January  2018, 14(1): 165-182. doi: 10.3934/jimo.2017041

Integrated order acceptance and scheduling decision making in product service supply chain with hard time windows constraints

a. 

School of Economics and Business Administration, Chongqing University, Chongqing 400044, China

b. 

Research Center of Business Administration & Economic Development, Chongqing University, Chongqing 400030, China

c. 

School of Management, Southwest University of Political Science & Law, Chongqing 401120, China

* Corresponding author: danbin@cqu.edu.cn (B Dan)

Received  January 2015 Revised  December 2016 Published  April 2017

Fund Project: This research was supported by the National Natural Science Foundation of China (Grant Number: 71272086), the National Science and Technology supporting Program of China (Grant Number: 2015BAF05B01), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (20120191110042).

A product service supply chain (PSSC) supplies customers with product-service systems (PSS) consist of integrated products and services. The product manufacturing should match the service supply in the order delivery planning. For PSS orders are usually delivered under time window constraints, this paper is concerned with the integrated order acceptance and scheduling (OAS) decision of the PSSC. Defined the PSS orders by their revenues, product processing times, serving offering times and hard time window constraints, we formulate the OAS problem as a MILP model to optimize total revenue of PSSC and propose two effective value for big-M to solve the problem with small size optimally. The simulated annealing algorithm based on the priority rule of servable orders first (SOF-SA) and the dynamic acceptance and scheduling heuristic (DASH) algorithm are presented. The performance of the model and the two algorithms are proved through simulating instances with different order sizes. Computational tests show that the SOF-SA algorithm is more effective when used for small size problems while the DASH algorithm is more effective for problems with larger size; negotiating with customers to make reasonable delivery time windows should be beneficial to increasing total revenue and improving the decision efficiency.

Citation: Bin Dan, Huali Gao, Yang Zhang, Ru Liu, Songxuan Ma. Integrated order acceptance and scheduling decision making in product service supply chain with hard time windows constraints. Journal of Industrial & Management Optimization, 2018, 14 (1) : 165-182. doi: 10.3934/jimo.2017041
References:
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F. H. BeurenM. G. G. Ferreira and P. A. C. Miguel, Product-service systems: a literature review on integrated products and services, Journal of Cleaner Production, 47 (2013), 222-231.  doi: 10.1016/j.jclepro.2012.12.028.  Google Scholar

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[4]

H. K. ChenC. F. Hsueh and M. S. Chang, Production scheduling and vehicle routing with time windows for perishable food products, Computers & Operations Research, 36 (2009), 2311-2319.  doi: 10.1016/j.cor.2008.09.010.  Google Scholar

[5]

R. EsmaeilbeigiP. Charkhgard and H. Charkhgard, Order acceptance and scheduling problems in two-machine flow shops: New mixed integer programming formulations, European Journal of Operational Research, 251 (2016), 419-431.  doi: 10.1016/j.ejor.2015.11.036.  Google Scholar

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M. GarettiP. Rosa and S. Terzi, Life Cycle Simulation for the design of Product-Service Systems, Computers in Industry, 63 (2012), 361-369.  doi: 10.1016/j.compind.2012.02.007.  Google Scholar

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T. C. Kuo, Simulation of purchase or rental decision-making based on product service system, The International Journal of Advanced Manufacturing Technology, 52 (2011), 1239-1249.  doi: 10.1007/s00170-010-2768-2.  Google Scholar

[8]

T. C. Kuo and W. M. Ling, The optimisation of maintenance service levels to support the product service system, International Journal of Production Research, 50 (2012), 6691-6708.  doi: 10.1080/00207543.2011.616916.  Google Scholar

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I. S. Lee, Minimizing total tardiness for the order scheduling problem, International Journal of Production Economics, 144 (2013), 128-134.  doi: 10.1016/j.ijpe.2013.01.025.  Google Scholar

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S. LeeY. GeumH. Lee and Y. Park, Dynamic and multidimensional measurement of product-service system (PSS) sustainability: a triple bottom line (TBL)-based system dynamics approach, Journal of Cleaner Production, 32 (2012), 173-182.  doi: 10.1016/j.jclepro.2012.03.032.  Google Scholar

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N. Li and Z. Jiang, Modeling and optimization of a product-service system with additional service capacity and impatient customers, Computers & Operations Research, 40 (2013), 1923-1937.  doi: 10.1016/j.cor.2013.02.015.  Google Scholar

