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Modeling order assignment for semiconductor assembly hierarchical outsourcing and developing the decision support system

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Abstract

Outsourcing has become increasingly important in supply chain management. As the semiconductor industry is capital-intensive, semiconductor manufacturing companies focus on wafer fabrication as their core competence and outsource assembly and testing to a number of specialized vendors. The involved decision-making has multiple objectives such as (1) minimizing the number of delayed orders, (2) minimizing the allocation ratio differences, (3) minimizing the assembly cost, and (4) minimizing the product changeover times. To meet these objectives in practice, this study proposes an approach that employs mixed integer linear programming and goal programming to integrate multiple objectives and operational feasibility by considering mass orders, order fulfillment, capacity limits, logistics timetables, and a rolling mechanism in a real setting. Furthermore, we developed an order assignment decision support system embedded with the proposed approach for assigning assembly outsourcing orders and validated the system in a semiconductor company in Taiwan. The results have shown the practical viability of the proposed approach in terms of decision quality and computational efficiency. This study concludes with empirical findings and a discussion of future research directions.

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Acknowledgments

This research is partially supported by the National Science Council (NSC97-2221-E-007- 111-MY3; NSC99-2410-H-031-002) and Macronix International Co. Ltd, Taiwan. Special thanks go to domain experts including Dr. CY Lu, Paul Hsu, YL Whang, Fred Su, Hero Chen, TS Huang, Sophie Li, and Ryan Lin. The authors also appreciate the insightful and constructive comments from the editors of this special issue and anonymous reviewers.

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Authors and Affiliations

  1. Department of Industrial Engineering and Engineering Management, National Tsing Hua University, Hsinchu, Taiwan

    Chen-Fu Chien & Yu-De Weng

  2. Department of Business Administration, Soochow University, Taipei, Taiwan

    Jei-Zheng Wu

Authors
  1. Chen-Fu Chien
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  2. Jei-Zheng Wu
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  3. Yu-De Weng
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Corresponding author

Correspondence to Jei-Zheng Wu.

Appendix: Numerical example

Appendix: Numerical example

Assume two qualified vendors {A, B} are considered and their relative shares of orders are 0.7 and 0.3. The six orders of three products {1, 2, 3} consuming the same material m will be outsourced to these two vendors. The planning horizon is 3-day. There are two daily transportation shuttles, i.e., day and night shuttles. Hence, the time buckets range from 0 to 5 = 3 × 2 − 1. Tables 3, 4, 5, 6, 7, 8, and 9 represent the detailed information which can derive a model of DOAP-GR structured as minimizing (23)–(26) subject to (27)–(102). The priorities of the objectives, in this order, consist of (1) minimizing the number of delayed orders, (2) minimizing the differences between the target and actual monetary value, (3) minimizing the assembly cost, and (4) minimizing the number of times of product changeover. ILOG® OPL® (ILOG 2001) solved the preemptive goal programming problem within one second on a personal computer with an Intel© Core™2 Quad CPU Q8200 at 2.33 and 3.21 GB RAM. The solution contained no delayed order and total allocation differences were 197 (Table 10). Three switch-ons happened on buckets 2, 3, 4, respectively for product 3 (order 6) in vendor A, product 2 (order 3) in vendor B, and product 3 (order 5) in vendor B.

