• Characterizing order processes of continuous review (s,S) and (r,nQ) policies

      Noblesse, Ann; Boute, Robert; Lambrecht, Marc; Van Houdt, Benny (2014)
      We provide a novel approach to characterize the order process of continuous review and inventory policies, and study the impact of the batching parameter (the value of Q or ) on the variability in the order process. First, we characterize the distribution of the time between orders, as well as the distribution of order sizes. We find that the coefficient of variation (cv) of the time between orders is smaller than the cv of the time between demands. The size of the orders can exhibit either variance amplification or dampening, compared to the demand sizes, depending on the demand size distribution and the value of the batching parameter. This may motivate a supplier to adjust his imposed fixed order cost to influence the batching size. Second, we look at the compound order process, defined by the number of units ordered during an arbitrary interval. The compound order process always exhibits variance amplification compared to the compound demand, which increases linearly in the batching parameter for large values of Q or ; for small values, the variance amplification is fluctuating. We point out that the time interval, during which the number of units ordered/demanded is observed, also impacts the level of variance amplification, and we show to what extent larger time intervals (resulting in more aggregation of the data) lead to lower values of variance amplification. Both perspectives (looking at time between orders and order quantities, or observing the compound order process) provide useful information for the upstream supplier.
    • Lot sizing and lead time decisions in production/inventory systems

      Noblesse, Ann; Boute, Robert; Lambrecht, Marc; Van Houdt, Benny (2014)
      Traditionally, lot sizing decisions in inventory management trade-off the cost of placing orders against the cost of holding inventory. However, when these lot sizes are to be produced in a finite capacity production/inventory system, the lot size has an important impact on the lead times, which in turn determine inventory levels (and costs). In this paper we study the lot sizing decision in a production/inventory setting, where lead times are determined by a queueing model that is linked endogenously to the orders placed by the inventory model. Assuming a continuous review (s, S) inventory policy, we develop a procedure to obtain the distribution of lead times and the distribution of inventory levels, when lead times are endogenously determined by the inventory model. This procedure allows to determine the optimal inventory parameters within the class of (s, S) policies that minimize the expected ordering and inventory related costs over time. We numerically show that ignoring the endogeneity of lead times may lead to inappropriate lot sizing decisions and significantly higher costs. This cost discrepancy is very outspoken if the lot size based on the economic order quantity deviates significantly from desirable production lot sizes. In these cases, the endogenous treatment of lead times is of particular importance.
    • Matrix-analytic methods in supply chain management: recent developments

      Boute, Robert; Colen, Pieter; Creemers, Stefan; Noblesse, Ann; Van Houdt, Benny (2012)