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H. LockettM. JohnsonS. Evans and M. Bastl, Product Service Systems and supply network relationships: An exploratory case study, Journal of Manufacturing Technology Management, 22 (2011), 293-313.  doi: 10.1108/17410381111112684.  Google Scholar

[14]

C. LowR. Li and C. Chang, Integrated scheduling of production and delivery with time windows, International Journal of Production Research, 51 (2012), 897-909.  doi: 10.1080/00207543.2012.677071.  Google Scholar

[15]

E. Manzini and C. Vezzoli, A strategic design approach to develop sustainable product service systems: Examples taken from the 'environmentally friendly innovation' Italian prize, Journal of Cleaner Production, 11 (2003), 851-857.  doi: 10.1016/S0959-6526(02)00153-1.  Google Scholar

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O. K. Mont, Clarifying the concept of product-service system, Journal of Cleaner Production, 10 (2002), 237-245.  doi: 10.1016/S0959-6526(01)00039-7.  Google Scholar

[18]

F. T. Nobibon and R. Leus, Exact algorithms for a generalization of the order acceptance and scheduling problem in a single-machine environment, Computers & Operations Research, 38 (2011), 367-378.  doi: 10.1016/j.cor.2010.06.003.  Google Scholar

[19]

C. OguzF. S. Salman and Z. B. Yalçin, Order acceptance and scheduling decisions in make-to-order systems, International Journal of Production Economics, 125 (2010), 200-211.   Google Scholar

[20]

T. SakaoA. Ö. Rönnbäck and G. Ö. Sandström, Uncovering benefits and risks of integrated product service offerings—Using a case of technology encapsulation, Journal of Systems Science and Systems Engineering, 22 (2013), 421-439.  doi: 10.1007/s11518-013-5233-6.  Google Scholar

[21]

L. H. SuP. S. Chen and S. Y. Chen, Scheduling on parallel machines to minimise maximum lateness for the customer order problem, International Journal of Systems Science, 44 (2013), 926-936.  doi: 10.1080/00207721.2011.649366.  Google Scholar

[22]

C. A. Ullrich, Integrated machine scheduling and vehicle routing with time windows, European Journal of Operational Research, 227 (2013), 152-165.  doi: 10.1016/j.ejor.2012.11.049.  Google Scholar

[23]

UNEP, The role of product service systems in a sustainable society, In. http://www.unep.fr/scp/design/pdf/pss-brochure-final.pdf, (2001). Google Scholar

[24]

X. WangX. Xie and T. C. E. Cheng, Order acceptance and scheduling in a two-machine flowshop, International Journal of Production Economics, 141 (2013), 366-376.  doi: 10.1016/j.ijpe.2012.08.020.  Google Scholar

[25]

X. WangX. Xie and T. C. E. Cheng, A modified artificial bee conoly algorithm for order acceptance in two-machine flowshop, International Journal of Production Economics, 141 (2013), 14-23.   Google Scholar

[26]

Y. XiaoR. ZhangQ. Zhao and I. Kaku, Permutation flow shop scheduling with order acceptance and weighted tardiness, Applied Mathematics and Computation, 218 (2012), 7911-7926.  doi: 10.1016/j.amc.2012.01.073.  Google Scholar

[27]

W. XieZ. JiangY. Zhao and X. Shao, Contract design for cooperative product service system with information asymmetry, International Journal of Production Research, 52 (2014), 1658-1680.  doi: 10.1080/00207543.2013.847293.  Google Scholar

[28]

Z. Xu, X. Ming, W. Song, M. ~Li, L. He and X. Li, Towards a new framework: Understanding and managing the supply chain for product-service systems, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 0954405414521189, (2014). doi: 10.1177/0954405414521189.  Google Scholar

[29]

L. ZhangL. Lu and J. Yuan, Single machine scheduling with release dates and rejection, European Journal of Operational Research, 198 (2009), 975-978.  doi: 10.1016/j.ejor.2008.10.006.  Google Scholar

[30]

C. ZhaoY. YinT. C. E. Cheng and C. C. Wu, Single-machine scheduling and due date assignment with rejection and position-dependent processing times, Journal of Industrial and Management Optimization, 10 (2014), 691-700.  doi: 10.3934/jimo.2014.10.691.  Google Scholar

[31]

