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An EPQ model with inflation in an imperfect production system. (English) Zbl 1208.90012
Summary: A production inventory model is considered for stochastic demand with the effect of inflation. Generally, every manufacturing system wants to produce perfect quality items. However, due to real-life problems (labor problems, machine breakdown, etc.), a certain percentage of products are of imperfect quality. The imperfect items are reworked at a cost. The lifetime of a defective item follows a Weibull distribution. Due to the production of imperfect quality items, a product shortage occurs. The profit function is derived by using both a general distribution of demand and the uniform rectangular distribution of demand. Computational experiments along with graphical illustrations are presented to discuss the optimality of the probability functions.
Reviewer: Reviewer (Berlin)

90B05 Inventory, storage, reservoirs
90B30 Production models
90B25 Reliability, availability, maintenance, inspection in operations research
Full Text: DOI
[1] Harris, F.W., How many parts to make at once, factory, The mag. manage., 10, 135-136, (1913), 152
[2] P.A. Moran, The theory of storage, Metuen, London, 1959. · Zbl 0086.13602
[3] Wagner, H.M., Statistical management of inventory systems, (1962), J. Wiley USA · Zbl 0101.36901
[4] Miller, Jr. R.G., Continuous time stochastic storage processes with random linear inputs and outputs, J. math. mech., 12, 275-291, (1963) · Zbl 0126.16102
[5] Faddy, M.J., Optimal control for finite dams, Adv. appl. probab., 6, 689-710, (1974) · Zbl 0297.60043
[6] Harrison, J.M.; Resnic, S.I., The stationary distribution and first exit probabilities of a storage process with general release rules, Math. oper. res., 1, 347-358, (1976) · Zbl 0381.60092
[7] Nahmias, S., Inventory models in encyclopedia of computer science and technology, (), 447-483, vol. 9
[8] Meyer, R.R.; Rothkopf, M.H.; Smith, S.A., Reliability and inventory in a production-storage system, Manage. sci., 25, 799-807, (1979) · Zbl 0435.90055
[9] Scarf, H.E., The optimality of (s,S) policies in the dynamic inventory problem, () · Zbl 0183.24003
[10] Iglehart, D.L., Optimality of (s,S) inventory policies in the infinite horizon dynamic inventory problem, Manage. sci., 9, 259-267, (1963)
[11] Veinott, A.; Wagner, H., Computing optimal (s,S), inventory policies, Manage. sci., 11, 525-552, (1965) · Zbl 0137.14102
[12] Archibald, B.; Silver, E., (s,S) policies under continuous review and discrete compound Poisson demand, Manage. sci., 24, 899-908, (1978) · Zbl 0385.90044
[13] Silver, E.A., Operations research in inventory management: a review and critique, Oper. res., 29, 628-645, (1980)
[14] Federgruen, A.; Zipkin, P., An efficient algorithm for computing optimal (s,S) policies, Oper. res., 32, 1268-1285, (1984) · Zbl 0553.90031
[15] Zheng, Y.S.; Federgruen, A., Finding optimal (s,S) policies is about as simple as evaluating a single policy, Oper. res., 39, 654-665, (1991) · Zbl 0749.90024
[16] Ke, H.; Ma, W.; Ni, Y., Optimization models and a GA-based algorithm for stochastic time-cost trade-off problem, Appl. math. comput., 215, 08-313, (2009) · Zbl 1187.90158
[17] Zhou, Y.W., A production-inventory model for a finite time horizon with linear trend in demand and shortages, Syst. eng.-theor. prac., 5, 43-49, (1995)
[18] Khouja, M.; Mehrej, A., Economic production lot size model with variable production rate and imperfect quality, J. comput. oper. res., 45, 1405-1417, (1995) · Zbl 0814.90020
[19] Zhou, Y.W., Optimal production policy for an item with shortages and increasing time-varying demand, J. oper. res. soc., 47, 1175-1183, (1996) · Zbl 0869.90032
[20] Chen, J.; Li, K-H.; Lam, Y., Bayesian single and double variable sampling plan for the Weibull distribution with censoring, Eur. J. oper. res., 177, 1062-1073, (2007) · Zbl 1111.91021
[21] Dutta, P.; Chakraborty, D.; Roy, A.R., Continuous review inventory model in mixed fuzzy and stochastic environment, Appl. math. comput., 188, 970-980, (2007) · Zbl 1137.90756
[22] Chiu, S.W.; Wang, S.L.; Chiu, Y.S.P., Determining the optimal run time for EPQ model with scrap, rework, and stochastic breakdowns, Eur. J. oper. res., 180, 664-676, (2007) · Zbl 1123.90002
[23] Chiu, Y.S.P.; Ting, C.K., A note on determining the optimal run time for EPQ model with scrap, rework, and stochastic breakdowns, Eur. J. oper. res., 201, 641-643, (2010) · Zbl 1175.90016
[24] Sohn, S.Y.; Chang, I.S.; Moon, T.H., Random effects Weibull regression model for occupational lifetime, Eur. J. oper. res., 179, 124-131, (2007) · Zbl 1163.91457
[25] Wienke, A.; Kuss, O., Random effects Weibull regression model for occupational lifetime, Eur. J. oper. res., 196, 1249-1250, (2009) · Zbl 1176.90389
