Two-Stage Stochastic Program for Supply Chain Network Design under Facility Disruptions
Abstract
:1. Introduction
2. Literature Review
3. Model Formulation
3.1. Problem Description
- (1)
- Given that the problem deals with strategic decision to design a supply chain network, therefore this paper assumes that demands at the retailers are deterministic for observing the effect of disruption easily.
- (2)
- A disruption may occur at any supplier, manufacturer, or DC. To incorporate disruption into the model and measure its impact, this paper generates scenarios based on the probability distribution of the disruption by setting the binary parameters from one to zero. If the disruption occurs at any facility, it will be completely disrupted. In addition, this paper assumes that the probabilities of disruption occurs at each facility are independent.
- (3)
- The set of all possible disruptive scenarios is finite.
3.2. Mathematical Model
- S = Set of suppliers
- M = Set of manufacturers
- W = Set of DCs
- C = Set of retailers
- L = Set of DC capacities
- R = Set of countries
- K = Set of disruptive scenarios
- s = Index of suppliers, s ∈ S
- m = Index of manufacturers, m ∈ M w = Index of DCs, w ∈ W
- c = Index of retailers, c ∈ C
- l = Index of DC capacities, l ∈ L
- r = Index of countries, r ∈ R
- k = Index of disruptive scenarios, k ∈ K
- capm = Production capacity at manufacturer m
- caps = Capacity at supplier s
- = Capacity at DC w of size l
- dc = Demand for products at retailer c
- msm = Minimum transportation quantity from suppliers to manufacturers
- = Fixed cost of opening a DC w of capacity l
- pmsm = Purchasing cost per unit of material from supplier s by manufacturer m
- trmw = Transportation cost per unit from manufacturer m to DC w
- trwc = Transportation cost per unit from DC w to retailer c
- pcm = Production cost for a product at manufacturer m
- np = Price of a product
- lsc = Lost sales cost at retailer c
- pr = Probability of disruption occurs at country r
if supplier s operates in scenario k (with probability 1 − pc) | |
if a disruption occurs at supplier s in scenario k (with probability pc) | |
if DC w operates in scenario k (with probability 1 − pc) | |
if a disruption occurs at DC w in scenario k (with probability pc) | |
if manufacturer m operates in scenario k (with probability 1 − pc) | |
if a disruption occurs at manufacturer m in scenario k (with probability pc) |
if DC w operates with size l | |
otherwise | |
if supplier s is selected | |
otherwise |
QSMsmk = | Quantity of raw material purchased from supplier s by manufacturer m in scenario k |
QMWmwk = | Quantity of products shipped from manufacturer m to DC w in scenario k |
QWCwck = | Quantity of products shipped from DC w to retailer c in scenario k |
LDck = | Quantity of sales lost at retailer c in scenario k |
3.2.1. Objective Function
3.2.2. Constraints
4. Solution Methodology
4.1. Simulated Annealing (SA)
- r = Index of iterations
- cr = Control parameter at iteration r
- c0 = Initial value of the control parameter
- cmin = Minimum value of the control parameter
- a, b = First-stage solution vectors
- T = Number of solutions evaluated in each iteration
- N = Sample size (number of sampled scenarios)
- = Estimate of the objective function value by using sample size N
- P = Probability vector of the first-stage variables (x and y)
- U = Random number in [0, 1)
- ρ = Coefficient of the control parameter update
- λ = Coefficient of the probabilities update
4.2. Solution Construction
Algorithm 1 Simulated Annealing Algorithm |