$$ \min y_{1}^{1} + y_{3}^{2} + y_{3}^{3} + y_{3}^{4} + y_{5}^{5} + y_{5}^{6} $$
(23)
$$ \min r_{A}^{ + } + r_{A}^{ - } + r_{B}^{ + } + r_{B}^{ - } $$
(24)
$$ \begin{aligned} & \min \, 10x_{A0}^{1} + 20x_{A2}^{2} + 32x_{B1}^{3} + 32x_{B2}^{3} + 32x_{B3}^{3} + 48x_{B2}^{4} + 48x_{B3}^{4} \\ & \quad + 100x_{A2}^{5} + 100x_{A4}^{5} + 125x_{B2}^{5} + 125x_{B3}^{5} + 125x_{B4}^{5} + 125x_{B5}^{5} \\ & \quad + 120x_{A2}^{6} + 120x_{A4}^{6} + 150x_{B1}^{6} + 150x_{B2}^{6} + 150x_{B3}^{6} + 150x_{B4}^{6} + 150x_{B5}^{6} \\ \end{aligned} $$
(25)
$$ \min \phi_{A0}^{1} + \phi_{A2}^{1} + \phi_{A4}^{1} + \phi_{B1}^{2} + \phi_{B2}^{2} + \phi_{B3}^{2} + \phi_{B4}^{2} + \phi_{B5}^{2} + \phi_{A0}^{3} + \phi_{A2}^{3} + \phi_{A4}^{3} + \phi_{B1}^{3} + \phi_{B2}^{3} + \phi_{B3}^{3} + \phi_{B4}^{3} + \phi_{B5}^{3} $$
(26)
$$ x_{A0}^{1} + y_{0}^{1} = 1 $$
(27)
$$ y_{1}^{2} = 1 $$
(28)
$$ x_{B1}^{3} + y_{1}^{3} = 1 $$
(29)
$$ x_{B2}^{4} + y_{2}^{4} = 1 $$
(30)
$$ x_{A2}^{5} + x_{B2}^{5} + y_{2}^{5} = 1 $$
(31)
$$ x_{B1}^{6} + y_{1}^{6} = 1 $$
(32)
$$ y_{1}^{1} = y_{0}^{1} $$
(33)
$$ x_{A2}^{2} + y_{2}^{2} = y_{1}^{2} $$
(34)
$$ y_{3}^{2} = y_{2}^{2} $$
(35)
$$ x_{B2}^{3} + y_{2}^{3} = y_{1}^{3} $$
(36)
$$ x_{B3}^{3} + y_{3}^{3} = y_{2}^{3} $$
(37)
$$ x_{B3}^{4} + y_{3}^{4} = y_{2}^{4} $$
(38)
$$ x_{B3}^{5} + y_{3}^{5} = y_{2}^{5} $$
(39)
$$ x_{A4}^{5} + x_{B4}^{5} + y_{4}^{5} = y_{3}^{5} $$
(40)
$$ x_{B5}^{5} + y_{5}^{5} = y_{4}^{5} $$
(41)
$$ x_{A2}^{6} + x_{B2}^{6} + y_{2}^{6} = y_{1}^{6} $$
(42)
$$ x_{B3}^{6} + y_{3}^{6} = y_{2}^{6} $$
(43)
$$ x_{A4}^{6} + x_{B4}^{6} + y_{4}^{6} = y_{3}^{6} $$
(44)
$$ x_{B5}^{6} + y_{5}^{6} = y_{4}^{6} $$
(45)
$$ 10x_{A0}^{1} + z_{mA0} = 120 $$
(46)
$$ 20x_{B1}^{3} + 60x_{B1}^{6} + z_{mB1} = 160 $$
(47)
$$ 20x_{A2}^{2} + 50x_{A2}^{5} + 60x_{A2}^{6} + z_{mA2} = z_{mA0} $$
(48)
$$ 50x_{A4}^{5} + 60x_{A4}^{6} + z_{mA4} = z_{mA2} $$
(49)
$$ 20x_{B2}^{3} + 30x_{B2}^{4} + 50x_{B2}^{5} + 60x_{B2}^{6} + z_{mB2} = z_{mB1} $$
(50)
$$ 20x_{B3}^{3} + 30x_{B3}^{4} + 50x_{B3}^{5} + 60x_{B3}^{6} + z_{mB3} = z_{mB2} $$
