Stochastic inventory control models for single item replenishment with variable demand under constrained and unconstrained conditions

  • Authors

    • Nse Udoh Department of Statistics, University of Uyo
    • Wisdom Ekpenyong Department of Statistics, University of Uyo
    2024-10-10
    https://doi.org/10.14419/q8ytpx54
  • Unconstrained Models; Constrained Models; Variable Demand; Probability Distribution; Single Replenishment; Tax-Cost.

  • Abstract

    This work examined stochastic inventory control models for single-items with and without constraints in a building material company, with equal importance to similar distribution companies with large inventories. The study is an improvement on inventory control for single-items with probabilistic demand. The chi-square goodness-of-fit test was used to identify the best-fit probability distribution of the number of demands of each considered items. The different costs considered in this work were purchase cost with added tax-cost, ordering cost, holding cost and shortage cost while the items covered were: 2 inches zinc nail (in cartons) which number of demand follows a W

    This work examined stochastic inventory control models for single-items with and without constraints in a building material company, with equal importance to similar distribution companies with large inventories. The study is an improvement on inventory control for single-items with probabilistic demand. The chi-square goodness-of-fit test was used to identify the best-fit probability distribution of the number of demands of each considered items. The different costs considered in this work were purchase cost with added tax-cost, ordering cost, holding cost and shortage cost while the items covered were: 2 inches zinc nail (in cartons) which number of demand follows a Weibull distribution with estimated parameters,  and ; 10mm rod (in lengths) which number of demand equally follows a Weibull distribution with estimated parameters,  and  5 inches nail (in cartons) which number of demand follows a normal distribution with estimated parameters,  and  and urban zinc (in bundles) which number of demand follows a Rayleigh distribution with estimated parameter, . These estimated parameters were used for computing the mean of each item as the basis for obtaining the Economic Order Quantity for the respective items. A modified Hadley Whitin algorithm and the trimming methods were respectively used to obtain the optimum order quantity and reorder point of items for the replenishment models without constraint and with constraints. Results obtained from models with constraint yields lower total variable cost and were therefore recommended for single-item replenishment.

    eibull distribution with estimated parameters,  and ; 10mm rod (in lengths) which number of demand equally follows a Weibull distribution with estimated parameters,  and  5 inches nail (in cartons) which number of demand follows a normal distribution with estimated parameters,  and  and urban zinc (in bundles) which number of demand follows a Rayleigh distribution with estimated parameter, . These estimated parameters were used for computing the mean of each item as the basis for obtaining the Economic Order Quantity for the respective items. A modified Hadley Whitin algorithm and the trimming methods were respectively used to obtain the optimum order quantity and reorder point of items for the replenishment models without constraint and with constraints. Results obtained from models with constraint yields lower total variable cost and were therefore recommended for single-item replenishment.