Initialized(ρ, λ, c0, cmin,T, N, P) Generate (a) r:=1 cr:= c0 repeat for t:=1 to T do Generate (b) if then a:=b else if then a:=b end if end for Update(P) cr:= ρ ∙ cr r:= r + 1 until cr < cmin |
4.3. Monte Carlo Sampling and Solution Evaluation
4.4. Information Update
5. Illustrative Example
5.1. Supply Chain Network Design without Disruption
5.2. Supply Chain Network Design with Disruption Consideration
5.2.1. Disruptive Scenarios
5.2.2. Computational Results
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Haraguchi, M.; Lall, U. Flood risks and impacts: A case study of Thailand’s floods in 2011 and research questions for supply chain decision making. Int. J. Disaster Risk Reduct. 2015, 14, 256–272. [Google Scholar] [CrossRef]
- Chopra, S.; Sodhi, M.S. Managing risk to avoid supply-chain breakdown. MIT Sloan Manag. Rev. 2004, 46, 53. [Google Scholar]
- Ivanov, D.; Dolgui, A.; Sokolov, B. Supply Chain Design with Disruption Considerations: Review of Research Streams on the Ripple Effect in the Supply Chain. IFAC Pap. 2015, 48, 1700–1707. [Google Scholar] [CrossRef]
- Soni, U.; Jain, V.; Kumar, S. Measuring supply chain resilience using a deterministic modeling approach. Comput. Ind. Eng. 2014, 74, 11–25. [Google Scholar] [CrossRef]
- Ivanov, D.; Dolgui, A.; Sokolov, B.; Ivanova, M. Literature review on disruption recovery in the supply chain. Int. J. Prod. Res. 2017, 55, 6158–6174. [Google Scholar] [CrossRef]
- Xu, S.; Zhang, X.; Feng, L.; Yang, W. Disruption risks in supply chain management: A literature review based on bibliometric analysis. Int. J. Prod. Res. 2020, 58, 3508–3526. [Google Scholar] [CrossRef]
- Azaron, A.; Brown, K.; Tarim, S.; Modarres, M. A multi-objective stochastic programming approach for supply chain design considering risk. Int. J. Prod. Econ. 2008, 116, 129–138. [Google Scholar] [CrossRef]
- Cui, T.; Ouyang, Y.; Shen, Z.-J.M. Reliable Facility Location Design under the Risk of Disruptions. Oper. Res. 2010, 58, 998–1011. [Google Scholar] [CrossRef] [Green Version]
- Snyder, L.V.; Daskin, M.S. Reliability Models for Facility Location: The Expected Failure Cost Case. Transp. Sci. 2005, 39, 400–416. [Google Scholar] [CrossRef]
- Fattahi, M.; Govindan, K.; Keyvanshokooh, E. Responsive and resilient supply chain network design under operational and disruption risks with delivery lead-time sensitive customers. Transp. Res. Part E Logist. Transp. Rev. 2017, 101, 176–200. [Google Scholar] [CrossRef]
- Jabbarzadeh, A.; Fahimnia, B.; Sabouhi, F. Resilient and sustainability analysis under disruption risks. Int. J. Prod. Res. 2018, 56, 5945–5968. [Google Scholar] [CrossRef]
- Hosseini, S.; Morshedlou, N.; Ivanov, D.; Sarder, M.; Barker, K.; Al Khaled, A. Resilient supplier selection and optimal order allocation under disruption risks. Int. J. Prod. Econ. 2019, 213, 124–137. [Google Scholar] [CrossRef]
- Malik, A.I.; Sarkar, B. Disruption management in a constrained multi-product imperfect production system. J. Manuf. Syst. 2020, 56, 227–240. [Google Scholar] [CrossRef] [PubMed]
- Fattahi, M.; Govindram, K.; Maihami, R. Stochastic optimization of disruption-driven supply chain network design with a new resilience mettic. Int. J. Prod. Econ. 2020, 230, 1–16. [Google Scholar] [CrossRef]
- Haghjoo, N.; Tavakkoli-Moghaddam, R.; Shahmoradi-Moghadam, H.; Rahimi, Y. Reliable blood supply chain network design with facility disruption: A real-world application. Eng. Appl. Artif. Intell. 2020, 90, 103493. [Google Scholar] [CrossRef]
- Baghalian, A.; Rezapour, S.; Farahani, R.Z. Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case. Eur. J. Oper. Res. 2013, 227, 199–215. [Google Scholar] [CrossRef]
