemes for Minimum Lateness/Tardiness Scheduling with Rejection , 2003, WADS.

[15]  Vincent T'Kindt,et al.  A note on "Two-machine flow-shop scheduling with rejection" and its link with flow-shop scheduling and common due date assignment , 2012, Comput. Oper. Res..

[16]  Qiang Gao,et al.  Two-Machine Flow shop Scheduling with Individual Operation's rejection , 2014, Asia Pac. J. Oper. Res..

[17]  Byung-Cheon Choi,et al.  Two-machine flow shop scheduling problem with an outsourcing option , 2010, Eur. J. Oper. Res..

[18]  Guochuan Zhang,et al.  On Two-machine Flow Shop Scheduling , 2014 .

[19]  Prabuddha De,et al.  Optimal Delivery Time Quotation and Order Sequencing , 1991 .

[20]  David Simchi-Levi,et al.  Fully polynomial time approximation schemes for stochastic dynamic programs , 2008, SODA '08.

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

[22]  Lingfa Lu,et al.  New results on two-machine flow-shop scheduling with rejection , 2016, J. Comb. Optim..

[23]  Ceyda Oguz,et al.  A tabu search algorithm for order acceptance and scheduling , 2012, Comput. Oper. Res..

[24]  Dvir Shabtay,et al.  A survey on offline scheduling with rejection , 2013, J. Sched..

[25]  P. B. Coaker,et al.  Applied Dynamic Programming , 1964 .

[26]  Byung-Cheon Choi,et al.  Minimizing maximum completion time in a proportionate flow shop with one machine of different speed , 2007, Eur. J. Oper. Res..

[27]  Mikhail Y. Kovalyov,et al.  An FPTAS for a single-item capacitated economic lot-sizing problem with monotone cost structure , 2006, Math. Program..

[28]  Zhigang Cao,et al.  Scheduling with Rejection and Non-Identical Job Arrivals , 2007, J. Syst. Sci. Complex..

[29]  David R. Karger,et al.  Techniques for scheduling with rejection , 2003, J. Algorithms.

[30]  Shijie Sun,et al.  Scheduling linear deteriorating jobs with rejection on a single machine , 2009, Eur. J. Oper. Res..

[31]  Eugene L. Lawler,et al.  Fast approximation algorithms for knapsack problems , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[32]  Samir Khuller,et al.  An Optimal Incremental Algorithm for Minimizing Lateness with Rejection , 2008, ESA.

[33]  Sartaj Sahni,et al.  Algorithms for Scheduling Independent Tasks , 1976, J. ACM.

[34]  S. S. Panwalkar,et al.  Sequencing Research and the Industrial Scheduling Problem , 1973 .

[35]  David R. Karger,et al.  Techniques for scheduling with rejection , 1998, J. Algorithms.

[36]  Oscar H. Ibarra,et al.  Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems , 1975, JACM.

[37]  Wieslaw Kubiak,et al.  Scheduling shops to minimize the weighted number of late jobs , 1994, Oper. Res. Lett..

[38]  Hans Kellerer,et al.  A New Fully Polynomial Approximation Scheme for the Knapsack Problem , 1998, APPROX.

[39]  Ikou Kaku,et al.  Permutation flow shop scheduling with order acceptance and weighted tardiness , 2012, Appl. Math. Comput..

[40]  Abdullah Konak,et al.  Non-permutation flow shop scheduling with order acceptance and weighted tardiness , 2015, Appl. Math. Comput..

[41]  Dvir Shabtay,et al.  A bicriteria approach to scheduling a single machine with job rejection and positional penalties , 2012, J. Comb. Optim..

[42]  Han Hoogeveen,et al.  Minimizing total weighted completion time in a proportionate flow shop , 1998 .

[43]  Hans Kellerer,et al.  A New Fully Polynomial Time Approximation Scheme for the Knapsack Problem , 1999, J. Comb. Optim..

[44]  Jean-Charles Billaut,et al.  Multicriteria scheduling , 2005, Eur. J. Oper. Res..

[45]  Federico Della Croce,et al.  Enumeration of Pareto Optima for a Flowshop Scheduling Problem with Two Criteria , 2007, INFORMS J. Comput..

[46]  Yingjie Liu.  The Fully Polynomial Approximation Algorithm for the 0-1 Knapsack Problem , 2002, Theory of Computing Systems.

[47]  Jacques Carlier,et al.  Handbook of Scheduling - Algorithms, Models, and Performance Analysis , 2004 .

[48]  Stuart E. Dreyfus,et al.  Applied Dynamic Programming , 1965 .

[49]  T.C.E. Cheng,et al.  Order acceptance and scheduling in a two-machine flowshop , 2013 .