Abstract
This paper develops a risk management tool for a productioninventory system that involves an imperfect production process and faces production disruption and demand uncertainty. In this paper, the demand uncertainty is represented as fuzzy variable and the imperfectness is expressed as process reliability. To deal with the production scheduling in this environment, a non-linear constrained optimization model has been formulated with an objective of maximizing the graded mean integration value (GMIV) of the total expected profit. The model is applied to solve the production-inventory problem with single as well as multiple disruptions on a real time basis that basically revises the production quantity in each cycle in the recovery time window. We propose a genetic algorithm (GA) based heuristic to solve the model and obtain an optimal recovery plan. A numerical example is presented to explain usefulness of the developed model.
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Graves, S.C.: A single-item inventory model for a nonstationary demand process. Manufacturing & Service Operations Management 1(1), 50–61 (1999)
Dave, U.: A deterministic lot‐size inventory model with shortages and a linear trend in demand. Naval Research Logistics 36(4), 507–514 (2006)
Chan, G.H., Song, Y.: A dynamic analysis of the single-item periodic stochastic inventory system with order capacity. European Journal of Operational Research 146(3), 529–542 (2003)
Kiesmüller, G.P., De Kok, A.G., Dabia, S.: Single item inventory control under periodic review and a minimum order quantity. International Journal of Production Economics 133(1), 280–285 (2011)
Lin, G.C., Gong, D.C.: On a production-inventory system of deteriorating items subject to random machine breakdowns with a fixed repair time. Mathematical and Computer Modelling 43(7), 920–932 (2006)
Widyadana, G.A., Wee, H.M.: Optimal deteriorating items production inventory models with random machine breakdown and stochastic repair time. Applied Mathematical Modelling 35(7), 3495–3508 (2011)
Hishamuddin, H., Sarker, R.A., Essam, D.: A disruption recovery model for a single stage production-inventory system. European Journal of Operational Research 222(3), 464–473 (2012)
Hishamuddin, H., Sarker, R.A., Essam, D.: A Recovery Model for a Two–Echelon Serial Supply Chain with Consideration of Transportation Disruption. Computers & Industrial Engineering 64(2), 552–561 (2013)
Parlar, M., Perry, D.: Inventory models of future supply uncertainty with single and multiple suppliers. Naval Research Logistics 43(2), 191–210 (1998)
Özekici, S., Parlar, M.: Inventory models with unreliable suppliers in a random environment. Annals of Operations Research 91, 123–136 (1999)
Mohebbi, E., Hao, D.: An inventory model with non-resuming randomly interruptible lead time. International Journal of Production Economics 114(2), 755–768 (2008)
Qi, L., Shen, Z.J.M., Snyder, L.V.: A continuous‐review inventory model with disruptions at both supplier and retailer. Production and Operations Management 18(5), 516–532 (2009)
Cheng, T.C.E.: An economic production quantity model with flexibility and reliability considerations. European Journal of Operational Research 39(2), 174–179 (1989)
Bag, S., Chakraborty, D., Roy, A.R.: A production inventory model with fuzzy random demand and with flexibility and reliability considerations. Computers & Industrial Engineering 56(1), 411–416 (2009)
Sana, S.S.: A production–inventory model in an imperfect production process. European Journal of Operational Research 200(2), 451–464 (2010)
Sarkar, B.: An inventory model with reliability in an imperfect production process. Applied Mathematics and Computation 218(9), 4881–4891 (2012)
Lee, H.M., Yao, J.S.: Economic production quantity for fuzzy demand quantity, and fuzzy production quantity. European Journal of Operational Research 109(1), 203–211 (1998)
Chang, S.C.: Fuzzy production inventory for fuzzy product quantity with triangular fuzzy number. Fuzzy Sets and Systems 107(1), 37–57 (1999)
Yao, J.S., Chang, S.C., Su, J.S.: Fuzzy inventory without backorder for fuzzy order quantity and fuzzy total demand quantity. Computers & Operations Research 27(10), 935–962 (2000)
Dutta, P., Chakraborty, D., Roy, A.R.: A single-period inventory model with fuzzy random variable demand. Mathematical and Computer Modelling 41(8), 915–922 (2005)
Islam, S., Roy, T.K.: Fuzzy multi-item economic production quantity model under space constraint: A geometric programming approach. Applied Mathematics and Computation 184(2), 326–335 (2007)
Sarker, R.A., Khan, L.R.: An optimal batch size for a production system operating under periodic delivery policy. Computers & Industrial Engineering 37(4), 711–730 (1999)
Paul, S.K., Azeem, A., Sarker, R., Essam, D.: Development of a production inventory model with uncertainty and reliability considerations. Optimization & Engineering, Accepted manuscript (2013), doi:10.1007/s11081-013-9218-6
Chen, S.H., Hsieh, C.H.: Graded mean integration representation of generalized fuzzy number. Journal of Chinese Fuzzy Systems 5(2), 1–7 (1999)
Homaifar, A., Qi, C.X., Lai, S.H.: Constrained optimization via genetic algorithms. Simulation 62(4), 242–253 (1994)
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Paul, S.K., Sarker, R., Essam, D. (2013). A Disruption Recovery Model in a Production-Inventory System with Demand Uncertainty and Process Reliability. In: Saeed, K., Chaki, R., Cortesi, A., Wierzchoń, S. (eds) Computer Information Systems and Industrial Management. CISIM 2013. Lecture Notes in Computer Science, vol 8104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40925-7_47
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