- Hasani, A.; Khosrojerdi, A. Robust global supply chain network design under disruption and uncertainty considering resilience strategies: A parallel memetic algorithm for a real-life case study. Transp. Res. Part E Logist. Transp. Rev. 2016, 87, 20–52. [Google Scholar] [CrossRef]
- Poudel, S.R.; Marufuzzaman, M.; Bian, L. Designing a reliable bio-fuel supply chain network considering link failure probabilities. Comput. Ind. Eng. 2016, 91, 85–99. [Google Scholar] [CrossRef]
- Margolis, J.T.; Sullivan, K.M.; Mason, S.J.; Magagnotti, M. A multi-objective optimization model for designing resilient supply chain networks. Int. J. Prod. Econ. 2018, 204, 174–185. [Google Scholar] [CrossRef]
- Albertzeth, G.; Pujawan, I.N.; Hilletofth, P.; Tjahjono, B. Mitigating transportation disruptions in a supply chain: A cost-effectiveness stragegy. Int. J. Logist. Res. Appl. 2020, 23, 139–158. [Google Scholar] [CrossRef]
- Johnson, A.R.; Johnson, M.E.; Nagarur, N. Supply chain design under disruptions considering risk mitigation strategies for robustness and resiliency. Int. J. Logist. Syst. Manag. 2021, 38, 1–29. [Google Scholar] [CrossRef]
- Singh, C.S.; Soni, G.; Badhotiya, G.K. Performance indicators for supply chain resilience: Review and conceptual framework. J. Ind. Eng. Int. 2019, 15, 105–117. [Google Scholar] [CrossRef] [Green Version]
- Azad, N.; Davoudpour, H.; Saharidis, G.K.D.; Shiripour, M. A new model to mitigating random disruption risks of facility and transportation in supply chain network design. Int. J. Adv. Manuf. Technol. 2013, 70, 1757–1774. [Google Scholar] [CrossRef]
- Marufuzzaman, M.; Eksioglu, S.D.; Huang, Y. (Eric). Two-stage stochastic programming supply chain model for biodiesel production via wastewater treatment. Comput. Oper. Res. 2014, 49, 1–17. [Google Scholar] [CrossRef]
- Sadghiani, N.S.; Torabi, S.; Sahebjamnia, N. Retail supply chain network design under operational and disruption risks. Transp. Res. Part E Logist. Transp. Rev. 2015, 75, 95–114. [Google Scholar] [CrossRef]
- Torabi, S.A.; Baghersad, M.; Mansouri, S.A. Resilient supplier selection and order allocation under operational and disruption risks. Transp. Res. Part E Logist. Transp. Rev. 2015, 79, 22–48. [Google Scholar] [CrossRef]
- Giri, B.C.; Bardhan, S. Coordinating a supply chain under uncertain demand and random yield in presence of supply disruption. Int. J. Prod. Res. 2015, 53, 5070–5084. [Google Scholar] [CrossRef]
- Tolooie, A.; Maity, M.; Sinha, A.K. A two-stage stochastic mixed-integer program for reliable supply chain network design under uncertain disruptions and demand. Comput. Ind. Eng. 2020, 148, 106722. [Google Scholar] [CrossRef]
- Sawik, T. Supply Chain Disruption Management Using Stochastic Mixed Interger Programming. In International Series in Operations Research & Management Science; Springer: Berlin/Heidelberg, Germany, 2018. [Google Scholar]
- Rienkhemaniyom, K.; Pazhani, S. A Supply Chain Network Design Considering Network Density. In Smart and Sustainable Supply Chain and Logistics—Trends, Challenges, Methods and Best Practices; Springer International Publishing: Berlin/Heidelberg, Germany, 2015; pp. 3–19. [Google Scholar]
- Shapiro, A. Monte Carlo Sampling Methods. Financ. Eng. 2003, 10, 353–425. [Google Scholar] [CrossRef]
- Aarts, E.; Korst, J.; Michiels, W. Simulated Annealing. In Search Methodologies; Springer: Berlin/Heidelberg, Germany, 2014. [Google Scholar]
- Guha-Sapir, D.; Below, R.; Hoyois, P. EM-DAT: The CRED/OFDA International Disaster Database; Université Catholique de Louvain: Brussels, Belgium, 2015. [Google Scholar]