[26] Arizono, I.; Kawamura, Y.; Takemoto, Y., Reliability test for Weibull distribution with variational shape parameter based on sudden death lifetime data, Eur. J. oper. res., 189, 570-574, (2008) · Zbl 1149.90325
[27] Seliaman, M.E.; Ahmad, A.R., Optimizing inventory decisions in a multi-stage supply chain under stochastic demands, Appl. math. comput., 206, 538-542, (2008) · Zbl 1177.90028
[28] Skouri, K.; Konstantaras, I.; Papachristos, S.; Ganas, I., Inventory model with ramp type demand rate, partial backlogging and Weibull deterioration rate, Eur. J. oper. res., 192, 79-92, (2009) · Zbl 1171.90326
[29] Xu, N., Optimal policy for a dynamic, non-stationary stochastic inventory problem with capacity commitment, Eur. J. oper. res., 199, 400-408, (2009) · Zbl 1176.90040
[30] Perea, F.; Puerto, J.; Fernandez, F.R., Modeling cooperation on a class of distribution problems, Eur. J. oper. res., 198, 726-733, (2009) · Zbl 1176.90075
[31] Liao, G.L.; Chen, Y.H.; Sheu, S.H., Optimal economic production policy for imperfect process with imperfect repair and maintenance, Eur. J. oper. res., 195, 348-357, (2009) · Zbl 1161.90005
[32] Sana, S., Optimal selling price and lotsize with time varying deterioration 3 and partial backlogging, Appl. math. comput., 217, 185-194, (2010) · Zbl 1231.90055
[33] Salameh, M.K.; Jaber, M.Y., Economic production quantity model for items with imperfect quality, Int. J. prod. econ., 26, 59-64, (2000)
[34] Cardenas-Barron, L.E., Observation on: economic production quantity model for items with imperfect quality [ int. J. prod. econ. 64 (2000) 59-64], Int. J. prod. econ., 67, 201, (2000)
[35] Goyal, S.K.; Cardenas-Barron, L.E., Note on economic production quantity model for items with imperfect quality a practical approach, Int. J. prod. econ., 77, 85-87, (2002)
[36] Goyal, S.K.; Huang, C.K.; Chang, K.C., A simple integrated production policy of an imperfect item for vendor and buyer, Prod. plan. cont., 14, 596-602, (2003)
[37] Sana, S.; Goyal, S.K.; Chaudhuri, K.S., A production-inventory model for a deteriorating item with trended demand and shortages, Eur. J. oper. res., 157, 357-371, (2004) · Zbl 1103.90335
[38] Mandal, N.K.; Roy, T.K., Multi-item imperfect production lot size model with hybrid number cost parameters, Appl. math. comput., 182, 1219-1230, (2006) · Zbl 1114.90001
[39] Buzacott, J.A., Economic order quantities with inflation, Oper. res. qua., 26, 553-558, (1975)
[40] Bierman, H.; Thomas, J., Inventory decisions under inflation condition, Decision sci., 8, 151-155, (1977)
[41] Misra, R.B., A note on optical inventory management under inflation, Nav. res. log. qua., 26, 161-165, (1979) · Zbl 0396.90031
[42] Yang, H.L.; Teng, J.T.; Chern, M.S., Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand, Nav. res. log., 48, 144-158, (2001) · Zbl 0981.90003
[43] Sarker, B.R.; Jamal, A.M.M.; Wang, S., Supply chain model for permissible products under inflation and permissible delay in payment, Comput. oper. res., 27, 59-75, (2000) · Zbl 0935.90013
[44] Moon, I.; Lee, S., The effects of inflation and time-value of money on an economic order quantity models with random product life cycle, Eur. J. oper. res., 125, 140-153, (2000)
[45] Yang, H.L., Two warehouse inventory models for deteriorating items with shortages under inflation, Eur. J.oper. res., 157, 344-356, (2004) · Zbl 1103.90312
[46] Moon, I.; Giri, B.C.; Ko, B., Economic order quantity models for accelerating/deteriorating items under inflation and time discounting, Eur. J. oper. res., 162, 773-785, (2005) · Zbl 1067.90004
[47] Jolai, F.; Moghaddam, R.T.; Rabbani, M.; Sadoughian, M.R., An economic production lot size model with deteriorating items, stock-dependent demand, inflation, and partial backlogging, Appl. math. comput., 181, 380-389, (2006) · Zbl 1142.90385
[48] Dey, J.K.; Mondal, S.K.; Maity, M., Two storage inventory problem with dynamic demand and interval valued lead time over finite time horizon under inflation and time value of money, Eur. J. oper. res., 185, 170-194, (2008) · Zbl 1142.90005
[49] Chern, M-S.; Yang, H-L.; Teng, J-T.; Papachristos, S., Partial backlogging inventory lot size models for deteriorating items with fluctuating demand under inflation, Eur. J. oper. res., 191, 127-141, (2008) · Zbl 1144.90004
[50] Sarkar, B.; Sana, S.S.; Chaudhuri, K.S., A finite replenishment model with increasing demand under inflation, Int. J. math. oper. res., 2, 347-385, (2010) · Zbl 1188.90016
[51] Sarkar, B.; Sana, S.S.; Chaudhuri, K.S., A stock dependent inventory model in an imperfect production process, Int. J. proc. manage., 3, 361-378, (2010)
[52] B. Sarkar, S.S. Sana, K.S. Chaudhuri, An economic production quantity model with stochastic demand in an imperfect production system, Int. J. Serv. Oper. Manage (2011), in press.
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