Abstract
To transport the commodities in minimum time with maximum safety, the difficulties arise due to mutiny, territory slide, bad road and crashed communication systems, etc. and to overcome these kind of problems, the stochastic solid transportation models with safety and time objective functions under essential constraints are formulated. Taking expected value criterion, Chance-constrained programming technique, uniform distribution \( {\mathfrak{U}}\left( {a,b} \right) \), exponential distribution \( {\mathcal{E}\mathcal{X}\mathcal{P}}\left( \beta \right) \) and normal distribution \( {\mathcal{N}}\left( {\mu ,\sigma^{2} } \right) \), four new de-randomization processes are proposed to handle the stochastic programming problem. Finally, the deterministic form of the model is solved using generalized reduced gradient techniques (LINGO.13.0 optimization software). Finally, an enlarge comparison of the proposed concept with the earlier concept are presented and the nature of the solutions is discussed.
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References
Lee, H.L., Padmanabhan, V., Whang, S.: Information distortion in the supply chain: the bullwhip effect. Manage. Sci. 50, 1875–1886 (2004)
Svensson, G.: The bullwhip effect in intra-organisational echelons. Int. J. Phys. Distrib. Logist. Manag. 33(2), 103–131 (2003)
Bagchi, P.K., Ha, B.C., Skjoett-Larsen, T., Soerensen, L.B.: Supply chain integration: a European survey. Int. J. Logist. Manag. 16, 275–294 (2005)
Croxton, K.L., García-Dastugue, S.J., Lambert, D.M., Rogers, D.S.: The supply chain management processes. Int. J. Logist. Manag. 12, 13–36 (2001)
Min, S., Roath, A.S., Daugherty, P.J., Genchev, S.E., Chen, H., Arndt, A.D., Richey, R.G.: Supply chain collaboration: What’s happening? Int. J. Logist. Manag. 16, 237–256 (2005)
Beamon, B.M.: Humanitarian relief chains: Issues and challenges. In: Proceedings of the 34th International Conference on Computers and Industrial Engineering. San Francisco, CA, USA (2004)
Tomasini, R.M., van Wassenhove, L.N.: Pan-American health organization’s humanitarian supply management system: de-politicization of the humanitarian supply chain by creating accountability. J. Public Procure. 4, 437–449 (2004)
Lee, H.W., Zbinden, M.: Marrying logistics and technology for effective relief. Forced Migr. Rev. 18, 34–45 (2003)
Hitchcock, F.L.: The distribution of a product from several sources to numerous localities. J. Math. Phys. 20, 224–230 (1941)
Shell, E.: Distribution of a product by several properties. In: Proceedings of the Second Symposium in Linear Programming, Directorate of Management Analysis, DCS/Comptroller H.Q.U.S.A.F., vol. 2, pp. 615–642. Washington, DC. (1955)
Haley, K.B.: The solid transportation problem. Oper. Res. 10, 448–463 (1962)
Liu, B.: Theory and Practice of Uncertain Programing. Physica-Verlag, Heidelberg (2002)
Kundu, P., Kar, S., Maiti, M.: Fixed charge transportation problem with type-2 fuzzy variable. Inf. Sci. 255, 170–186 (2014)
Yang, L., Liu, L.: Fuzzy fixed charge solid transportation problem and algorithm. Appl. Soft Comput. 7, 879–889 (2007)
Kundu, P., Kar, S., Maiti, M.: Multi-objective multi-item solid transportation problem in fuzzy environment. Appl. Math. Modell. 37, 2028–2038 (2012)
Molla-Alizadeh-Zavardehi, S., Sadi Nazhad, S., Tavakkoli-Moghaddam, R., Yazdani, M.: Solving a fuzzy fixed charge solid transportation problem and by metaheuristics. Math. Comput. Modell. 57, 1543–1558 (2013)
Liu, P., Yang, L., Wang, L., Liu, S.: A solid transportation problem with type-2 fuzzy variables. Appl. Soft Comput. 24, 543–558 (2014)
Yang, L., Liu, P., Li, S., Gao, Y., Ralescu, D.A.: Reduction method of type-2 uncertain variables and their applications to solid transportation problems. Inf. Sci. 291, 204–237 (2015)
Giri, P.K., Maiti, M.K., Maiti, M.: Fully fuzzy fixed charge multi-item solid transportation problem. Appl. Soft Comput. 27, 77–91 (2015)
Kall, P.: Stochastic Linear Programming. Springer, Berlin (1976)
Liu, B.: Uncertain Programing. Wiley, New York (1999)
Baidya, A., Bera, U.K., Maiti, M.: Solution of multi-item interval valued solid transportation problem with safety measure using different methods. OPSEARCH 51, 1–22 (2014)
Gen, M., Altiparmak, F., Lin, L.: A genetic algorithm for two-stage transportation problem using priority-based encoding. OR Spectrum 28, 337–354 (2006)
Amiri, Ali: Designing a distribution network in a supply chain system: formulation and efficient solution procedure. Eur. J. Oper. Res. 171, 567–576 (2006)
Gani, N.A., Razak, A.K.: Two stage fuzzy transportation problem. J. Phys. Sci. 10, 63–69 (2006)
Sudhakar, V.J., Kumar, V.N.: Solving the multi-objective two stage fuzzy transportation problem by zero suffix method. J. Math. Res. 2(4), 135–140 (2010)
Yang, L., Feng, Y.: A bi-criteria solid transportation problem with fixed charge under stochastic environment. Appl. Math. Model. 31, 2668–2683 (2007)
Charnes, A., Copper, W.W.: Chance constrained programming. Manage. Sci. 6, 73–79 (1959)
Chunlin, D., Liu, Y.: Sample average approximation method for chance constrained stochastic programming in transportation model of emergency management. Syst. Eng. Procedia 5, 137–143 (2012)
Baidya, A., Bera, U.K., Maiti, M.: Interval oriented entropy based multi-item solid transportation problem with budget and breakability. Int. J. Appl. Comput. Math. 1, 279–292 (2015)
Song, R., Zhao, H.: Study on bus dispatching based on chance-constraint. Math. Practice Theory 35, 89–92 (2005)
Li, F., Jin, C., Wang, L.: Quasi-linear stochastic programming model based on expectation and variance and its application in transportation problem. Appl. Math. Model. 38, 1919–1928 (2014)
Ojha, A., Das, B., Mondal, S.K., Maiti, M.: A transportation problem with fuzzy-stochastic cost. Appl. Math. Model. 38, 1464–1481 (2014)
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Baidya, A. Stochastic supply chain, transportation models: implementations and benefits. OPSEARCH 56, 432–476 (2019). https://doi.org/10.1007/s12597-019-00370-7
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DOI: https://doi.org/10.1007/s12597-019-00370-7