Two-machine flowshop scheduling with flexible operations and controllable processing times

Abstract

a b s t r a c tWe consider a two-machine flowshop scheduling problem with identical jobs. Each of these jobs has three operations, where the first operation must be performed on the first machine, the second operation must be performed on the second machine, and the third operation (named as flexible operation) can be performed on either machine but cannot be preempted. Highly flexible CNC machines are capable of performing different operations. Furthermore, the processing times on these machines can be changed easily in albeit of higher manufacturing cost by adjusting the machining parameters like the speed and/or feed rate of the machine. The overall problem is to determine the assignment of the flexible operations to the machines and processing times for each operation to minimize the total manufacturing cost and makespan simultaneously. For such a bicriteria problem, there is no unique optimum but a set of nondominated solutions. Using E-constraint approach, the problem could be transformed to be minimizing total manufacturing cost for a given upper limit on the makespan. The resulting single criterion problem can be reformulated as a mixed integer nonlinear problem with a set of linear constraints. We use this formulation to optimally solve small instances of the problem while a heuristic procedure is constructed to solve larger instances in a reasonable time.

Green scheduling of a two-machine flowshop: Trade-off between makespan and energy consumption

“…We develop a mathematical model to minimize makespan, a measure of service level and total energy consumption, an indicator of environmental sustainability in a two-machine permutation flowshop scheduling problem that is characterized by sequence dependent setups. Twomachine flowshop scheduling problems have many real world applications including metalworking (Uruk, Gultekin, & Akturk, 2013), printed circuit board (PCB) manufacturing (Sabouni & Logendran, 2013) and shampoo industry (Belaid, T'kindt, & Esswein, 2012) among others. As a result, two-machine scheduling problems have attracted significant attention from practitioners and researchers.…”

A Review on Optimization of Manufacturing Process Performance

“…The authors propose two separate models: minimizing a cost function of makespan, total completion time, total absolute differences in completion times and total resource cost; minimizing a cost function of makespan, total waiting time, total absolute differences in waiting times and total resource cost. Uruk et al describe in [28] the study the problem of scheduling n identical jobs each of which has three operations to be performed on two machines placed in series. One of the operations can only be performed on the first, the other one by the second machine.…”

Batch scheduling of identical jobs with controllable processing times

“…Some of the early papers are: Van Wassenhove and Baker [4], Nowicki and Zdrzalka [5], Janiak and Kovalyov [6], Wan et al [7], Hoogeveen and Woeginger [8], Janiak et al [9], Shakhlevich and Strusevich [10], Wang [11] Akturk et al [12] and Wang and Xia [13]. More recently, Tseng et al [14] studied a single machine setting with controllable processing times and an objective of minimum total tardiness; Turkcan et al [15] studied a setting of parallel machines and objective functions of minimum manufacturing cost and total weighted earliness and tardiness; Shakhlevich et al [16] focused on the trade-off between the maximum cost (which is a function of the completion times) and the total compression cost; Shabtay et al [17] addressed due date assignment problems in a group technology environment; Gurel et al [18] considered failures of the machine and repair time, and focused on an anticipative scheduling approach; Wan et al [19] studied the problem of scheduling jobs of two-agents on a single machine with controllable processing times; Choi et al [20] focused on minimizing weighted completion time subject to an upper bound on the maximum compression cost; Leyvand et al [21] considered just-in-time scheduling on parallel machines; Yin and Wang [22] studied a model combining controllable processing times and learning; Wang and Wang [23] addressed the single machine problem of minimizing the total resource consumption subject to an upper bound on the total weighted flowtime; Wei et al [24] focused on a model in which the job processing times are a function of both resource consumption and the job starting times; Uruk et al [25] studied a two-machine flowshop problem with flexible operations and controllable processing times; and Wang and Wang [26] focused on convex resource dependent processing times and job deterioration.…”