Base-stock policies for the lost sales inventory system with Poisson demand and Erlangian lead times

The base-stock policies for the studied inventory system can easily be evaluated through Erlang's loss formula when the lead times are mutually independent. This is often the case only if the base-stock $S$ is one. If $S$ is larger than one, the Erlangian lead times become stochastically dependent under the realistic assumption that the replenishment orders do not cross in time. We make this assumption and show for any positive $S$ that the number of replenishment orders outstanding has an equilibrium distribution which is a slightly modified truncated version of a negative binomial distribution. It turns out to be easy to compute the stock-out frequency recursively for $S=1,2,\dots .$ For each $S$, the average stock can be specified in terms of this frequency. We prove that the frequency is convex in $S$. It is therefore straightforward to compute the base-stock for which the average cost is minimized and to compute the minimum average cost. Our numerical study illustrates that the minimum average cost is very sensitive to the shape parameter describing the Erlangian lead times, which is in sharp contrast to the complete insensitivity when lead times are independent.     

Stackelberg versus Cournot oligopoly with private information

We compare an $n$-firm Cournot model with a Stackelberg model, where $n$-firms choose outputs sequentially, in a stochastic demand environment with private information. The expected total output, consumer surplus, and total surplus are lower, while expected price and total profits are higher in the Stackelberg perfect revealing equilibrium than in the Cournot equilibrium. These rankings are the opposite of the rankings of prices, total output, surplus, and profits under perfect information. We also show that the first $n-1$ firms’ expected profits form a decreasing sequence from the first to the $(n-1){}^{st}$ in the Stackelberg game. The last mover earns more expected profit than the first mover if $n\le 4,$ or the ratio of the signals’ informativeness to the prior certainty is sufficiently low. Lastly, there is a discontinuity between the Stackelberg equilibrium of the perfect information game and the limit of Stackelberg perfect revealing equilibria, as the noise of the demand information of firms vanishes to zero at the same rate. We provide various robustness checks for the results when the precision of signals are asymmetric, there is public information or cost/quality uncertainty, or the products are differentiated.     

Near cost-optimal inventory control policies for divergent networks under fill rate constraints

We deal with the optimisation of stock levels in general divergent networks under a periodic review, order-up-to ($\text{R,}\text{S}$) policy. The goal is to attain target fill rates, while the total holding costs in the entire network are minimised. To this end, we first present a method for the fast calculation of the control parameters, given central and intermediate stock levels. Next we develop an approximate procedure to determine stock levels sequentially. Extensive numerical experimentation shows that this procedure yields satisfactory results. It also shows that significant stocks at intermediate stockpoints are only useful if unit holding costs in these stockpoints are considerably less than in the end stockpoints that deliver directly to the final customers.     

An economic-statistical design of double sampling control chart

The double sampling (DS) chart can reduce the sample size when monitoring the process mean. In this study, Duncan's cost model was modified by adding the statistical constraints to develop the design model of DS chart for the optimization of design parameters—sample size, control limit coefficient, warning limit coefficient and sampling interval. A numerical example was provided to illustrate the use of this model. A sensitivity analysis of the effects of model parameters and statistical constraints on the optimal design of DS chart was also performed.