zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
A multi-objective production inventory model with backorder for fuzzy random demand under flexibility and reliability. (English) Zbl 1235.90018
Summary: In this paper, an economic production quantity (EPQ) model is developed with flexibility and reliability consideration of production process in an imprecise and uncertain mixed environment. The model has incorporated fuzzy random demand, an imprecise production preparation time and shortage. Here, the setup cost and the reliability of the production process along with the backorder replenishment time and production run period are the decision variables. Due to fuzzy-randomness of the demand, expected average demand is a fuzzy quantity and also imprecise preparation time is represented by fuzzy number. Therefore, both are first transformed to a corresponding interval number and then using the interval arithmetic, the single objective function for expected profit over the time cycle is changed to respective multi-objective functions. Due to highly nonlinearity of the expected profit functions it is optimized using a multi-objective genetic algorithm (MOGA). The associated profit maximization problem is illustrated by numerical examples and also its sensitivity analysis is carried out.

90B05Inventory, storage, reservoirs
90C70Fuzzy programming
Full Text: DOI
[1] Bag, S., Chakraborty, D., Roy, A.R.: A production inventory model with fuzzy random demand and with flexibility and reliability considerations. Comput. Ind. Eng. 56, 411--416 (2009) · doi:10.1016/j.cie.2008.07.001
[2] Bector, R.C., Chandra, S.: Fuzzy Mathematical Programming and Fuzzy Matrix Games. Springer, New York (2005) · Zbl 1078.90071
[3] Bhandari, R.M., Sharma, P.K.: The economic production lot size model with variable cost function. Opsearch 36, 137--150 (1999)
[4] Cheng, T.C.E.: An economic production quantity model with flexibility and reliability considerations. Eur. J. Oper. Res. 39, 174--179 (1989a) · Zbl 0672.90039 · doi:10.1016/0377-2217(89)90190-2
[5] Cheng, T.C.E.: An economic order quantity model with demand-dependent unit cost. Eur. J. Oper. Res. 40, 252--256 (1989b) · Zbl 0665.90017 · doi:10.1016/0377-2217(89)90334-2
[6] Cheng, T.C.E.: An economic order quantity model with demand-dependent unit production cost and imperfect production processes. IIE Trans. 23, 23--28 (1991) · doi:10.1080/07408179108963838
[7] Chung, K., Hou, K.: An optimal production run time with imperfect production processes and allowable shortages. Comput. Oper. Res. 30, 483--490 (2003) · Zbl 1026.90029 · doi:10.1016/S0305-0548(01)00091-0
[8] Deb, K.: Multi-objective Optimization Using Evolutionary Algorithms. Wiley, Chichester (2001) · Zbl 0970.90091
[9] Deb, K., Goel, T.: Controlled elitist non-dominated sorting genetic algorithms for better convergence. In: Proceedings of the First International Conference on Evolutionary Multi-criterion Optimization, Zurich, pp. 67--81 (2001)
[10] Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6, 182--197 (2002) · doi:10.1109/4235.996017
[11] Dubois, D., Prade, H.: Operations of fuzzy numbers. Int. J. Syst. Sci. 9, 613--626 (1978) · Zbl 0383.94045 · doi:10.1080/00207727808941724
[12] Grzegorzewski, P.: Nearest interval approximation of a fuzzy number. Fuzzy Sets Syst. 130, 321--330 (2002) · Zbl 1011.03504 · doi:10.1016/S0165-0114(02)00098-2
[13] Hansen, E., Walster, G.: Global Optimization Using Interval Analysis. Marcel Dekker Inc., New York (2004) · Zbl 1103.90092
[14] Hax, A.C., Canada, D.: Production and Inventory Management. Prentice-Hall, New Jersey (1984)
[15] Holland, H.J.: Adaptation in Natural and Artifcial Systems. University of Michigan (1975)
[16] Islam, S., Roy, T.K.: A fuzzy EPQ model with flexibility and reliability consideration and demand dependent unit production cost under a space constraint: a fuzzy geometric programming approach. Appl. Math. Comput. 176, 531--544 (2006) · Zbl 1126.90429 · doi:10.1016/j.amc.2005.10.001
[17] Karmakar, S., Mahato, S.K., Bhunia, A.K.: Interval oriented multi-section techniques for global optimization. J. Comput. Appl. Math. 224, 476--491 (2009) · Zbl 1158.65041 · doi:10.1016/j.cam.2008.05.025
[18] Knowles, J., Corne, D.: Approximating the non-dominated front using the Pareto archived evolution strategy. Evol. Comput. 8, 149--172 (2000) · doi:10.1162/106365600568167
[19] Khouja, M.: The economic production lot size model under volume flexibility. J. Comput. Oper. Res. 22, 515--523 (1995) · Zbl 0830.90067 · doi:10.1016/0305-0548(94)00032-4
[20] Kwakernaak, H.: Fuzzy random variables: definition and theorems. Inform. Sci. 15, 1--29 (1978) · Zbl 0438.60004 · doi:10.1016/0020-0255(78)90019-1
