# American Institute of Mathematical Sciences

• Previous Article
Differential equation method based on approximate augmented Lagrangian for nonlinear programming
• JIMO Home
• This Issue
• Next Article
Pricing dynamic fund protection under a Regime-switching Jump-diffusion model with stochastic protection level
doi: 10.3934/jimo.2019062

## Minimizing total completion time in a two-machine no-wait flowshop with uncertain and bounded setup times

 1 Department of Mathematical Sciences, Kean University, New Jersey, USA 2 Department of Industrial and Management Systems Engineering, Kuwait University, Kuwait

1Corresponding Author: Muberra Allahverdi

Received  October 2018 Revised  February 2019 Published  May 2019

We address a two-machine no-wait flowshop scheduling problem with respect to the performance measure of total completion time. Minimizing total completion time is important when inventory cost is of concern. Setup times are treated separately from processing times. Furthermore, setup times are uncertain with unknown distributions and are within some lower and upper bounds. We develop a dominance relation and propose eight algorithms to solve the problem. The proposed algorithms, which assign different weights to the processing and setup times on both machines, convert the two-machine problem into a single-machine one for which an optimal solution is known. We conduct computational experiments to evaluate the proposed algorithms. Computational experiments reveal that one of the proposed algorithms, which assigns the same weight to setup and processing times, is superior to the rest of the algorithms. The results are statistically verified by constructing confidence intervals and test of hypothesis.

Citation: Muberra Allahverdi, Ali Allahverdi. Minimizing total completion time in a two-machine no-wait flowshop with uncertain and bounded setup times. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019062
##### References:

show all references

##### References:
Flowchart of the algorithms
The distributions used for generating $s_{i, k}$ within $Ls_{i, k}$ and $Us_{i, k}$
Overall Avg. Error of Algorithms
Avg. Std. of Algorithms
Overall Avg. Error of Algorithms with respect to $H$
Overall Avg. Error of Algorithms with respect to $H$
Overall Avg. Error of Algorithm $ALG-6$ with respect to $H$
