Stochastic inventory control models for single item replenishment with variable demand under constrained and unconstrained conditions
Authors: Udoh Nse , Ekpenyong Wisdom 
Published: October 2024

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.