Modelling and optimal lot-sizing of integrated multi-level multi-wholesaler supply chains under the shortage and limited warehouse space: generalised outer approximation

References

• Adeinat, H. , & Ventura, J.A. (2018). Integrated pricing and lot-sizing decisions in a serial supply chain. Applied Mathematical Modelling , 54 , 429–445.
   Web of Science ®Google Scholar
• Afshar, A. , & Haghani, A. (2012). Modeling integrated supply chain logistics in real-time large-scale disaster relief operations. Socio-Economic Planning Sciences , 46 (4), 327–338.
   Google Scholar
• Aqlan, F. (2016). A software application for rapid risk assessment in integrated supply chains. Expert Systems with Applications , 43 , 109–116.
   Web of Science ®Google Scholar
• Autry, C.W. , Rose, W.J. , & Bell, J.E. (2014). Reconsidering the supply chain integration–performance relationship: In search of theoretical consistency and clarity. Journal of Business Logistics , 35 (3), 275–276.
   Web of Science ®Google Scholar
• Ayoub, N. , Elmoshi, E. , Seki, H. , & Naka, Y. (2009). Evolutionary algorithms approach for integrated bioenergy supply chains optimization. Energy Conversion and Management , 50 (12), 2944–2955.
   Web of Science ®Google Scholar
• Bandaly, D. , Satir, A. , & Shanker, L. (2014). Integrated supply chain risk management via operational methods and financial instruments. International Journal of Production Research , 52 (7), 2007–2025.
   Web of Science ®Google Scholar
• Bidhandi, H.M. , & Yusuff, R.M. (2011). Integrated supply chain planning under uncertainty using an improved stochastic approach. Applied Mathematical Modelling , 35 (6), 2618–2630.
   Web of Science ®Google Scholar
• Bilir, C. , Ekici, S.O. , & Ulengin, F. (2017). An integrated multi-objective supply chain network and competitive facility location model. Computers & Industrial Engineering , 108 , 136–148.
   Web of Science ®Google Scholar
• Boukherroub, T. , LeBel, L. , & Lemieux, S. (2017). An integrated wood pellet supply chain development: Selecting among feedstock sources and a range of operating scales. Applied Energy , 198 , 385–400.
   Web of Science ®Google Scholar
• Chakraborty, D. , Jana, D.K. , & Roy, T.K. (2015). Multi-item integrated supply chain model for deteriorating items with stock dependent demand under fuzzy random and bifuzzy environments. Computers & Industrial Engineering , 88 , 166–180.
   Web of Science ®Google Scholar
• Chang, W. , Ellinger, A.E. , Kim, K.K. , & Franke, G.R. (2016). Supply chain integration and firm financial performance: A meta-analysis of positional advantage mediation and moderating factors. European Management Journal , 34 (3), 282–295.
   Web of Science ®Google Scholar
• Chung, K.J. , Cárdenas-Barrón, L.E. , & Ting, P.S. (2014). An inventory model with non-instantaneous receipt and exponentially deteriorating items for an integrated three layer supply chain system under two levels of trade credit. International Journal of Production Economics , 155 , 310–317.
   Web of Science ®Google Scholar
• Chung, S.H. , & Kwon, C. (2016). Integrated supply chain management for perishable products: Dynamics and oligopolistic competition perspectives with application to pharmaceuticals. International Journal of Production Economics , 179 , 117–129.
   Web of Science ®Google Scholar
• Cui, J. , Zhao, M. , Li, X. , Parsafard, M. , & An, S. (2016). Reliable design of an integrated supply chain with expedited shipments under disruption risks. Transportation Research Part E: Logistics and Transportation Review , 95 , 143–163.
   Web of Science ®Google Scholar
• Das, B.C. , Das, B. , & Mondal, S.K. (2013). Integrated supply chain model for a deteriorating item with procurement cost dependent credit period. Computers & Industrial Engineering , 64 (3), 788–796.
   Web of Science ®Google Scholar
• Das, D. , & Dutta, P. (2013). A system dynamics framework for integrated reverse supply chain with three way recovery and product exchange policy. Computers & Industrial Engineering , 66 (4), 720–733.