Overall Avg. Error of Algorithms with respect to distributions
Error of Algorithms for Positive Linear Distribution
 $n$ Algorithm $H$ 100 200 300 400 500 Avg. $ALG-1$ 20 9.08 9.11 9.17 9.17 9.27 9.16 $ALG-2$ 9.38 9.37 9.28 9.34 9.3 9.33 $ALG-3$ 3.05 2.98 2.95 2.96 2.97 2.98 $ALG-4$ 4.99 4.93 4.88 4.9 4.9 4.92 $ALG-5$ 4.85 4.81 4.76 4.81 4.83 4.79 $ALG-6$ 0.1 0.02 0 0 0 0.02 $ALG-7$ 4.23 4.1 4.02 4 3.95 4.06 $ALG-8$ 2.44 2.35 2.44 2.44 2.44 2.42 $ALG-1$ 30 9.17 9.33 9.42 9.4 9.4 9.34 $ALG-2$ 9.5 9.56 9.48 9.47 9.47 9.50 $ALG-3$ 3.04 3.1 3.03 3.03 3 3.04 $ALG-4$ 5.04 5.07 4.97 4.98 4.98 5.01 $ALG-5$ 4.81 4.93 4.95 4.95 4.95 4.92 $ALG-6$ 0.08 0.01 0 0 0 0.02 $ALG-7$ 4.2 4.12 4.02 4.04 3.96 4.07 $ALG-8$ 2.48 2.45 2.46 2.49 2.49 2.47 $ALG-1$ 40 9.37 9.47 9.49 9.54 9.56 9.49 $ALG-2$ 9.65 9.69 9.64 9.63 9.67 9.66 $ALG-3$ 3.01 3.07 3.06 3.05 3.08 3.05 $ALG-4$ 5.06 5.06 5.06 5.05 5.06 5.06 $ALG-5$ 4.93 5.01 4.96 5 5.05 4.99 $ALG-6$ 0.09 0.02 0 0 0 0.02 $ALG-7$ 4.24 4.17 4.03 4.1 4.12 4.13 $ALG-8$ 2.47 2.51 2.53 2.51 2.57 2.52 Avg. 4.80 4.80 4.78 4.79 4.79
 $n$ Algorithm $H$ 100 200 300 400 500 Avg. $ALG-1$ 20 9.08 9.11 9.17 9.17 9.27 9.16 $ALG-2$ 9.38 9.37 9.28 9.34 9.3 9.33 $ALG-3$ 3.05 2.98 2.95 2.96 2.97 2.98 $ALG-4$ 4.99 4.93 4.88 4.9 4.9 4.92 $ALG-5$ 4.85 4.81 4.76 4.81 4.83 4.79 $ALG-6$ 0.1 0.02 0 0 0 0.02 $ALG-7$ 4.23 4.1 4.02 4 3.95 4.06 $ALG-8$ 2.44 2.35 2.44 2.44 2.44 2.42 $ALG-1$ 30 9.17 9.33 9.42 9.4 9.4 9.34 $ALG-2$ 9.5 9.56 9.48 9.47 9.47 9.50 $ALG-3$ 3.04 3.1 3.03 3.03 3 3.04 $ALG-4$ 5.04 5.07 4.97 4.98 4.98 5.01 $ALG-5$ 4.81 4.93 4.95 4.95 4.95 4.92 $ALG-6$ 0.08 0.01 0 0 0 0.02 $ALG-7$ 4.2 4.12 4.02 4.04 3.96 4.07 $ALG-8$ 2.48 2.45 2.46 2.49 2.49 2.47 $ALG-1$ 40 9.37 9.47 9.49 9.54 9.56 9.49 $ALG-2$ 9.65 9.69 9.64 9.63 9.67 9.66 $ALG-3$ 3.01 3.07 3.06 3.05 3.08 3.05 $ALG-4$ 5.06 5.06 5.06 5.05 5.06 5.06 $ALG-5$ 4.93 5.01 4.96 5 5.05 4.99 $ALG-6$ 0.09 0.02 0 0 0 0.02 $ALG-7$ 4.24 4.17 4.03 4.1 4.12 4.13 $ALG-8$ 2.47 2.51 2.53 2.51 2.57 2.52 Avg. 4.80 4.80 4.78 4.79 4.79
Error of Algorithms for Negative Linear Distribution
