Solution of Interval-valued Manufacturing Inventory Models With Shortages

A manufacturing inventory model with shortages with carrying cost, shortage cost, setup cost and demand quantity as imprecise numbers, instead of real numbers, namely interval number is considered here. First, a brief survey of the existing works on comparing and ranking any two interval numbers on the real line is presented. A common algorithm for the optimum production quantity (Economic lot-size) per cycle of a single product (so as to minimize the total average cost) is developed which works well on interval number optimization under consideration. Finally, the designed algorithm is illustrated with numerical example.

Authors:

• Susovan Chakrabortty
• Madhumangal Pal
• Prasun Kumar Nayak

Keywords:

• EOQ
• Inventory
• Interval Number
• Demand
• Production
• Simulation

References:

[1] A. Sengupta and T. K. Pal, On comparing interval numbers, European
Journal of Operational Research, 127(1) (2000) 28-43.
[2] A. H. Lau and H. S. Lau, Effects of a demand-curve-s shape on the
optimal solutions of a multi-echelon inventory/pricing model, European
Journal of Operational Research, 147 (2003) 530 - 548.
[3] D. C. Lin and J.S. Yao, Fuzzy economic production for production
inventory,Fuzzy Sets and Systems, 111 (2000) 465-495.
[4] F. Haris, How many parts to make at once Factory, The Magazine of
Management, 1913, 10(2): 13-5-136, 152.
[5] G.C. Mahata and A. Goswami, Fuzzy EOQ models for deteriorating
items with stock dependent demand and non-linear holding costs,
International Journal of Applied Mathematics and Computer Sciences ,
5(2) (2009) 94 - 98.
[6] G.C. Mahata and A. Goswami, An EOQ models with fuzzy lead time
, fuzzy demand and fuzzy cost coefficients, International Journal of
Mathematical, Physical and Engineering Sciences , 3:1 2009.
[7] H.J.Zimmermann, Fuzzzy mathematical programming, Computer Operational
Research, 10(1983) 291-298.
[8] H. Ishibuchi and H. Tanaka, Multiobjective programming in optimization
of the interval objective function, European Journal of Operational
Research, 48 (1990) 219-225.
[9] J. Kacprzyk, P. Staniewski, Long term inventory policy making through
fuzzy decisionmaking models, Fuzzy Sets and Systems, 8 (1982) 117-
132.
[10] K. J. Chung, An algorithm for an inventory model with inventory-leveldependent
demand rate, Computational Operation Research, 30 (2003)
1311-1317.
[11] K. S. Park, Fuzzy set theoretic interpretation of economic order quantity,
IEEE Transactions on Systems, Man and Cybernetics, SMC, 17
(1987) 1082-1084.
[12] L.A.Zadeh, Fuzzy sets, Information and Control, 8 (1965) 338-352.
[13] M. Vujosevic, D. Petrovic and R. Petrovic, EOQ formula when inventory
cost is fuzzy, International Journal of Production Economics, 45(1996)
499-504.
[14] M. Gen, Y. Tsujimura and D. Zheng, An application of fuzzy set theory
to inventory contol models, Computers and Industrial Engineering, 33
(1997) 553-556.
[15] M. Sakawa, Interactive computer program for fuzzy linear programming
with multiple objectives, International Journal of Man-Machine Studies,
18 (1983) 489-503.
[16] N. Brahimi, S. Dauzere-Peres and A. Nordli, Single item lot sizing
problems, European Journal of Operational Research, 168(1) (2006)
1 - 16.
[17] P.K. Nayak and M. Pal, The Bi-matrix Games with Interval Payoffs
and its Nash Equilibrium Strategy, The Journal of Fuzzy Mathematics,
17(2)(2009) 421-435.
[18] R.E. Moore, Method and Application of Interval Analysis, SIAM,
Philadelphia, 1979.
[19] R.E. Steuer, Algorithm for linear programming problem with interval
objective function coefficients, Mathematics of Operation Research,
6(1981) 333-348.
[20] T. K.Roy and M. Maity, A fuzzy EOQ model with demand dependent
unit cost under limited stroage capacity, European Journal of Operational
Research, 99 (1997) 425 - 432.