[21] Leung, K.F.: A generalized geometric programming solution to an economic production quantity model with flexibility and reliability considerations. Eur. J. Oper. Res. 176, 240--251 (2007) · Zbl 1137.90453 · doi:10.1016/j.ejor.2005.06.049
[22] Maiti, M.K., Maiti, M.: Production policy of damageable items with variable cost function in an imperfect production process via genetic algorithm. Math. Comput. Model. 42, 977--990 (2005) · Zbl 1121.90330 · doi:10.1016/j.mcm.2005.04.006
[23] Mahapatra, N.K., Maiti, M.: Inventory model for breakable items with uncertain setup time. Tamsui Oxf. J. Manag. Sci. 20, 83--102 (2004) · Zbl 1063.90005
[24] Pal, P., Bhunia, A.K., Goyal, S.K.: On optimal partially integrated production and marketing policy with variable demand under flexibility and reliability considerations via Genetic Algorithm. Appl. Math. Comput. 188, 525--537 (2007) · Zbl 1137.90469 · doi:10.1016/j.amc.2006.10.012
[25] Panda, D., Maiti, M.: Multi-item inventory models with price dependent demand under flexibility and reliability consideration and imprecise space constraint: a geometric programming approach. Math. Comput. Model. 49, 1733--1749 (2009) · Zbl 1171.90316 · doi:10.1016/j.mcm.2008.10.019
[26] Porteus, E.L.: Investing in reduced set-ups in the EOQ model. Manag. Sci. 31, 998--1010 (1985) · Zbl 0609.90058 · doi:10.1287/mnsc.31.8.998
[27] Porteus, E.L.: Optimal lot sizing, process quality improvement and set-up cost reduction. Oper. Res. 34, 137--144 (1986) · Zbl 0591.90043 · doi:10.1287/opre.34.1.137
[28] Rosenblatt, M.J., Lee, H.L.: Economic production cycle with imperfect production processes. IIE Trans. 18, 47--55 (1986)
[29] Roy, M.D., Sana, S.S., Chaudhuri, K.: An economic order quantity model of imperfect quality items with partial backlogging. Int. J. Syst. Sci. 42, 1409--1419 (2011a) · Zbl 1233.90040 · doi:10.1080/00207720903576498
[30] Roy, M.D., Sana, S.S., Chaudhuri, K.: An optimal shipment strategy for imperfect items in a stock-out situation. Math. Comput. Model. 54, 2528--2543 (2011b) · Zbl 1235.90015 · doi:10.1016/j.mcm.2011.06.015
[31] Sana, S.S.: A production-inventory model in an imperfect production process. Eur. J. Oper. Res. 200, 451--464 (2010a) · Zbl 1177.90027 · doi:10.1016/j.ejor.2009.01.041
[32] Sana, S.S.: An economic production lot size model in an imperfect production system. Eur. J. Oper. Res. 201, 158--170 (2010b) · Zbl 1177.90133 · doi:10.1016/j.ejor.2009.02.027
[33] Sana, S.S.: A production-inventory model of imperfect quality products in a three-layer supply chain. Decis. Support Syst. 50, 539--547 (2011) · doi:10.1016/j.dss.2010.11.012
[34] Sana, S.S., Chaudhuri, K.: On a volume flexible production policy for a deteriorating item with time-dependent demand and shortages. Adv. Model. Optim. 6, 57--74 (2004a) · Zbl 1278.90136
[35] Sana, S.S., Chaudhuri, K.: On a volume flexible production policy for a deteriorating item with stock-dependent demand rate. Nonlinear Phenom. Complex Syst. 7, 61--68 (2004b) · Zbl 1278.90136
[36] Sana, S. S., Chaudhuri, K.: An EMQ model in an imperfect production process. Int. J. Syst. Sci. 41, 635--646 (2010) · Zbl 1200.90015 · doi:10.1080/00207720903144495
[37] Sana, S.S., Goyal, S.K., Chaudhuri, K.: An imperfect production process in a volume flexible inventory model. Int. J. Prod. Econ. 105, 548--559 (2007a) · Zbl 1278.90035 · doi:10.1016/j.ijpe.2006.05.005
[38] Sana, S.S., Goyal, S.K., Chaudhuri, K.: On a volume flexible inventory model for items with an imperfect production system. Int. J. Oper. Res. 2, 64--80 (2007b) · Zbl 1278.90035 · doi:10.1504/IJOR.2007.011444
[39] Sarkar, B., Sana, S.S., Chaudhuri, K.: An imperfect production process for time varying demand with inflation and time value of money - An EMQ model. Expert Syst. Appl. 38, 13543--13548 (2011)
[40] Silver, E.A.: Establishing the order quantity when the amount received is uncertain. INFOR 14, 32--39 (1976)
[41] Tersine, K.D.: Principles of Inventory and Materials Management. North-Holland, New York (1982)
[42] Van Beek, P., Putten, C.: OR contributions to flexibility improvement in production/inventory systems. Eur. J. Oper. Res. 31, 52--60 (1987) · Zbl 0614.90045 · doi:10.1016/0377-2217(87)90136-6
[43] Wright, C.M., Mehrez, A.: An overview of representative research of the relationships between quality and inventory. Omega 26, 29--47 (1998) · doi:10.1016/S0305-0483(97)00042-X
[44] Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338--353 (1965) · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
[45] Zitzler, E., Thiele, L.: An evolutionary algorithm for multi-objective optimization: the strength Pareto approach, Technical report no. 43. Zurich, Computer engineering and networks laboratory Switzerland (1998)