 $n$ Algorithm $H$ 100 200 300 400 500 Avg. $ALG-1$ 20 9.08 9.13 9.22 9.26 9.27 9.19 $ALG-2$ 9.38 9.26 9.33 9.35 9.27 9.32 $ALG-3$ 3.05 2.97 3.04 3.02 2.99 3.01 $ALG-4$ 4.99 4.85 4.92 4.9 4.87 4.91 $ALG-5$ 4.75 4.73 4.89 4.92 4.86 4.83 $ALG-6$ 0.1 0.02 0 0 0 0.02 $ALG-7$ 4.23 4.1 4.06 4.07 3.95 4.08 $ALG-8$ 2.44 2.41 2.44 2.5 2.43 2.44 $ALG-1$ 30 9.17 9.37 9.37 9.37 9.41 9.34 $ALG-2$ 9.5 9.51 9.53 9.5 9.51 9.51 $ALG-3$ 3.04 3.05 3.04 3.04 3.05 3.04 $ALG-4$ 5.04 5 5.03 5 4.99 5.01 $ALG-5$ 4.81 4.92 4.9 4.94 4.93 4.90 $ALG-6$ 0.08 0.01 0 0 0 0.02 $ALG-7$ 4.2 4.15 4.1 4.05 4.01 4.10 $ALG-8$ 2.48 2.54 2.46 2.55 2.53 2.51 $ALG-1$ 40 9.37 9.37 9.5 9.51 9.55 9.46 $ALG-2$ 9.65 9.54 9.59 9.64 9.62 9.61 $ALG-3$ 3.01 2.96 3.04 3.09 3.07 3.03 $ALG-4$ 5.06 4.97 5.01 5.06 5.05 5.03 $ALG-5$ 4.93 4.85 4.95 4.97 5.01 4.94 $ALG-6$ 0.09 0.01 0 0 0 0.02 $ALG-7$ 4.24 4.12 4.08 4.07 4.08 4.12 $ALG-8$ 2.47 2.44 2.58 2.54 2.57 2.52 Avg. 4.80 4.76 4.80 4.81 4.79
 $n$ Algorithm $H$ 100 200 300 400 500 Avg. $ALG-1$ 20 9.08 9.13 9.22 9.26 9.27 9.19 $ALG-2$ 9.38 9.26 9.33 9.35 9.27 9.32 $ALG-3$ 3.05 2.97 3.04 3.02 2.99 3.01 $ALG-4$ 4.99 4.85 4.92 4.9 4.87 4.91 $ALG-5$ 4.75 4.73 4.89 4.92 4.86 4.83 $ALG-6$ 0.1 0.02 0 0 0 0.02 $ALG-7$ 4.23 4.1 4.06 4.07 3.95 4.08 $ALG-8$ 2.44 2.41 2.44 2.5 2.43 2.44 $ALG-1$ 30 9.17 9.37 9.37 9.37 9.41 9.34 $ALG-2$ 9.5 9.51 9.53 9.5 9.51 9.51 $ALG-3$ 3.04 3.05 3.04 3.04 3.05 3.04 $ALG-4$ 5.04 5 5.03 5 4.99 5.01 $ALG-5$ 4.81 4.92 4.9 4.94 4.93 4.90 $ALG-6$ 0.08 0.01 0 0 0 0.02 $ALG-7$ 4.2 4.15 4.1 4.05 4.01 4.10 $ALG-8$ 2.48 2.54 2.46 2.55 2.53 2.51 $ALG-1$ 40 9.37 9.37 9.5 9.51 9.55 9.46 $ALG-2$ 9.65 9.54 9.59 9.64 9.62 9.61 $ALG-3$ 3.01 2.96 3.04 3.09 3.07 3.03 $ALG-4$ 5.06 4.97 5.01 5.06 5.05 5.03 $ALG-5$ 4.93 4.85 4.95 4.97 5.01 4.94 $ALG-6$ 0.09 0.01 0 0 0 0.02 $ALG-7$ 4.24 4.12 4.08 4.07 4.08 4.12 $ALG-8$ 2.47 2.44 2.58 2.54 2.57 2.52 Avg. 4.80 4.76 4.80 4.81 4.79
Error of Algorithm for Uniform Distribution
 $n$ Algorithm $H$ 100 200 300 400 500 Avg. $ALG-1$ 20 9.05 9.32 9.34 9.37 9.41 9.30 $ALG-2$ 9.39 9.45 9.43 9.49 9.43 9.44 $ALG-3$ 3.09 3.02 2.97 3.04 3.04 3.03 $ALG-4$ 4.98 4.96 4.92 4.98 4.96 4.96 $ALG-5$ 4.86 4.88 4.87 4.94 4.95 4.90 $ALG-6$ 0.1 0.02 0 0 0 0.02 $ALG-7$ 4.24 4.08 4.09 4.09 4.05 4.11 $ALG-8$ 2.42 4.08 4.09 4.09 4.05 4.11 $ALG-1$ 30 9.09 9.47 9.52 9.64 9.56 9.46 $ALG-2$ 9.59 9.61 9.63 9.67 9.59 9.63 $ALG-3$ 3.1 3.04 3.04 3.09 3.03 3.06 $ALG-4$ 5.13 5.03 5.02 5.06 5 5.05 $ALG-5$ 4.86 4.94 4.96 5.05 5.02 4.97 $ALG-6$ 0.1 0.02 0 0 0 0.02 $ALG-7$ 4.17 4.17 4.08 4.13 4.06 4.12 $ALG-8$ 2.44 2.49 2.53 2.59 2.56 2.52 $ALG-1$ 40 9.32 9.68 9.68 9.7 9.79 9.63 $ALG-2$ 9.67 9.89 9.85 9.87 9.89 9.83 $ALG-3$ 3.05 3.06 3.06 3.08 3.1 3.07 $ALG-4$ 5.07 5.14 5.13 5.13 5.13 5.12 $ALG-5$ 4.86 5.09 5.04 5.07 5.09 5.03 $ALG-6$ 0.09 0.01 0 0 0 0.02 $ALG-7$ 4.31 4.28 4.23 4.19 4.21 4.24 $ALG-8$ 2.43 2.61 2.64 2.68 2.68 2.61 Avg. 4.81 4.86 4.86 4.89 4.88
