مدیریت موجودی با هزینه تأمین تجهیزات وابسته "زمان انجام سفارش"متغیر

A reduction in the inventory replenishment lead-time allows reducing safety stock requirements and improving customer service. However, it might be accompanied by increased procurement costs because of premium charges imposed by suppliers, or higher transportation costs. This paper studies a single-stage variable lead-time inventory system with lead-time dependent procurement cost. Selection of the lead-time value represents finding the trade-off between benefits of lead-time reduction and increase in the procurement cost. A model for joint optimization of inventory and procurement costs is developed. Numerical studies are conducted to identify conditions under which lead-time reduction is favorable compared to procuring at the lowest cost.

Demand uncertainty coupled with inventory replenishment lead-time creates the inventory carrying risk. Lead-time reduction and application of risk reducing inventory management policies have been shown to improve efficiency in managing inventory. Tersine and Hummingbird [1], Jayaram et al. [2] and Disney and Towill [3] have demonstrated the positive impact of physical lead-time reduction. The lead-time reduction allows using more accurate demand information in making inventory replenishment decisions, which in turn reduces safety stock requirements and improves the customer service level. However, the lead-time reduction may be associated with some additional risks and costs [4]. For instance, a shorter lead-time may lead to higher purchasing costs and unavailability of supplies due to the limited supplier capacity. Burnetas and Gilbert [5] provide examples from travel industry, where late orders are charged a premium price. They also mention premium transportation charges for short lead-time orders as a source of increasing purchasing costs in other industries. Cachon [6] has discussed examples from the retail industry. Retailers placing late orders are not eligible for discounts and face the possibility of insufficient supplies because suppliers give priority to early orders. Das and Abdel-Malek [7] report that suppliers accept short lead-time orders at a higher unit price because of their disruptive impact on suppliers’ operations. These observations lead to the problem of finding the trade-off between lead-time reduction and additional procurement costs. The trade-off between purchasing cost and delivery lead-time from the manufacturing point is discussed by Elhafsi [8] and Slotnick and Sobel [9] among others. These authors show that manufacturers are interested in providing flexible pricing in response to more attractive delivery time conditions.

In this paper, the traditional continuous review re-order point inventory management policy has been modified by considering the variable lead-time and including the lead-time dependent procurement cost. Optimization of the total inventory and procurement cost yields values of the lead-time, the order quantity and the safety factor characterizing the trade-off between the inventory cost and the procurement cost. The trade-off depends upon the particular structure of the procurement cost function. Linear and nonlinear PCFs have been considered. The linear PCF causes the total cost to be a concave function according to the lead-time. In the case of nonlinear PCF, convexity properties of the total cost function depend upon the PCF's parameters and the parameters of inventory system and demand process. The added value parameter is particularly important. In the case of convex PCF, the minimum of the total cost function generally occurs at the inflection point. Concave nonlinear purchasing functions yield results similar to those of the linear function. The numerical studies conducted show that the lead-time reduction, which increases the procurement cost and is aimed to reduce the inventory cost, is justified only if, (a) the increase of the procurement cost is slow, (b) the external demand is highly uncertain, and (c) a product has large added value. Therefore, the lead-time reduction under covariance stationary demand reduces the total inventory and procurement cost only for marginal situations. This occurs because the procurement cost comprises a major share of the total cost. Additionally, procuring at the higher cost also contributes to an increase of the inventory cost through the higher variable cost v′v′. If these conclusions are viewed from the supply chain perspective, then there are many situations when a retailer is willing to consider a supply discount in return for an early commitment. The model has been presented under the assumption that demand is a first order autoregressive process. If higher order autoregressive processes are considered, a discontinuous approach to finding the optimal lead-time can be used (illustrative results are presented in [24]). One of the future research directions is the analysis of serial multi-stage systems utilizing re-order point policies under autoregressive demand and lead-time dependent procurement cost. Under some circumstances depending upon the type of collaboration, suppliers may prefer the retailer to use shorter lead-times because the retailer's lead-time also affects safety stock requirements for suppliers. Therefore, the product exchange price may not be a monotonically decreasing function of the lead-time. Another research direction is establishing a link between manufacturing scheduling models that consider cost and lead-time trade-off at the supply side and the proposed inventory management models at the demand side.