Fuzzy modeling approach to on-hand stock levels estimation in (R, S) inventory system with lost sales

Purpose: One challenge in inventory control models is to know the stock available at the beginning of the cycle to satisfy future demands, i.e. to know the on-hand stock levels at order delivery. For inventory managers, this knowledge is necessary to both determine service levels and establish the control parameters of the inventory policy. However, the calculation of on-hand stock levels when unfilled demand is lost is mathematically complex since on-hand stock cannot be negative by definition. The purpose of this paper is to propose a new approach to estimate on-hand stock levels when the inventory is periodically reviewed and unfilled demand is lost, through the use of fuzzy techniques. Design/methodology/approach: This paper applies fuzzy set techniques for the calculation of the on-hand stock levels at order delivery in the lost sales context, based on the uncertainty that real demand introduces. To this end, we propose a new approach based on modeling the on-hand stock as an imprecise Markov chain using possibility functions, which reduces significantly the computational effort required to obtain the on-hand stock levels. Findings: To illustrate the performance of the proposed method, two experiments are carried out. The first experiment shows that the proposed fuzzy method correctly calculates on-hand stock levels with insignificant deviation with respect the exact vector. Additionally, the results illustrate that the fuzzy method simplifies the calculation and highly reduces the computational efforts. The second experiment shows the performance of the fuzzy method when it is used to estimate service levels by means of the fill rate. The results show that the proposed method accurately estimates the fill rate with average deviations lower than 0.00015. Practical implications: Knowing the on-hand stock vector is important for inventory managers to establish the control parameters of the system, i.e. to determine the minimum base stock level, S, that guarantees the achievement of a target service level. The difficulty of this estimation is that to obtain the on-hand stock vector in a lost sales context requires a huge computational effort and it is difficult to implement in companies' information systems. However, the proposed fuzzy method leads to a very accurate calculation of the on-hand stock vector significantly reducing the computational costs, which makes this method easily implementable in practical environments. Originality/value: Fuzzy set techniques have been widely used in inventory models to introduce the uncertainty of demand, costs or shortage. However, to the best of our knowledge, this is the first paper which deals directly with fuzzy estimation of on-hand levels.