 $n$ Algorithm $H$ 100 200 300 400 500 Avg. $ALG-1$ 20 9.05 9.32 9.34 9.37 9.41 9.30 $ALG-2$ 9.39 9.45 9.43 9.49 9.43 9.44 $ALG-3$ 3.09 3.02 2.97 3.04 3.04 3.03 $ALG-4$ 4.98 4.96 4.92 4.98 4.96 4.96 $ALG-5$ 4.86 4.88 4.87 4.94 4.95 4.90 $ALG-6$ 0.1 0.02 0 0 0 0.02 $ALG-7$ 4.24 4.08 4.09 4.09 4.05 4.11 $ALG-8$ 2.42 4.08 4.09 4.09 4.05 4.11 $ALG-1$ 30 9.09 9.47 9.52 9.64 9.56 9.46 $ALG-2$ 9.59 9.61 9.63 9.67 9.59 9.63 $ALG-3$ 3.1 3.04 3.04 3.09 3.03 3.06 $ALG-4$ 5.13 5.03 5.02 5.06 5 5.05 $ALG-5$ 4.86 4.94 4.96 5.05 5.02 4.97 $ALG-6$ 0.1 0.02 0 0 0 0.02 $ALG-7$ 4.17 4.17 4.08 4.13 4.06 4.12 $ALG-8$ 2.44 2.49 2.53 2.59 2.56 2.52 $ALG-1$ 40 9.32 9.68 9.68 9.7 9.79 9.63 $ALG-2$ 9.67 9.89 9.85 9.87 9.89 9.83 $ALG-3$ 3.05 3.06 3.06 3.08 3.1 3.07 $ALG-4$ 5.07 5.14 5.13 5.13 5.13 5.12 $ALG-5$ 4.86 5.09 5.04 5.07 5.09 5.03 $ALG-6$ 0.09 0.01 0 0 0 0.02 $ALG-7$ 4.31 4.28 4.23 4.19 4.21 4.24 $ALG-8$ 2.43 2.61 2.64 2.68 2.68 2.61 Avg. 4.81 4.86 4.86 4.89 4.88
Error of Algorithm for Normal Distribution
 $n$ Algorithm $H$ 100 200 300 400 500 Avg. $ALG-1$ 20 9.04 9.3 9.32 9.35 9.38 9.28 $ALG-2$ 9.5 9.46 9.45 9.46 9.5 9.47 $ALG-3$ 3.03 3 3 3.03 3.06 3.02 $ALG-4$ 5.01 4.97 4.92 4.96 4.95 4.90 $ALG-5$ 4.81 4.88 4.9 4.94 4.95 4.90 $ALG-6$ 0.08 0.01 0 0 0 0.02 $ALG-7$ 4.27 4.09 4.13 4.08 4.06 4.13 $ALG-8$ 2.47 2.46 2.45 2.5 2.55 2.49 $ALG-1$ 30 9.43 9.43 9.54 9.57 9.71 9.54 $ALG-2$ 9.8 9.71 9.66 9.7 9.72 9.72 $ALG-3$ 3.11 3 3.09 3.08 3.12 3.08 $ALG-4$ 5.16 5.06 5.06 5.05 5.11 5.09 $ALG-5$ 4.99 4.92 5 4.99 5.08 5.00 $ALG-6$ 0.1 0.02 0 0 0 0.02 $ALG-7$ 4.38 4.15 4.17 4.17 4.17 4.21 $ALG-8$ 2.52 2.52 2.59 2.57 2.62 2.56 $ALG-1$ 40 9.57 9.7 9.77 9.78 9.86 9.74 $ALG-2$ 10.04 9.96 9.9 9.86 9.86 9.92 $ALG-3$ 3.12 3.03 3.05 3.07 3.05 3.06 $ALG-4$ 5.25 5.17 5.14 5.11 5.12 5.16 $ALG-5$ 5.01 5.03 5.05 5.11 5.1 5.06 $ALG-6$ 0.08 0.01 0 0 0 0.02 $ALG-7$ 4.47 4.2 4.21 4.24 4.19 4.26 $ALG-8$ 2.69 2.6 2.73 2.71 2.7 2.69 Avg. 4.91 4.86 4.88 4.89 4.91