  • References

    1. Abou-El-Ata. (2014). Muti-item EOQ Inventory Model with Varying Holding Cost Under two restrictions: A Geometric programming Approach, Production planning & control, 6: 608-61. https://doi.org/10.1080/095372897234948.
    2. Adoga, P. I., Muazu, H. G. and Barma, M. (2022). Design of a demand forecast module of a decision support system for course material production and inventory management in the National Open University. Dutse Journal of Pure and Applied Sciences (DUJOPAS), 8(4b). https://doi.org/10.4314/dujopas.v8i4b.5.
    3. Ben Daya, M., S.M. Noman and M. Hariga, (2006). Integrated inventory control and inspection policies with deterministic demand. Comput. Oper. Res., 33: 1625-1638. https://doi.org/10.1016/j.cor.2004.11.010.
    4. Cheng, T. C. E., (1989). An economic order quantity model with demand-dependent unit cost. Eur. J. Oper. Res., 40: 252-256. https://doi.org/10.1016/0377-2217(89)90334-2.
    5. Das, K., T.K. Roy and M. Maiti, (2000). Multi-item inventory model with quantity-dependent inventory costs and demand-dependent unit cost under imprecise objective and restrictions: A geometric programming approach. Product. Planning. Control, 11: 781-788. https://doi.org/10.1080/095372800750038382.
    6. El-Sodany, N. H. (2011). Periodic review probabilistic multi-item inventory system with zero lead time under constraint and varying holding cos. J. Math. Stat., 7:12-19. https://doi.org/10.3844/jmssp.2011.12.19.
    7. Fabrycky, W. J. and Banks, J. (1967). Procurement and Inventory Systems: Theory and Analysis, Reinhold Publishing Corporation, New York, USA, 22: 112 -158.
    8. Hadley, G. and Whitin, T. (1963). Analysis of Inventory Systems, Prentice Hall, Inc. Englewood Cliffs, NJ:79-81
    9. Hale, T. S. (2016) ‘Closed form models for dwell point locations in a multi-aisle automated Storage and retrieval system’, International Journal and System Engineering, 19(3):364-388. https://doi.org/10.1504/IJISE.2015.068202.
    10. Harris, F. W. (1915). What quantity to make at once. In: The Library of Factory Management. Operation and Costs, The Factory Man-agement Series, Chicago: 47–52.
    11. Jung, H. and C.M. Klein (2001). Optimal inventory policies under decreasing cost functions via geometric programming. Eur. J. Oper. Res., 132: 628-642. https://doi.org/10.1016/S0377-2217(00)00168-5
    12. Kotb, K. .A. M and Fergany, H. A. (2011). Multi-item EOQ model with varying holding cost: A geometric programming approach. Int. Math Forum, 6: 1135-1144.
    13. Lesmona, D and Limansyah, T. (2017). A multi-item probabilistic inventory model. Phys confsers893012024. Journal Teknik Industri. 19(1):29-38.
    14. Maihami, R., Karimi, B. and Ghomi, S.M.T.F. (2017) ‘Effect of two-echelon trade credit on Pricing-inventory policy for non-instantaneous deteriorating products with probabilistic demand and deterioration functions, Annals of Operations Research, 257(1-2), 237-273. https://doi.org/10.1007/s10479-016-2195-3.
    15. Mandal, N.K. T.K. Roy et al. (2006). Inventory model of deteriorated items with a constraint: A geometric programming approach. Eur. J. Oper. Res., 173: 199-210. https://doi.org/10.1016/j.ejor.2004.12.002.
    16. Mousavi, K., Mehrdad, L., Ganjeali, A. and Entezari, H. (2014). Multi-item multiperiodic inventory control problem with variable de-mand and discounts: A particle swarm optimization algorithm Scientific world Journal, 2014. https://doi.org/10.1155/2014/136047.
    17. Sarbjit, S. and S.S. Raj, (2010). A stock dependent economic order quantity model for perishable items under inflationary conditions. Am. J. Econ. Bus. Admin., 2:317-322. https://doi.org/10.3844/ajebasp.2010.317.322.
    18. Sharma, K. J. (2013). Operations Research: Theory and Applications. Macmillan Publishers, India Ltd.: 502-506
    19. Sarwar, F., Rahman, M. and Ahmed M. (2019). A Multi-Item Inventory Control Model using Multi Objective Particle Swarm Optimiza-tion (MOPSO). Thailand. Journal of Operations Management, 11(2): 39-47.
    20. Teng, J.T. and H.L Yang, (2007). Deterministic inventory lot-size models with time-varying Demand and cost under generalized holding costs. Inform. Manage. Sci., 18: 113-125
    21. Udoh, N. S. (2018). Probabilistic inventory control models with variable demand over a planning horizon for consumable products, World Journal of Applied Science and Technology, 10 (1B): 237 -243
    22. Udoh, N. S, Ukpongessien, R. F. and Iseh, M. J. (2022). Constrained stochastic inventory control models for multi-item with variable demand, Asian Journal of Probability and Statistics, 20(2): 1-15. https://doi.org/10.9734/ajpas/2022/v20i2415.
    23. Wilson, R. H. (1934). A Scientific routine for stock control, Harvard Business Review, 13: 116-128.

  • Downloads