   Web of Science ®Google Scholar
• Diabat, A. , & Al-Salem, M. (2015). An integrated supply chain problem with environmental considerations. International Journal of Production Economics , 164 , 330–338.
   Web of Science ®Google Scholar
• Duran, M.A. , & Grossmann, I.E. (1986). An outer-approximation algorithm for a class of mixed-integer nonlinear programs. Mathematical Programming , 36 (3), 307–339.
   Web of Science ®Google Scholar
• Ensafian, H. , Yaghoubi, S. , & Yazdi, M.M. (2017). Raising quality and safety of platelet transfusion services in a patient-based integrated supply chain under uncertainty. Computers & Chemical Engineering , 106 , 355–372.
   Web of Science ®Google Scholar
• Feng, X. , Moon, I. , & Ryu, K. (2017). Warehouse capacity sharing via transshipment for an integrated two-echelon supply chain. Transportation Research Part E: Logistics and Transportation Review , 104 , 17–35.
   Web of Science ®Google Scholar
• Fletcher, R. , & Leyffer, S. (1994). Solving mixed integer nonlinear programs by outer approximation. Mathematical Programming , 66 (1), 327–349.
   Google Scholar
• Floudas, C.A. (1995). Nonlinear and mixed-integer optimization: Fundamentals and applications . Oxford University Press.
   Google Scholar
• Gharaei, A. , Naderi, B. , & Mohammadi, M. (2015). Optimization of rewards in single machine scheduling in the rewards-driven systems. Management Science Letters , 5 (6), 629–638.
   Google Scholar
• Gharaei, A. , & Pasandideh, S.H.R. (2016). Modelling and optimization the four-level integrated supply chain: Sequential quadratic programming. International Journal of Computer Science and Information Security , 14(7), 650–669.
   Google Scholar
• Gharaei, A. , & Pasandideh, S.H.R. (2017a). Four-echelon integrated supply chain model with stochastic constraints under shortage condition. Industrial Engineering & Management Systems , 16 (3), 316–329.
   Web of Science ®Google Scholar
• Gharaei, A. , & Pasandideh, S.H.R. (2017b). Modeling and optimization of four-level integrated supply chain with the aim of determining the optimum stockpile and period length: Sequential quadratic programming. Journal of Industrial and Production Engineering , 34 (7), 529–541.
   Web of Science ®Google Scholar
• Gharaei, A. , Pasandideh, S.H.R. , & Niaki, S.T.A. , Arshadi Khamseh, A. (2016). Modeling and optimization of four levels integrated supply chain under shortage condition: Sequential quadratic programming and interior point algorithms. In Proceedings of the 12th international industrial engineering conference . (pp. 4542–4561), Tehran, Iran.
   Google Scholar
• Gharaei, A. , Pasandideh, S.H.R. , & Akhavan Niaki, S.T. (2017). An optimal integrated lot sizing policy of inventory in a bi-objective multi-level supply chain with stochastic constraints and imperfect products. Journal of Industrial and Production Engineering , 35(1), 1–15.
   Web of Science ®Google Scholar
• Gharaei, A. , Pasandideh, S.H.R. , Akhavan Niaki, S.T.A. , & Arshadi Khamseh, A. (2016). Design the reliability model in four-level integrated supply chain with stochastic constraints. In Proceedings of the 2nd international conference on industrial and systems engineering (pp. 409–416).
   Google Scholar
• Gharaei, A. , Pasandideh, S.H.R. , & Arshadi Khamseh, A. (2017). Inventory model in a four-echelon integrated supply chain: Modeling and optimization. Journal of Modelling in Management , 12 (4), 739–762.
   Web of Science ®Google Scholar
• Gilbert, K.C. , & Chatpattananan, V. (2006). An ARIMA supply chain model with a generalized ordering policy. Journal of Modelling in Management , 1 (1), 33–51.
   Google Scholar
• Hasrulnizzam Wan Mahmood, W. , Mat Tahar, N. , Nizam Ab Rahman, M. , Baba , & Deros, M. (2011). Supply chain enhancement through product and vendor development programme. Journal of Modelling in Management , 6 (2), 164–177.