 $n$ Algorithm $H$ 100 200 300 400 500 Avg. $ALG-1$ 20 9.04 9.3 9.32 9.35 9.38 9.28 $ALG-2$ 9.5 9.46 9.45 9.46 9.5 9.47 $ALG-3$ 3.03 3 3 3.03 3.06 3.02 $ALG-4$ 5.01 4.97 4.92 4.96 4.95 4.90 $ALG-5$ 4.81 4.88 4.9 4.94 4.95 4.90 $ALG-6$ 0.08 0.01 0 0 0 0.02 $ALG-7$ 4.27 4.09 4.13 4.08 4.06 4.13 $ALG-8$ 2.47 2.46 2.45 2.5 2.55 2.49 $ALG-1$ 30 9.43 9.43 9.54 9.57 9.71 9.54 $ALG-2$ 9.8 9.71 9.66 9.7 9.72 9.72 $ALG-3$ 3.11 3 3.09 3.08 3.12 3.08 $ALG-4$ 5.16 5.06 5.06 5.05 5.11 5.09 $ALG-5$ 4.99 4.92 5 4.99 5.08 5.00 $ALG-6$ 0.1 0.02 0 0 0 0.02 $ALG-7$ 4.38 4.15 4.17 4.17 4.17 4.21 $ALG-8$ 2.52 2.52 2.59 2.57 2.62 2.56 $ALG-1$ 40 9.57 9.7 9.77 9.78 9.86 9.74 $ALG-2$ 10.04 9.96 9.9 9.86 9.86 9.92 $ALG-3$ 3.12 3.03 3.05 3.07 3.05 3.06 $ALG-4$ 5.25 5.17 5.14 5.11 5.12 5.16 $ALG-5$ 5.01 5.03 5.05 5.11 5.1 5.06 $ALG-6$ 0.08 0.01 0 0 0 0.02 $ALG-7$ 4.47 4.2 4.21 4.24 4.19 4.26 $ALG-8$ 2.69 2.6 2.73 2.71 2.7 2.69 Avg. 4.91 4.86 4.88 4.89 4.91
Error of Algoithms with respect to $n$
 n Algorithm 100 200 300 400 500 Avg. $ALG-1$ 9.27 9.39 9.45 9.47 9.51 9.42 $ALG-2$ 9.64 9.58 9.56 9.58 9.57 9.59 $ALG-3$ 3.07 3.02 3.03 3.05 3.05 3.04 $ALG-4$ 5.09 5.02 5.01 5.02 5.01 5.03 $ALG-5$ 4.88 4.92 4.94 4.97 4.99 4.94 $ALG-6$ 0.09 0.02 0.00 0.00 0.00 0.02 $ALG-7$ 4.28 4.14 4.10 4.10 4.07 4.14 $ALG-8$ 2.49 2.49 2.53 2.55 2.56 2.52
 n Algorithm 100 200 300 400 500 Avg. $ALG-1$ 9.27 9.39 9.45 9.47 9.51 9.42 $ALG-2$ 9.64 9.58 9.56 9.58 9.57 9.59 $ALG-3$ 3.07 3.02 3.03 3.05 3.05 3.04 $ALG-4$ 5.09 5.02 5.01 5.02 5.01 5.03 $ALG-5$ 4.88 4.92 4.94 4.97 4.99 4.94 $ALG-6$ 0.09 0.02 0.00 0.00 0.00 0.02 $ALG-7$ 4.28 4.14 4.10 4.10 4.07 4.14 $ALG-8$ 2.49 2.49 2.53 2.55 2.56 2.52
Error of Algorithms with respect to $H$
 $H$ Algorithm 20 30 40 Avg. $ALG-1$ 9.24 9.42 9.59 9.42 $ALG-2$ 9.40 9.60 9.77 9.59 $ALG-3$ 3.01 3.06 3.06 3.04 $ALG-4$ 4.94 5.04 5.10 5.03 $ALG-5$ 4.86 4.94 5.01 4.94 $ALG-6$ 0.02 0.02 0.02 0.02 $ALG-7$ 4.10 4.13 4.19 4.14 $ALG-8$ 2.46 2.52 2.59 2.52
 $H$ Algorithm 20 30 40 Avg. $ALG-1$ 9.24 9.42 9.59 9.42 $ALG-2$ 9.40 9.60 9.77 9.59 $ALG-3$ 3.01 3.06 3.06 3.04 $ALG-4$ 4.94 5.04 5.10 5.03 $ALG-5$ 4.86 4.94 5.01 4.94 $ALG-6$ 0.02 0.02 0.02 0.02 $ALG-7$ 4.10 4.13 4.19 4.14 $ALG-8$ 2.46 2.52 2.59 2.52
Confidence Intervals for Average Errors
 Algorithm 95$\%$ Confidence Interval on the Avg. Error $ALG-1$ (09.33-9.51) $ALG-2$ (9.50-9.68) $ALG-3$ (2.98-3.11) $ALG-4$ (4.95-5.10) $ALG-5$ (4.86-5.01) $ALG-6$ (0.02-0.03) $ALG-7$ (4.07-4.21) $ALG-8$ (2.45-2.59)