- Linderoth, J.; Shapiro, A.; Wright, S.J. The empirical behavior of sampling methods for stochastic programming. Ann. Oper. Res. 2006, 142, 215–241. [Google Scholar] [CrossRef]
- Ivanov, D.; Dolgui, A. Low-Certainty-Need (LCN) supply chains: A new perspective in managing disruption risks and resilience. Int. J. Prod. Res. 2019, 57, 5119–5136. [Google Scholar] [CrossRef] [Green Version]
Ref | Disruption | Decision Variables | ||||
---|---|---|---|---|---|---|
Facility | Link | Location | Production Quantity | Purchasing Quantity | Distribution Quantity | |
[16] | V | V | V | V | ||
[23] | V | V | V | V | ||
[24] | V | V | V | |||
[27] | V | V | V | |||
[26] | V | V | ||||
[17] | V | V | V | V | V | |
[18] | V | V | V | |||
[10] | V | V | V | V | ||
[14] | V | V | V | |||
[19] | V | V | V | V | ||
[29] | V | V | V | |||
[11] | V | V | V | |||
[12] | V | V | V | |||
[13] | V | V | V | |||
[20] | V | V | ||||
[28] | V | V | V | V | ||
[15] | V | V | ||||
This paper | V | V | V | V | V |
Ref | Stage of Supply Chain | Type of Disruption | Level of Disruption | |||||
---|---|---|---|---|---|---|---|---|
Supplier | Manufacturer | DC | Link | Random | Premeditate | Partial | Complete | |
[16] | V | V | V | V | ||||
[23] | V | V | V | V | ||||
[24] | V | V | V | |||||
[27] | V | V | V | V | ||||
[26] | V | V | V | V | ||||
[17] | V | V | V | V | V | |||
[18] | V | V | V | |||||
[10] | V | V | V | V | ||||
[14] | V | V | V | |||||
[19] | V | V | V | V | V | |||
[29] | V | V | V | V | ||||
[11] | V | V | V | V | V | |||
[12] | V | V | V | |||||
[13] | V | V | V | |||||
[28] | V | V | V | |||||
[20] | V | V | V | V | V | |||
[15] | V | V | V | V | ||||
This paper | V | V | V | V | V |
Region | Supplier | Manufacturer | DC |
---|---|---|---|
Region 1 | S16 | M3 | - |
Region 2 | S8, S10, S11, S15, S17 | M1, M2 | - |
Region 3 | S6, S7, S9, S14 | M4 | W8 |
Region 4 | S4, S13 | M5 | W12, W13 |
Region 5 | - | - | - |
Region 6 | S1 | - | - |
Total | 13 | 5 | 3 |
Country | Suppliers | Manufacturers | DCs | Probability of Occurrence |
---|---|---|---|---|
Argentina | S11 | - | - | 0.017 |
Australia | S14 | - | W13 | 0.035 |
Austria | - | - | W4 | 0.007 |
Belgium | S13 | - | W12 | 0.010 |
Brazil | S7 | - | - | 0.034 |
Canada | S4 | - | W6 | 0.020 |
Cayman Islands | S16 | M3 | W17 | 0.001 |
China | - | W19 | 0.133 | |
France | S17 | W20, W25 | 0.023 | |
Germany | S5 | M1 | W7 | 0.011 |
India | S10 | - | - | 0.105 |
Indonesia | S18 | - | W21 | 0.073 |
Italy | S3 | - | W5 | 0.022 |
Japan | - | - | W14 | 0.051 |
Korea (the Republic of) | S6 | - | W8 | 0.017 |
Malaysia | - | - | W15 | 0.012 |
Mexico | - | - | W11 | 0.038 |
Netherlands (the) | S15 | - | W16 | 0.005 |
Pakistan | - | - | W18 | 0.031 |
Philippines (the) | S20 | M4, M5 | W23, W24 | 0.092 |
Russian Federation (the) | S19 | - | W22 | 0.024 |
South Africa | S12 | - | - | 0.015 |
Sweden | S2 | - | W2 | 0.002 |
Taiwan (Province of China) | - | - | W3 | 0.016 |
Thailand | S1 | - | W1 | 0.021 |
Turkey | S9 | - | - | 0.024 |
United Kingdom of Great Britain and Northern Ireland (the) | S8 | M2 | W9 | 0.013 |
United States of America (the) | - | - | W10 | 0.147 |
Total | 1.000 |
Replication | Optimal (CPLEX) | SA | Difference | Difference (%) |
---|---|---|---|---|
1 | 12,259,408.30 | 234,270.30 | 1.88 | |
2 | 12,178,013.94 | 315,664.66 | 2.53 | |
3 | 12,309,582.24 | 184,096.36 | 1.47 | |
4 | 12,178,665.69 | 315,012.91 | 2.52 | |
5 | 12,324,980.65 | 168,697.95 | 1.35 | |
6 | 12,493,678.60 | 12,035,623.28 | 458,055.32 | 3.67 |
7 | 12,370,727.82 | 122,950.78 | 0.98 | |
8 | 12,364,367.23 | 129,311.37 | 1.04 | |
9 | 12,097,164.50 | 396,514.10 | 3.17 | |
10 | 12,350,310.94 | 143,367.66 | 1.15 | |
Average | 12,246,884.46 | 246,794.14 | 1.98 |