(51)
$$ 50x_{B4}^{5} + 60x_{B4}^{6} + z_{mB4} = z_{mB3} $$
(52)
$$ 50x_{B5}^{5} + 60x_{B5}^{6} + z_{mB5} = z_{mB4} $$
(53)
$$ \begin{aligned} & 10x_{A0}^{1} + 20x_{A2}^{2} + 100x_{A2}^{5} + 100x_{A4}^{5} + 120x_{A2}^{6} + 120x_{A4}^{6} \\ & \quad = 0.7(10x_{A0}^{1} + 20x_{A2}^{2} + 32x_{B1}^{3} + 32x_{B2}^{3} + 32x_{B3}^{3} + 48x_{B2}^{4} + 48x_{B3}^{4} \\ & \quad \quad + 100x_{A2}^{5} + 100x_{A4}^{5} + 125x_{B2}^{5} + 125x_{B3}^{5} + 125x_{B4}^{5} + 125x_{B5}^{5} \\ & \quad \quad + 120x_{A2}^{6} + 120x_{A4}^{6} + 150x_{B1}^{6} + 150x_{B2}^{6} + 150x_{B3}^{6} + 150x_{B4}^{6} + 150x_{B5}^{6} ) + r_{A}^{ + } - r_{A}^{ - } \\ \end{aligned} $$
(54)
$$ \begin{aligned} & 32x_{B1}^{3} + 32x_{B2}^{3} + 32x_{B3}^{3} + 48x_{B2}^{4} + 48x_{B3}^{4} + 125x_{B2}^{5} + 125x_{B3}^{5} + 125x_{B4}^{5} + 125x_{B5}^{5} \\ & \quad \quad + 150x_{B1}^{6} + 150x_{B2}^{6} + 150x_{B3}^{6} + 150x_{B4}^{6} + 150x_{B5}^{6} \\ & \quad = 0.3(10x_{A0}^{1} + 20x_{A2}^{2} + 32x_{B1}^{3} + 32x_{B2}^{3} + 32x_{B3}^{3} + 48x_{B2}^{4} + 48x_{B3}^{4} \\ & \quad \quad + 100x_{A2}^{5} + 100x_{A4}^{5} + 125x_{B2}^{5} + 125x_{B3}^{5} + 125x_{B4}^{5} + 125x_{B5}^{5} \\ & \quad \quad + 120x_{A2}^{6} + 120x_{A4}^{6} + 150x_{B1}^{6} + 150x_{B2}^{6} + 150x_{B3}^{6} + 150x_{B4}^{6} + 150x_{B5}^{6} ) + r_{B}^{ + } - r_{B}^{ - } \\ \end{aligned} $$
(55)
$$ 10x_{A0}^{1} \le 10 $$
(56)
$$ 20x_{A2}^{1} \le 20 $$
(57)
$$ 50x_{A2}^{5} + 60x_{A2}^{6} + 50x_{A4}^{5} + 60x_{A4}^{6} \le 60 $$
(58)
$$ 20x_{B1}^{3} \le 30 $$
(59)
$$ 20x_{B2}^{3} + 20x_{B3}^{3} + 30x_{B2}^{4} + 30x_{B3}^{4} \le 30 $$
(60)
$$ 60x_{B1}^{6} + 50x_{B2}^{5} + 50x_{B3}^{5} + 60x_{B2}^{6} + 60x_{B3}^{6} + 50x_{B4}^{5} + 50x_{B5}^{5} + 60x_{B4}^{6} + 60x_{B5}^{6} \le 100 $$
(61)
$$ 50x_{B2}^{5} + 50x_{B3}^{5} \le 50 $$
(62)
$$ 50x_{B2}^{5} + 50x_{B3}^{5} + 60x_{B2}^{6} + 60x_{B3}^{6} + 50x_{B4}^{5} + 50x_{B5}^{5} + 60x_{B4}^{6} + 60x_{B5}^{6} \le 100 $$
(63)
$$ 50x_{B4}^{5} + 50x_{B5}^{5} \le 50 $$
(64)
$$ \theta_{A2}^{1} - \theta_{A0}^{1} \le \phi_{A2}^{1} $$
(65)