 Algorithm 95$\%$ Confidence Interval on the Avg. Error $ALG-1$ (09.33-9.51) $ALG-2$ (9.50-9.68) $ALG-3$ (2.98-3.11) $ALG-4$ (4.95-5.10) $ALG-5$ (4.86-5.01) $ALG-6$ (0.02-0.03) $ALG-7$ (4.07-4.21) $ALG-8$ (2.45-2.59)
 [1] P. Liu, Xiwen Lu. Online scheduling of two uniform machines to minimize total completion times. Journal of Industrial & Management Optimization, 2009, 5 (1) : 95-102. doi: 10.3934/jimo.2009.5.95 [2] Hongtruong Pham, Xiwen Lu. The inverse parallel machine scheduling problem with minimum total completion time. Journal of Industrial & Management Optimization, 2014, 10 (2) : 613-620. doi: 10.3934/jimo.2014.10.613 [3] Ran Ma, Jiping Tao. An improved 2.11-competitive algorithm for online scheduling on parallel machines to minimize total weighted completion time. Journal of Industrial & Management Optimization, 2018, 14 (2) : 497-510. doi: 10.3934/jimo.2017057 [4] Jinjiang Yuan, Weiping Shang. A PTAS for the p-batch scheduling with pj = p to minimize total weighted completion time. Journal of Industrial & Management Optimization, 2005, 1 (3) : 353-358. doi: 10.3934/jimo.2005.1.353 [5] Chengxin Luo. Single machine batch scheduling problem to minimize makespan with controllable setup and jobs processing times. Numerical Algebra, Control & Optimization, 2015, 5 (1) : 71-77. doi: 10.3934/naco.2015.5.71 [6] Xingong Zhang. Single machine and flowshop scheduling problems with sum-of-processing time based learning phenomenon. Journal of Industrial & Management Optimization, 2020, 16 (1) : 231-244. doi: 10.3934/jimo.2018148 [7] Muberra Allahverdi, Harun Aydilek, Asiye Aydilek, Ali Allahverdi. A better dominance relation and heuristics for Two-Machine No-Wait Flowshops with Maximum Lateness Performance Measure. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020054 [8] Shuang Zhao. Resource allocation flowshop scheduling with learning effect and slack due window assignment. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020096 [9] Wen-Hung Wu, Yunqiang Yin, Wen-Hsiang Wu, Chin-Chia Wu, Peng-Hsiang Hsu. A time-dependent scheduling problem to minimize the sum of the total weighted tardiness among two agents. Journal of Industrial & Management Optimization, 2014, 10 (2) : 591-611. doi: 10.3934/jimo.2014.10.591 [10] Ping Yan, Ji-Bo Wang, Li-Qiang Zhao. Single-machine bi-criterion scheduling with release times and exponentially time-dependent learning effects. