Approximations for the delivery splitting model

Consumer Demand;Operational Research;Stocks

Demand management in Multi-Stage Distribution Chain

In this paper we discuss demand management problems in a multi-stage distribution chain.We focus on distribution chains where demand processes have high variability due to a few large customer orders.We give a possible explanation, and suggest two simple procedures that help to smooth demand.It is shown that these procedures yield stock reductions of 40%-50% in practical situations.The quantitative results are based on the analysis of the underlying model related to the two procedures proposed, called large order overflow, applicable if the supplying organization executes a multi-stage distribution chain, and delivery splitting, applicable to any situation.

A Two-Supplier Inventory Model

In this paper we consider an inventory system with two suppliers.A supply agreement is made with one of the suppliers, to deliver a xed quantity Q every review period.The replenishment decisions for the other supplier are governed by a (R; S) replenishment policy; that is, when the inventory position at a review period is below the order-up-to level S, an order is placed at the second supplier such that the inventory position is raised up to S.In this paper an algorithm is developed for the determination of the decision parameters S and Q such that the total relevant costs are minimized, subject to a service level constraint; these costs are de ned as the sum of the holding, purchasing, and ordering costs.Based on the numerical results, conclusions follow about the division of the purchase volume among the two suppliers.

A Two-Supplier Inventory Model

In this paper we consider an inventory system with two suppliers.A supply agreement is made with one of the suppliers, to deliver a xed quantity Q every review period.The replenishment decisions for the other supplier are governed by a (R; S) replenishment policy; that is, when the inventory position at a review period is below the order-up-to level S, an order is placed at the second supplier such that the inventory position is raised up to S.In this paper an algorithm is developed for the determination of the decision parameters S and Q such that the total relevant costs are minimized, subject to a service level constraint; these costs are de ned as the sum of the holding, purchasing, and ordering costs.Based on the numerical results, conclusions follow about the division of the purchase volume among the two suppliers.inventory models

The significance of glucosinolates for sulfur storage in Brassicaceae seedlings

Brassica juncea seedlings contained a twofold higher glucosinolate content than B. rapa and these secondary sulfur compounds accounted for up to 30% of the organic sulfur fraction. The glucosinolate content was not affected by H2S and SO2 exposure, demonstrating that these sulfur compounds did not form a sink for excessive atmospheric supplied sulfur. Upon sulfate deprivation, the foliarly absorbed H2S and SO2 replaced sulfate as the sulfur source for growth of B. juncea and B. rapa seedlings. The glucosinolate content was decreased in sulfate-deprived plants, though its proportion of organic sulfur fraction was higher than that of sulfate-sufficient plants, both in absence and presence of H2S and SO2. The significance of myrosinase in the in situ turnover in these secondary sulfur compounds needs to be questioned, since there was no direct co-regulation between the content of glucosinolates and the transcript level and activity of myrosinase. Evidently, glucosinolates cannot be considered as sulfur storage compounds upon exposure to excessive atmospheric sulfur and are unlikely to be involved in the re-distribution of sulfur in B. juncea and B. rapa seedlings upon sulfate deprivation

On the (R,s,Q) Inventory Model when Demand is Modelled as a Compound Process

In this paper we present an approximation method to compute the reorder point s in a (R; s; Q) inventory model with a service level restriction, where demand is modelled as a compound Bernoulli process, that is, with a xed probability there is positive demand during a time unit, otherwise demand is zero.The demand size and replenishment leadtime are stochastic variables.It is shown that this kind of mod- elling is especially suitable for intermittent demand.Furthermore, an approximation for the expected average physical stock is derived.The quality of both the reorder point determination as well as the approximation for the expected average physical stock turn out to be excellent, as is veri ed by discrete event simulation.

The Value of Information in an (R,s,Q) Inventory Model

In this paper we compare three methods for the determination of the reorder point s in an (R; s; Q) inventory model subject to a service level constraint. The three methods di er in the modelling assumptions of the demand process which in turn leads to three di erent approximations for the distribution function of the demand during the lead time.The rst model is most common in the literature, and assumes that the time axis is divided in time units (e.g. days).It is assumed that the demands per time unit are independent and identically distributed random variables.The second model monitors the customers individually.In this model it is assumed that the demand process is a compound renewal process, and that the distribution function of the interarrival times as well as that of the demand per customer are approximated by the rst two moments of the associated random variable.The third method directly collects information about the demand during the lead time plus undershoot, avoiding convolutions of stochastic random variables and residual lifetime distributions.Consequently, the three methods require di erent types of information for the calculation of the reorder point in an operational setting.The purpose of this paper is to derive insights into the value of information; therefore it compares the target service level with the actual service level associated with the calculated reorder point.It will be shown that the performance of the rst model (discrete time model) depends on the coe cient ofvariation of the interarrival times. Furthermore, because we use asymptotic relations in the compound renewal model, we derive some bounds for the input parameters within which this model applies. Finally we show that the aggregated information model is superior to the other two models.