X. ZhongJ. Ou and G. Wang, Order acceptance and scheduling with machine availability constraints, European Journal of Operational Research, 232 (2014), 435-441.  doi: 10.1016/j.ejor.2013.07.032.  Google Scholar

show all references

References:
[1]

T. S. BainesH. W. LightfootS. Evans... and J. R. Alcock, State-of-the-art in product-service systems, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 221 (2007), 1543-1552.  doi: 10.1243/09544054JEM858.  Google Scholar

[2]

F. H. BeurenM. G. G. Ferreira and P. A. C. Miguel, Product-service systems: a literature review on integrated products and services, Journal of Cleaner Production, 47 (2013), 222-231.  doi: 10.1016/j.jclepro.2012.12.028.  Google Scholar

[3]

B. CesaretC. Oǧuz and F. S. Salman, A tabu search algorithm for order acceptance and scheduling, Computers & Operations Research, 39 (2012), 1197-1205.  doi: 10.1016/j.cor.2010.09.018.  Google Scholar

[4]

H. K. ChenC. F. Hsueh and M. S. Chang, Production scheduling and vehicle routing with time windows for perishable food products, Computers & Operations Research, 36 (2009), 2311-2319.  doi: 10.1016/j.cor.2008.09.010.  Google Scholar

[5]

R. EsmaeilbeigiP. Charkhgard and H. Charkhgard, Order acceptance and scheduling problems in two-machine flow shops: New mixed integer programming formulations, European Journal of Operational Research, 251 (2016), 419-431.  doi: 10.1016/j.ejor.2015.11.036.  Google Scholar

[6]

M. GarettiP. Rosa and S. Terzi, Life Cycle Simulation for the design of Product-Service Systems, Computers in Industry, 63 (2012), 361-369.  doi: 10.1016/j.compind.2012.02.007.  Google Scholar

[7]

T. C. Kuo, Simulation of purchase or rental decision-making based on product service system, The International Journal of Advanced Manufacturing Technology, 52 (2011), 1239-1249.  doi: 10.1007/s00170-010-2768-2.  Google Scholar

[8]

T. C. Kuo and W. M. Ling, The optimisation of maintenance service levels to support the product service system, International Journal of Production Research, 50 (2012), 6691-6708.  doi: 10.1080/00207543.2011.616916.  Google Scholar

[9]

I. S. Lee, Minimizing total tardiness for the order scheduling problem, International Journal of Production Economics, 144 (2013), 128-134.  doi: 10.1016/j.ijpe.2013.01.025.  Google Scholar

[10]

S. LeeY. GeumH. Lee and Y. Park, Dynamic and multidimensional measurement of product-service system (PSS) sustainability: a triple bottom line (TBL)-based system dynamics approach, Journal of Cleaner Production, 32 (2012), 173-182.  doi: 10.1016/j.jclepro.2012.03.032.  Google Scholar

[11]

N. Li and Z. Jiang, Modeling and optimization of a product-service system with additional service capacity and impatient customers, Computers & Operations Research, 40 (2013), 1923-1937.  doi: 10.1016/j.cor.2013.02.015.  Google Scholar

[12]

Y. K. Lin and C. S. Chong, A tabu search algorithm to minimize total weighted tardiness for the job shop scheduling problem, Journal of Industrial and Management Optimization, 12 (2016), 703-717.  doi: 10.3934/jimo.2016.12.703.  Google Scholar

[13]

H. LockettM. JohnsonS. Evans and M. Bastl, Product Service Systems and supply network relationships: An exploratory case study, Journal of Manufacturing Technology Management, 22 (2011), 293-313.  doi: 10.1108/17410381111112684.  Google Scholar

[14]

C. LowR. Li and C. Chang, Integrated scheduling of production and delivery with time windows, International Journal of Production Research, 51 (2012), 897-909.  doi: 10.1080/00207543.2012.677071.  Google Scholar

[15]

E. Manzini and C. Vezzoli, A strategic design approach to develop sustainable product service systems: Examples taken from the 'environmentally friendly innovation' Italian prize, Journal of Cleaner Production, 11 (2003), 851-857.  doi: 10.1016/S0959-6526(02)00153-1.  Google Scholar

[16]

R. MaullA. Smart and L. Liang, A process model of product service supply chains, Production Planning & Control, 25 (2014), 1091-1106.  doi: 10.1080/09537287.2013.808840.  Google Scholar

[17]

O. K. Mont, Clarifying the concept of product-service system, Journal of Cleaner Production, 10 (2002), 237-245.  doi: 10.1016/S0959-6526(01)00039-7.  Google Scholar