$$ \theta_{A4}^{1} - \theta_{A2}^{1} \le \phi_{A4}^{1} $$
(66)
$$ \theta_{A2}^{3} - \theta_{A0}^{3} \le \phi_{A2}^{3} $$
(67)
$$ \theta_{A4}^{3} - \theta_{A2}^{3} \le \phi_{A4}^{3} $$
(68)
$$ \theta_{B2}^{2} - \theta_{B1}^{2} \le \phi_{B2}^{2} $$
(69)
$$ \theta_{B3}^{2} - \theta_{B2}^{2} \le \phi_{B3}^{2} $$
(70)
$$ \theta_{B4}^{2} - \theta_{B3}^{2} \le \phi_{B4}^{2} $$
(71)
$$ \theta_{B5}^{2} - \theta_{B4}^{2} \le \phi_{B5}^{2} $$
(72)
$$ \theta_{B2}^{3} - \theta_{B1}^{3} \le \phi_{B2}^{3} $$
(73)
$$ \theta_{B3}^{3} - \theta_{B2}^{3} \le \phi_{B3}^{3} $$
(74)
$$ \theta_{B4}^{3} - \theta_{B3}^{3} \le \phi_{B4}^{3} $$
(75)
$$ \theta_{B5}^{3} - \theta_{B4}^{3} \le \phi_{B5}^{3} $$
(76)
$$ \theta_{A0}^{1} - 1 \le \phi_{A0}^{1} $$
(77)
$$ \theta_{B1}^{2} \le \phi_{B1}^{2} $$
(78)
$$ \theta_{A0}^{3} \le \phi_{A0}^{3} $$
(79)
$$ \theta_{B1}^{3} - 1 \le \phi_{B1}^{3} $$
(80)
$$ \theta_{A0}^{1} \le x_{A0}^{1} + x_{A0}^{2} \le 2\theta_{A0}^{1} $$
(81)
$$ \theta_{A2}^{1} \le 0 $$
(82)
$$ \theta_{A4}^{1} \le 0 $$
(83)
$$ \theta_{A0}^{3} \le 0 $$
(84)
$$ \theta_{A2}^{3} \le x_{A2}^{5} + x_{A2}^{6} \le 2\theta_{A2}^{3} $$
(85)
$$ \theta_{A4}^{3} \le x_{A4}^{5} + x_{A4}^{6} \le 2\theta_{A4}^{3} $$
(86)
$$ \theta_{B1}^{2} \le x_{B1}^{3} \le \theta_{B1}^{2} $$
(87)
$$ \theta_{B2}^{2} \le x_{B2}^{3} + x_{B2}^{4} \le 2\theta_{B2}^{2} $$
(88)
$$ \theta_{B3}^{2} \le x_{B3}^{3} + x_{B3}^{4} \le 2\theta_{B3}^{2} $$
(89)
$$ \theta_{B4}^{2} \le 0 $$
(90)
$$ \theta_{B5}^{2} \le 0 $$
(91)
$$ \theta_{B1}^{3} \le x_{B1}^{6} \le 2\theta_{B1}^{3} $$
(92)
$$ \theta_{B2}^{3} \le x_{B2}^{5} + x_{B2}^{6} \le 2\theta_{B2}^{3} $$
(93)
$$ \theta_{B3}^{3} \le x_{B3}^{5} + x_{B3}^{6} \le 2\theta_{B3}^{3} $$
(94)
$$ \theta_{B4}^{3} \le x_{B4}^{5} + x_{B4}^{6} \le 2\theta_{B4}^{3} $$
(95)
$$ \theta_{B5}^{3} \le x_{B5}^{5} + x_{B5}^{6} \le 2\theta_{B5}^{3} $$
(96)
$$ x_{A0}^{1} ,\,x_{A2}^{2} ,\,x_{B1}^{3} ,\,x_{B2}^{3} ,\,x_{B3}^{3} ,\,x_{B2}^{4} ,\,x_{B3}^{4} ,\,x_{A2}^{5} ,\,x_{A4}^{5} ,\,x_{B2}^{5} ,\,x_{B3}^{5} ,\,x_{B4}^{5} ,\,x_{B5}^{5} ,\,x_{A2}^{6} ,\,x_{A4}^{6} ,\,x_{B1}^{6} ,\,x_{B2}^{6} ,\,x_{B3}^{6} ,\,x_{B4}^{6} ,\,x_{B5}^{6} \in \{ 0,1\} $$
