Constrained Stochastic Inventory Control Models for Multi-Item with Variable Demand
Asian Journal of Probability and Statistics,
Page 1-15
DOI:
10.9734/ajpas/2022/v20i2415
Abstract
Constrained multi-item inventory system with variable demands are considered. The demand rates of five selected multi-item - Cowbell, Milo, SMA, Cerelac and Golden Morn were modeled as Weibull, Normal and Lognormal probability distributions respectively with the aid of chi-squared multinomial goodness-of-fit test. The respective probability distributions with estimated location parameters: 491.55, 536.92, 10.5, 2.1926 and 5.3103 were used as the basis of probabilistic inventory models to obtain dynamic EOQ for each item under each constraint subject to Kuhn, Karush and Tucker (KKT) conditions as against the use of simple averages in deterministic inventory models. The optimal values of these constraints: available warehouse space (124sq.ft), specified level of inventory (94 units), limited capital (76,671.52 naira) and number of orders (1/month) were obtained using the optimal EOQ values to establish optimal inventory level and constraints level/capacity for each item in order to avoid shortage or excess stock.
Keywords:
- Constrained inventory model
- multi-item
- variable demand
- optimal inventory
- probability distribution
How to Cite
References
Roy TK, Maiti M. Multi-objective inventory models of deteriorating items with some constraints in a fuzzy environment. Computers and Operations Research. 1998;25(12):1085 - 1095.
Williams M. Making consignment and vendor-managed inventory work for you. Hospital Material Management Quarterly. 2001;21(4):59-63.
Ould-Louly MA. A dynamic single-stage multi-item inventory control model. Large Scale Systems: Theory and Applications. 2001;34(8):73-78.
Hsieh CH. Optimization of Fuzzy production inventory models. Information Sciences. 2011;146(1-4):29-40.
Haung TK. The optimal retailer’s ordering policies for deteriorating items with limited storage capacity under trade credit financing. International Journal of Production Economics. 2014;106:127-145.
Hadley G, Whitin TM. Analysis of Inventory Systems. Englewood Cliffs, NJ: Prentice Hall Inc; 1963.
Fabrycky WJ, Banks J. Procurement and inventory systems: Theory and analysis. New York:Reinhold Publishing Corporation; 1967.
Maiti M. Deterministic inventory model with two-levels of storage: a linear trend in demand and a fixed time horizon. Computers and Operations Research. 2001;28:1315-1331.
Rosenblatt BS. Modern business: A systems approach. 2nd Ed. Boston: Houghton Mifflin Co; 1977.
Datta TK, Pal AK. Order level inventory system with power demand pattern for items with variable rate of deterioration. Indian Journal of Pure and Applied Mathematics. 1988;19:1043–1053.
Goh M. Some results for inventory models having inventory level dependent demand rate. International Journal of Production Economics. 1992;27(1):155–160.
Lenard JD, Roy B. Multi-item inventory control: A multi-criteria view. European Journal of Operation Research. 1995;87:685-692.
Abou-El-Ata. Probabilistic multi-item inventory model with varying order cost under two restrictions: A geometric programming approach. International Journal of Production Economics. 2003;83:223-231.
Beb-Daya M, Darvish MA, Rahim A. Two-stage imperfect production system with inspection errors. International Journal of Operations and Quantitative Management. 2005;9(2):117–131.
Purohit GN, Rathore H. Multi-item inventory control model with space constraints for perishable items. The IUP Journal of Operations Management. 2012;11(1):35-41.
Vasanthi P, Seshaiah CV. multi item inventory model with shortages under limited storage space and set up cost constraints via Karush Kuhn Tucker conditions approach. Applied Mathematical Sciences. 2013;7(102):5085-5094.
Sana SS. Optimal selling price and lot size with time varying deterioration and partial backlogging. Applied Mathematics and Computation. 2013;217:185-194.
Mousavi SM, Niaki ST, Bahreininejad A, Musa SN. Multi-item multi-periodic inventory control problem with variable demand and discounts: A particle swarm optimization algorithm. Scientific World Journal. 2014;2014:1-16.
Fergany HA. Probabilistic multi-item inventory model with varying mixture shortage cost under restrictions. Springerplus. 2016;5(1):1351.
Udoh NS. Probabilistic inventory control models with variable demand over a planning horizon for consumable products. World Journal of Applied Science and Technology. 2018;10(1B):37-243.
Sarwar F, Rahman M, Ahmed M. A multi-item inventory control model using multi objective particle swarm optimization (MOPSO). Proceedings of the International Conference on Industrial Engineering and Operations Management. Bangkok, Thailand; 2019.
Hale TS. Closed form models for dwell point locations in a multi-aisle automated storage and retrieval system. International Journal of Industrial and Systems Engineering. 2016;19(3):364 -388.
Sharma JK. Operations research: Theory and applications. India: Macmillan Publishers Ltd.; 2013.
Gafour KM, Rashid R. Development of multi-item EOQ when the constraints of investment and storage capacity are active. AIP Conference Proceedings. 2016;1691.
Available:htpp://dx.doi.org/10.1063/1.4937024
-
Abstract View: 167 times
PDF Download: 54 times