[18]

F. T. Nobibon and R. Leus, Exact algorithms for a generalization of the order acceptance and scheduling problem in a single-machine environment, Computers & Operations Research, 38 (2011), 367-378.  doi: 10.1016/j.cor.2010.06.003.  Google Scholar

[19]

C. OguzF. S. Salman and Z. B. Yalçin, Order acceptance and scheduling decisions in make-to-order systems, International Journal of Production Economics, 125 (2010), 200-211.   Google Scholar

[20]

T. SakaoA. Ö. Rönnbäck and G. Ö. Sandström, Uncovering benefits and risks of integrated product service offerings—Using a case of technology encapsulation, Journal of Systems Science and Systems Engineering, 22 (2013), 421-439.  doi: 10.1007/s11518-013-5233-6.  Google Scholar

[21]

L. H. SuP. S. Chen and S. Y. Chen, Scheduling on parallel machines to minimise maximum lateness for the customer order problem, International Journal of Systems Science, 44 (2013), 926-936.  doi: 10.1080/00207721.2011.649366.  Google Scholar

[22]

C. A. Ullrich, Integrated machine scheduling and vehicle routing with time windows, European Journal of Operational Research, 227 (2013), 152-165.  doi: 10.1016/j.ejor.2012.11.049.  Google Scholar

[23]

UNEP, The role of product service systems in a sustainable society, In. http://www.unep.fr/scp/design/pdf/pss-brochure-final.pdf, (2001). Google Scholar

[24]

X. WangX. Xie and T. C. E. Cheng, Order acceptance and scheduling in a two-machine flowshop, International Journal of Production Economics, 141 (2013), 366-376.  doi: 10.1016/j.ijpe.2012.08.020.  Google Scholar

[25]

X. WangX. Xie and T. C. E. Cheng, A modified artificial bee conoly algorithm for order acceptance in two-machine flowshop, International Journal of Production Economics, 141 (2013), 14-23.   Google Scholar

[26]

Y. XiaoR. ZhangQ. Zhao and I. Kaku, Permutation flow shop scheduling with order acceptance and weighted tardiness, Applied Mathematics and Computation, 218 (2012), 7911-7926.  doi: 10.1016/j.amc.2012.01.073.  Google Scholar

[27]

W. XieZ. JiangY. Zhao and X. Shao, Contract design for cooperative product service system with information asymmetry, International Journal of Production Research, 52 (2014), 1658-1680.  doi: 10.1080/00207543.2013.847293.  Google Scholar

[28]

Z. Xu, X. Ming, W. Song, M. ~Li, L. He and X. Li, Towards a new framework: Understanding and managing the supply chain for product-service systems, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 0954405414521189, (2014). doi: 10.1177/0954405414521189.  Google Scholar

[29]

L. ZhangL. Lu and J. Yuan, Single machine scheduling with release dates and rejection, European Journal of Operational Research, 198 (2009), 975-978.  doi: 10.1016/j.ejor.2008.10.006.  Google Scholar

[30]

C. ZhaoY. YinT. C. E. Cheng and C. C. Wu, Single-machine scheduling and due date assignment with rejection and position-dependent processing times, Journal of Industrial and Management Optimization, 10 (2014), 691-700.  doi: 10.3934/jimo.2014.10.691.  Google Scholar

[31]

X. ZhongJ. Ou and G. Wang, Order acceptance and scheduling with machine availability constraints, European Journal of Operational Research, 232 (2014), 435-441.  doi: 10.1016/j.ejor.2013.07.032.  Google Scholar

