On the (R,s,Q) inventory model when demand is modelled as a compound Bernoulli process

In this paper, we consider a periodic review order-up-to-level (or base stock) inventory control system under normally distributed demand. For such circumstances, an expression for the exact fill rate (fraction of demand satisfied without backordering) has been available in the literature, but has not been widely known, let alone used by practitioners. In this paper, we redevelop the expression and contrast our derivation with the earlier published one. The paper has two purposes. First, we hope that the reappearance of the exact result in this journal will lead to its wider adoption. Second, showing two contrasting approaches to obtaining the same result may be useful for both research and pedagogical purposes.

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The exact fill rate in a periodic review base stock system under normally distributed demand

Assessing the impact of perishability and the use of time temperature technologies on inventory management

X-Firm is known as an innovative company that manufactures and markets high quality foods and beverages. X-firm started with only one manufacturing facility and distribution warehouse at Site I. To deal with the promising market developments, X-Frim expanded to Site II in 2013 andf has decided to execute the second expansion plan, i.e. adding a new production plant at Site II and opening a manufacturing faciltity at Site III in 2015. X-Firm has made a capacity plan for the second expansion based on experience and comon sense, but they are a bit doubtful about the reslult. X-firm wants to validat their current capacity plan with another capacity plan that atkes into account a scientific approach in its calculation. Therefore, the main objective of this research is: To find an approach to come up with a capacity plan for X-Firm's distribution warehouses.

/pdf/an-approach-to-capacity-planning-of-distribution-warehouses-4rwug6vrgy.pdf

An Approach to Capacity Planning of Distribution Warehouses for X-Firm

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.

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

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.

R.M.J. Heuts

Papers

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