Replication | N = 20 | N = 50 | N = 100 |
---|---|---|---|
1 | 12,926,743.17 | 12,936,504.50 | 12,418,851.37 |
2 | 12,418,814.86 | 12,537,833.87 | 12,125,486.15 |
3 | 12,919,320.51 | 12,464,742.63 | 12,274,587.18 |
4 | 12,546,105.51 | 12,504,353.57 | 12,059,285.24 |
5 | 12,288,548.63 | 12,366,851.17 | 12,412,839.32 |
6 | 12,846,196.02 | 12,621,856.67 | 11,995,844.01 |
7 | 12,952,681.61 | 12,346,809.29 | 12,403,648.33 |
8 | 12,797,331.73 | 12,415,321.97 | 12,493,808.13 |
9 | 12,882,444.22 | 12,549,969.87 | 11,953,054.86 |
10 | 12,006,506.97 | 11,823,100.12 | 12,280,738.77 |
Average | 12,658,469.32 | 12,456,734.37 | 12,241,814.33 |
Standard Deviation | 327,145.91 | 278,571.02 | 195,392.62 |
Replication | Solution from Original Design | Solutions | from SA with Sample Size | |
---|---|---|---|---|
N = 20 | N = 50 | N = 100 | ||
1 | 13,096,522.68 | 13,051,966.74 | 13,184,154.53 | |
2 | 12,920,227.45 | 13,155,981.66 | 13,180,699.57 | |
3 | 12,942,537.45 | 13,003,074.42 | 13,057,226.19 | |
4 | 13,171,893.86 | 13,089,908.03 | 13,073,942.27 | |
5 | 13,248,679.26 | 13,065,948.69 | 12,983,342.65 | 13,007,254.34 |
6 | 13,149,727.22 | 12,932,378.48 | 13,193,867.37 | |
7 | 13,027,280.15 | 12,974,604.06 | 13,074,024.28 | |
8 | 13,154,910.60 | 13,168,145.63 | 13,149,428.82 | |
9 | 13,103,227.15 | 13,070,412.66 | 13,091,222.72 | |
10 | 13,149,634.13 | 13,123,011.48 | 13,060,618.83 | |
Average | 13,078,190.94 | 13,055,282.58 | 13,107,243.89 | |
Standard Deviation | 89,409.60 | 80,567.36 | 64,753.36 | |
Mitigation cost | 170,488.32 | 193,396.68 | 141,435.37 |
Replication | Solution from Original Design | Solutions | from SA with Sample Size | |
---|---|---|---|---|
N = 20 | N = 50 | N = 100 | ||
1 | 11,950,373.24 | 11,621,036.69 | 12,125,437.22 | 12,009,805.94 |
2 | 11,838,016.30 | 11,851,151.56 | 11,947,473.61 | 11,981,417.92 |
3 | 11,831,140.24 | 11,448,720.92 | 12,049,300.08 | 12,004,185.16 |
4 | 11,780,590.92 | 12,045,964.41 | 11,935,091.85 | 11,830,527.34 |
5 | 11,789,481.46 | 12,239,861.49 | 12,065,857.69 | 12,118,408.82 |
6 | 11,895,626.39 | 11,982,653.16 | 12,273,107.33 | 12,027,116.72 |
7 | 11,886,468.32 | 11,991,857.49 | 11,834,090.51 | 11,922,442.47 |
8 | 11,880,323.77 | 11,894,812.90 | 11,923,011.41 | 11,960,271.74 |
9 | 11,838,575.11 | 12,107,121.93 | 12,013,970.80 | 11,982,746.14 |
10 | 11,801,826.73 | 11,990,353.93 | 11,905,938.10 | 12,314,238.09 |
Average | 11,849,242.25 | 11,917,353.45 | 12,007,327.86 | 12,015,116.03 |
Standard Deviation | 53,573.30 | 231,904.94 | 127,375.64 | 128,360.49 |
Mitigation benefit | 68,111.20 | 158,085.61 | 165,873.78 |
Region | Supplier | Manufacturer | DC |
---|---|---|---|
Region 1 | S16 | M3 | W17 |
Region 2 | S5, S8, S10, S11, S12, S15, S17, S18 | M1, M2 | - |
Region 3 | S6, S7, S9, S14, S19 | M4 | W3, W21 |
Region 4 | S4, S13, S20 | M5 | - |
Region 5 | S2 | - | - |
Region 6 | S1, S3 | - | - |
Total | 20 | 5 | 3 |
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Kungwalsong, K.; Cheng, C.-Y.; Yuangyai, C.; Janjarassuk, U. Two-Stage Stochastic Program for Supply Chain Network Design under Facility Disruptions. Sustainability 2021, 13, 2596. https://doi.org/10.3390/su13052596
Kungwalsong K, Cheng C-Y, Yuangyai C, Janjarassuk U. Two-Stage Stochastic Program for Supply Chain Network Design under Facility Disruptions. Sustainability. 2021; 13(5):2596. https://doi.org/10.3390/su13052596
Chicago/Turabian StyleKungwalsong, Kanokporn, Chen-Yang Cheng, Chumpol Yuangyai, and Udom Janjarassuk. 2021. "Two-Stage Stochastic Program for Supply Chain Network Design under Facility Disruptions" Sustainability 13, no. 5: 2596. https://doi.org/10.3390/su13052596