Figure 1.  Graphical representation of the OAS problem in PSSC
Table 1.  The performance of MA
$\tau $$R$$M=\sum_{i=1, ..., n} {(t_{pi} +t_{si} )} $
CPU(s)
$\widehat{M_{ij} }=d_{li} +t_{sj} $
CPU(s)
$n\text{=}10$$n\text{=}12$$n\text{=}10$$n\text{=}12$
0.10.219.45684.9619.55675.23
0.10.41.28104.661.19103.99
0.10.60.3624.520.3424.75
0.20.22.45149.152.30126.21
0.20.40.4111.610.3911.5
0.20.60.130.070.280.07
0.30.21.204.571.194.08
0.30.41.970.161.910.23
0.30.60.060.540.060.54
$\tau $$R$$M=\sum_{i=1, ..., n} {(t_{pi} +t_{si} )} $
CPU(s)
$\widehat{M_{ij} }=d_{li} +t_{sj} $
CPU(s)
$n\text{=}10$$n\text{=}12$$n\text{=}10$$n\text{=}12$
0.10.219.45684.9619.55675.23
0.10.41.28104.661.19103.99
0.10.60.3624.520.3424.75
0.20.22.45149.152.30126.21
0.20.40.4111.610.3911.5
0.20.60.130.070.280.07
0.30.21.204.571.194.08
0.30.41.970.161.910.23
0.30.60.060.540.060.54
Table 2.  The algorithms' performance for $n = 10$
$n$$\tau $$R$GAP1(%)CPU(s)
SOF-SADASHSOF-SADASH
100.10.213.716.231.633.15
100.10.47.19.520.321.21
100.10.614.415.813.870.89
100.20.216.619.143.570.75
100.20.421.423.624.330.67
100.20.615.522.715.210.62
100.30.218.219.150.920.56
100.30.47.215.828.690.53
100.30.620.623.424.360.27
$n$$\tau $$R$GAP1(%)CPU(s)
SOF-SADASHSOF-SADASH
100.10.213.716.231.633.15
100.10.47.19.520.321.21
100.10.614.415.813.870.89
100.20.216.619.143.570.75
100.20.421.423.624.330.67
100.20.615.522.715.210.62
100.30.218.219.150.920.56
100.30.47.215.828.690.53
100.30.620.623.424.360.27
Table 3.  The algorithms' performance for $n = 20$
$n$}$\tau $$R$GAP2(%)CPU(s)
SOF-SADASHSOF-SADASH
200.10.25.811.097.043.76
200.10.411.719.145.731.61
200.10.69.214.439.971.45
200.20.211.912.3120.381.32
200.20.45.08.852.671.19
200.20.69.412.146.890.96
200.30.27.413.0168.420.88
200.30.412.215.638.540.73
200.30.69.113.537.450.65
$n$}$\tau $$R$GAP2(%)CPU(s)
SOF-SADASHSOF-SADASH
200.10.25.811.097.043.76
200.10.411.719.145.731.61
200.10.69.214.439.971.45
200.20.211.912.3120.381.32
200.20.45.08.852.671.19
200.20.69.412.146.890.96
200.30.27.413.0168.420.88
200.30.412.215.638.540.73
200.30.69.113.537.450.65
Table 4.  The algorithms' performance for $n = 50$
$n$$\tau $$R$GAP2(%)CPU(s)
SOF-SADASHSOF-SADASH
500.10.29.515.8735.1410.68
500.10.417.020.4530.875.49
500.10.620.921.3521.225.31
500.20.212.615.0822.365.16
500.20.416.217.7579.544.88
500.20.617.119.0566.974.79
500.30.218.422.6899.534.45
500.30.422.726.5620.284.15
500.30.615.315.8619.993.65
$n$$\tau $$R$GAP2(%)CPU(s)
SOF-SADASHSOF-SADASH
500.10.29.515.8735.1410.68
500.10.417.020.4530.875.49
500.10.620.921.3521.225.31
500.20.212.615.0822.365.16
500.20.416.217.7579.544.88
500.20.617.119.0566.974.79
500.30.218.422.6899.534.45
500.30.422.726.5620.284.15
500.30.615.315.8619.993.65
Table 5.  The algorithms' performance for $n = 100$
$n$$\tau $$R$GAP2(%)CPU(s)
SOF-SADASHSOF-SADASH
1000.10.225.819.21365.4932.54
1000.10.430.317.7954.2125.57
1000.10.619.710.4996.7324.66
1000.20.225.118.81681.3223.09
1000.20.427.926.11307.7621.85
1000.20.629.427.01178.5421.73
1000.30.232.019.91873.5520.42
1000.30.426.521.21054.2719.81
1000.30.635.225.51175.9217.65
$n$$\tau $$R$GAP2(%)CPU(s)
SOF-SADASHSOF-SADASH
1000.10.225.819.21365.4932.54
1000.10.430.317.7954.2125.57
1000.10.619.710.4996.7324.66
1000.20.225.118.81681.3223.09
1000.20.427.926.11307.7621.85
1000.20.629.427.01178.5421.73
1000.30.232.019.91873.5520.42
1000.30.426.521.21054.2719.81
1000.30.635.225.51175.9217.65
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