   Google Scholar
• Hoque, M.A. (2008). Synchronization in the single-manufacturer multi-buyer integrated inventory supply chain. European Journal of Operational Research , 188 (3), 811–825.
   Web of Science ®Google Scholar
• Hoque, M.A. (2011a). An optimal solution technique to the single-vendor multi-buyer integrated inventory supply chain by incorporating some realistic factors. European Journal of Operational Research , 215 (1), 80–88.
   Web of Science ®Google Scholar
• Hoque, M.A. (2011b). Generalized single-vendor multi-buyer integrated inventory supply chain models with a better synchronization. International Journal of Production Economics , 131 (2), 463–472.
   Web of Science ®Google Scholar
• Joshi, K. , Singh, K.N. , & Kumar, S. (2012). Two-sided supplier-manufacturer selection in BTO supply chain. Journal of Modelling in Management , 7 (3), 257–273.
   Google Scholar
• Kaminsky, P. , & Simchi-Levi, D. (2003). Production and distribution lot sizing in a two stage supply chain. IIE Transactions , 35 (11), 1065–1075.
   Web of Science ®Google Scholar
• Kauppi, K. , Longoni, A. , Caniato, F. , & Kuula, M. (2016). Managing country disruption risks and improving operational performance: Risk management along integrated supply chains. International Journal of Production Economics , 182 , 484–495.
   Web of Science ®Google Scholar
• Khan, M. , Jaber, M.Y. , & Ahmad, A.R. (2014). An integrated supply chain model with errors in quality inspection and learning in production. Omega , 42 (1), 16–24.
   Web of Science ®Google Scholar
• Kumar, P. , Shankar, R. , & Yadav, S.S. (2008). Flexibility in global supply chain: Modeling the enablers. Journal of Modelling in Management , 3 (3), 277–297.
   Google Scholar
• Kumar Sharma, S. , & Bhat, A. (2014). Modelling supply chain agility enablers using ISM. Journal of Modelling in Management , 9 (2), 200–214.
   Google Scholar
• Luu, T. (2017). Market responsiveness: Antecedents and the moderating role of external supply chain integration. Journal of Business & Industrial Marketing , 32 (1), 30–45.
   Web of Science ®Google Scholar
• Nasiri, G.R. , Zolfaghari, R. , & Davoudpour, H. (2014). An integrated supply chain production–distribution planning with stochastic demands. Computers & Industrial Engineering , 77 , 35–45.
   Web of Science ®Google Scholar
• Pan, Z. , Tang, J. , & Liu, O. (2009). Capacitated dynamic lot sizing problems in closed-loop supply chain. European Journal of Operational Research , 198 (3), 810–821.
   Web of Science ®Google Scholar
• Pasandideh, S.H.R. , Niaki, S.T.A. , & Gharaei, A. (2015). Optimization of a multiproduct economic production quantity problem with stochastic constraints using sequential quadratic programming. Knowledge-Based Systems , 84 , 98–107.
   Web of Science ®Google Scholar
• Pitty, S.S. , Li, W. , Adhitya, A. , Srinivasan, R. , & Karimi, I.A. (2008). Decision support for integrated refinery supply chains: Part 1. Dynamic simulation. Computers & Chemical Engineering , 32 (11), 2767–2786.
   Web of Science ®Google Scholar
• Prakash, S. , Prakash, S. , Soni, G. , Soni, G. , Rathore, A.P.S. , & Rathore, A.P.S. (2017). Embedding risk in closed-loop supply chain network design: Case of a hospital furniture manufacturer. Journal of Modelling in Management , 12 (3), 551–574.
   Web of Science ®Google Scholar
• Puigjaner, L. , & Laínez, J.M. (2008). Capturing dynamics in integrated supply chain management. Computers & Chemical Engineering , 32 (11), 2582–2605.
   Web of Science ®Google Scholar
• Rosenthal, E.C. (2008). A game-theoretic approach to transfer pricing in a vertically integrated supply chain. International Journal of Production Economics , 115 (2), 542–552.