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1117-1131. doi: 10.3934/jimo.2018088 [11] Feng Zhang, Jinting Wang, Bin Liu. Equilibrium joining probabilities in observable queues with general service and setup times. Journal of Industrial & Management Optimization, 2013, 9 (4) : 901-917. doi: 10.3934/jimo.2013.9.901 [12] Tuan Phung-Duc. Single server retrial queues with setup time. Journal of Industrial & Management Optimization, 2017, (3) : 1329-1345. doi: 10.3934/jimo.2016075 [13] Güvenç Şahin, Ravindra K. Ahuja. Single-machine scheduling with stepwise tardiness costs and release times. Journal of Industrial & Management Optimization, 2011, 7 (4) : 825-848. doi: 10.3934/jimo.2011.7.825 [14] Tuan Phung-Duc, Ken'ichi Kawanishi. Multiserver retrial queue with setup time and its application to data centers. Journal of Industrial & Management Optimization, 2019, 15 (1) : 15-35. doi: 10.3934/jimo.2018030 [15] A. Azhagappan, T. Deepa. Transient analysis of N-policy queue with system disaster repair preventive maintenance re-service balking closedown and setup times. Journal of Industrial & Management Optimization, 2019  doi: 10.3934/jimo.2019083 [16] Lalida Deeratanasrikul, Shinji Mizuno. Multiple-stage multiple-machine capacitated lot-sizing and scheduling with sequence-dependent setup: A case study in the wheel industry. Journal of Industrial & Management Optimization, 2017, 13 (1) : 413-428. doi: 10.3934/jimo.2016024 [17] Hideaki Takagi. Times until service completion and abandonment in an M/M/$m$ preemptive-resume LCFS queue with impatient customers. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1701-1726. doi: 10.3934/jimo.2018028 [18] Y. K. Lin, C. S. Chong. A tabu search algorithm to minimize total weighted tardiness for the job shop scheduling problem. Journal of Industrial & Management Optimization, 2016, 12 (2) : 703-717. doi: 10.3934/jimo.2016.12.703 [19] Peng Guo, Wenming Cheng, Yi Wang. A general variable neighborhood search for single-machine total tardiness scheduling problem with step-deteriorating jobs. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1071-1090. doi: 10.3934/jimo.2014.10.1071 [20] Z.G. Feng, K.L. Teo, Y. Zhao. Branch and bound method for sensor scheduling in discrete time. Journal of Industrial & Management Optimization, 2005, 1 (4) : 499-512. doi: 10.3934/jimo.2005.1.499

2019 Impact Factor: 1.366