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Marketing researches reveal that displayed inventory and allocated shelf space affect the demand of some retail items. We study periodic inventory policy when demand is uncertain and its probability distribution function depends on inventory level and period length. Profit function including sale revenue, holding, shortage, and ordering costs is presented. To capture real world situation we propose natural properties for demand probability distribution. Considering those properties well fitted demand distributions are presented. Finally optimal policy is explored via numerical examples. Numerical study reveals that optimal value of decision variables is not monotonic with respect to demand sensitivity to the inventory. [ABSTRACT FROM AUTHOR]

The objectives of this work were to study the influence of sugar, starch and Hydroxypropylmethylcellulose (HPMC) concentrations on Porosity and textural properties of sponge cakes for optimization of formulation for low-sugar cake. Response surface methodology (RSM) was performed to examine the effects of independent variables on porosity and firmness and to determine the optimum level of ingredients . Independent variables selected for the study were: sugar concentration (0, 10 and 20 % w/w), HPMC concentration (0, 0.5 and 1 %w/w) and starch concentration (0, 5 and 10 %w/w). For each response, second order polynomial models were developed using multiple linear regression analysis. Analysis of variance was performed to check the adequacy and accuracy of the fitted models. The optimum values for sugar, HPMC and starch concentrations were found to be 10, 0.5, and 5 %, respectively. These levels of ingredients led to porosity and firmness values of 76.56 % and 13.00 N respectively. The microstructures of samples were also analyzed using scanning electron microscopy and it was found that SEM pictures confirmed the RSM results about the effects of ingredients on porosity. [ABSTRACT FROM AUTHOR]

We consider an M/M/1 queueing system with inventory under the $$(r,Q)$$ policy and with lost sales, in which demands occur according to a Poisson process and service times are exponentially distributed. All arriving customers during stockout are lost. We derive the stationary distributions of the joint queue length (number of customers in the system) and on-hand inventory when lead times are random variables and can take various distributions. The derived stationary distributions are used to formulate long-run average performance measures and cost functions in some numerical examples. [ABSTRACT FROM AUTHOR]

We consider M/M/1/∞ systems with inventory in which completing each service in the queueing system requires an on-hand inventory. Continuous review (r, Q) policy is considered for the inventory system, and lead times are assumed to be mixed exponentially distributed. During stockout, arriving demands get rejected from the queue and become lost (lost sale situation). We derive stationary distribution of product form of joint queue length and on-hand inventory. The resulting distribution is employed to compute performance measures which can be used to derive the optimal policy. Optimal order size for predetermined reorder policy is initially determined and finally, optimal reorder point and corresponding optimal order size are simultaneously computed for several numerical examples. [ABSTRACT FROM AUTHOR]