   Web of Science ®Google Scholar
• Samaranayake, P. , & Laosirihongthong, T. (2016). Configuration of supply chain integration and delivery performance: Unitary structure model and fuzzy approach. Journal of Modelling in Management , 11 (1), 43–74.
   Web of Science ®Google Scholar
• Sarkar, B. , & Majumder, A. (2013). Integrated vendor–buyer supply chain model with vendor's setup cost reduction. Applied Mathematics and Computation , 224 , 362–371.
   Web of Science ®Google Scholar
• Singh, A. (2015). Multi-period demand allocation among supplier in a supply chain. Journal of Modelling in Management , 10 (2), 138–157.
   Web of Science ®Google Scholar
• Singh, R.K. , Koul, S. , & Kumar, P. (2017). Analyzing the interaction of factors for flexibility in supply chains. Journal of Modelling in Management , 12 (4), 671–689.
   Web of Science ®Google Scholar
• Sobhanallahi, M.A. , Gharaei, A. , & Pilbala, M. (2016a, January). Provide a new method to determine effectiveness or performance rate of organization strategies based on Freeman model and using improved dimensional analysis method. In Proceedings of the 12th international conference on industrial engineering (ICIE ) (pp. 125–133). IEEE.
   Google Scholar
• Sobhanallahi, M.A. , Gharaei, A. , & Pilbala, M. (2016b, January). Provide a practical approach for measuring the performance rate of organizational strategies. In Proceedings of the 12th international conference on industrial engineering (ICI E) (pp. 115–124). IEEE.
   Google Scholar
• Soni, G. , & Kodali, R. (2013). A decision framework for assessment of risk associated with global supply chain. Journal of Modelling in Management , 8 (1), 25–53.
   Google Scholar
• Susarla, N. , & Karimi, I.A. (2012). Integrated supply chain planning for multinational pharmaceutical enterprises. Computers & Chemical Engineering , 42 , 168–177.
   Web of Science ®Google Scholar
• Tiwari, M.K. , Raghavendra, N. , Agrawal, S. , & Goyal, S.K. (2010). A hybrid Taguchi–immune approach to optimize an integrated supply chain design problem with multiple shipping. European Journal of Operational Research , 203 (1), 95–106.
   Web of Science ®Google Scholar
• Van Dam, K.H. , Adhitya, A. , Srinivasan, R. , & Lukszo, Z. (2009). Critical evaluation of paradigms for modelling integrated supply chains. Computers & Chemical Engineering , 33 (10), 1711–1726.
   Web of Science ®Google Scholar
• White, A.S. , & Censlive, M. (2015). A state-space model of a three tier APVIOBPCS supply chain. Journal of Modelling in Management , 10 (1), 76–104.
   Web of Science ®Google Scholar
• Zhang, Y. , Hu, G. , & Brown, R.C. (2014). Integrated supply chain design for commodity chemicals production via woody biomass fast pyrolysis and upgrading. Bioresource Technology , 157 , 28–36.
   PubMed Web of Science ®Google Scholar
• Zhang, Z.H. , Jiang, H. , & Pan, X. (2012). A Lagrangian relaxation based approach for the capacitated lot sizing problem in closed-loop supply chain. International Journal of Production Economics , 140 (1), 249–255.
   Web of Science ®Google Scholar
• Zhang, Z.H. , Li, B.F. , Qian, X. , & Cai, L.N. (2014). An integrated supply chain network design problem for bidirectional flows. Expert Systems with Applications , 41 (9), 4298–4308.
   Web of Science ®Google Scholar
• Zhao, S.T. , Wu, K. , & Yuan, X.M. (2016a). Optimal integer-ratio inventory coordination policy for an integrated multi-stage supply chain. Applied Mathematical Modelling , 40 (5), 3876–3894.
   Web of Science ®Google Scholar
• Zhao, S.T. , Wu, K. , & Yuan, X.M. (2016b). Optimal production-inventory policy for an integrated multi-stage supply chain with time-varying demand. European Journal of Operational Research , 255 (2), 364–379.
   Web of Science ®Google Scholar