(97)
$$ y_{0}^{1} ,\,y_{1}^{1} ,\,y_{1}^{2} ,\,y_{2}^{2} ,\,y_{3}^{2} ,\,y_{1}^{3} ,\,y_{2}^{3} ,\,y_{3}^{3} ,\,y_{2}^{4} ,\,y_{3}^{4} ,\,y_{2}^{5} ,\,y_{3}^{5} ,\,y_{4}^{5} ,\,y_{5}^{5} ,\,y_{1}^{6} ,\,y_{2}^{6} ,\,y_{3}^{6} ,\,y_{4}^{6} ,\,y_{5}^{6} \in \{ 0,1\} $$
(98)
$$ z_{mA0} ,\,z_{mA2} ,\,z_{mA4} ,\,z_{mB1} ,\,z_{mB2} ,\,z_{mB3} ,\,z_{mB4} ,\,z_{mB5} \ge 0 $$
(99)
$$ 0 \le \phi_{A0}^{1} ,\,\phi_{A2}^{1} ,\,\phi_{A4}^{1} ,\,\phi_{B1}^{2} ,\,\phi_{B2}^{2} ,\,\phi_{B3}^{2} ,\,\phi_{B4}^{2} ,\,\phi_{B5}^{2} ,\,\phi_{A0}^{3} ,\,\phi_{A2}^{3} ,\,\phi_{A4}^{3} ,\,\phi_{B1}^{3} ,\,\phi_{B2}^{3} ,\,\phi_{B3}^{3} ,\,\phi_{B4}^{3} ,\,\phi_{B5}^{3} \le 1 $$
(100)
$$ \theta_{A0}^{1} ,\,\theta_{A2}^{1} ,\,\theta_{A4}^{1} ,\,\theta_{B1}^{2} ,\,\theta_{B2}^{2} ,\,\theta_{B3}^{2} ,\,\theta_{B4}^{2} ,\,\theta_{B5}^{2} ,\,\theta_{A0}^{3} ,\,\theta_{A2}^{3} ,\,\theta_{A4}^{3} ,\,\theta_{B1}^{3} ,\,\theta_{B2}^{3} ,\,\theta_{B3}^{3} ,\,\theta_{B4}^{3} ,\,\theta_{B5}^{3} \in \{ 0,1\} $$
(101)
$$ r_{A}^{ + } ,\,r_{A}^{ - } ,\,r_{B}^{ + } ,\,r_{B}^{ - } \ge 0 $$
(102)
Table 3 Order data
Full size table
Table 4 Product data
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Table 5 Vendor data
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Table 6 Bucket-related data
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Table 7 Capacity data (\( C_{vt}^{p} \))
Full size table
Table 8 Consumed capacity data (\( \bar{C}_{vt}^{p} \))
Full size table
Table 9 Adjusted capacity data (\( \tilde{C}_{vt}^{p} \))
Full size table
Table 10 Order assignment (\( x_{vb}^{j} \))
Full size table

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Chien, CF., Wu, JZ. & Weng, YD. Modeling order assignment for semiconductor assembly hierarchical outsourcing and developing the decision support system. Flex Serv Manuf J 22, 109–139 (2010). https://doi.org/10.1007/s10696-010-9073-0

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