On exhibiting inventory systems with Erlangian lifetimes under renewal demands

A continuous revies (s, S) inventory system with renewal demand in which one item is put into operation as an exhibiting piece is analyzed. The lifetime of any operating unit has Erlangian distribution, and on failure is replaced by another one from the stock and the failed item is disposed of. Replenishment of stock is instantaneous. The transient and stationary values of inventory level distribution and the mean reorder rate are obtained using the techniques of semi-regenerative processes. Decision rules for optimums andS that minimize the long-run expected cost rate are derived. The solution for a dual model with the distribution of lifetimes and inter-demand times interchanged is also given.     

Optimality conditions for regenerative inventory systems under batch demands

We consider a single-item, continuous-review, (s, S) inventory system, under complete backlogging and a constant procurement lead time. Demands occur in independent, identically distributed batches, separated by independent identically distributed intervals. The model also includes a class of periodic review systems as a special case. Of interest are the optimal control policies with respect to a stationary cost rate function, constructed to include ordering, holding and shortage costs. We study the structural properties of the cost rate function and report some new bounds and optimality conditions. An application of these to the computation and approximation of optimal policies is also discussed.     

Perishable inventory management system with a minimum volume constraint

The federal government maintains large quantities of medical supplies in stock as part of its Strategic National Stockpile (SNS) to protect the American public in case of a public health emergency. Managing these large perishable inventories effectively can help reduce the cost of the SNS and improves national security. In this paper, we propose a modified Economic Manufacturing Quantity (EMQ) model for perishable inventory with a minimum volume constraint, which is applicable to managing the inventory of medicines for the Strategic National Stockpile. We demonstrate that minimizing the cost of maintaining such a system can be formulated as a non-convex non-smooth unconstrained optimization problem. The property of this model is analysed and an efficient exact algorithm is presented to solve this problem. In the numerical experiment part, we perform sensitivity analysis on several government-controlled system parameters to illustrate how the government can obtain lower costs or a larger stockpile at the same cost by allowing more freedom in the management of the stocks.     

Evaluating shortfall distributions in periodic inventory systems with stochastic endogenous demands and lead-times

This paper addresses a multi-period production/inventory problem with two suppliers, where demand sizes and supplier lead time are stochastic and correlated. A discrete time, single item inventory system is considered, where inventory levels are reviewed periodically and managed using a base-stock policy. At the end of each period, a replenishment order is placed, which enters a queue at the buffer stage and is consequently forwarded to the first available supplier. We present a mathematical model of this inventory system and determine optimal safety stock levels for it, in closed form, using matrix analytic techniques and the properties of phase type distributions. To account for the effect of order crossovers, which occur whenever replenishment orders do not arrive in the sequence in which they were placed, the inventory shortfall distribution is analyzed. Finally, a set of numerical experiments with a system with two suppliers is presented, where the proposed model is compared to other existing models.     

Perishable inventory management subject to stochastic leadtime

This paper discusses the model for a perishable product with the stochastic procurement leadtime. Zero or 1 unit leadtime is considered and its optimal ordering policy is derived. This is a generalization of the one period horizon model of Nahmias [4]. Further, the chance constraint as for shortage is added and under this additional constraint, again optimal ordering policy is obtained.     

Perishable inventory theory: a review.

This paper reviews the relevant literature on the problem of determining suitable ordering policies for both fixed life perishable inventory, and inventory subject to continuous exponential decay. We consider both deterministic and stochastic demand for single and multiple products. Both optimal and suboptimal order policies are discussed. In addition, a brief review of the application of these models to blood bank management is included. The review concludes with a discussion of some of the interesting open research questions in the area.     

Perishable inventory management with stochastic leadtime and different selling prices

This paper discusses a model for a perishable product with stochastic procurement leadtime and different selling prices. This model is a generalization of the one period horizon model of Nahmias [4,5], Ishii et al. [3] and Nose et al. [7]. For the model, the optimal ordering policy and its properties are derived.     

A discrete time inventory system with postponed demands

In this article, we consider a discrete-time inventory model in which demands arrive according to a discrete Markovian arrival process. The inventory is replenished according to an (s,S)$(s,S)$ policy and the lead time is assumed to follow a discrete phase-type distribution. The demands that occur during stock-out periods either enter a pool which has a finite capacity N(<∞)$N(<\infty )$ or leave the system with a predefined probability. Any demand that arrives when the pool is full and the inventory level is zero, is assumed to be lost. The demands in the pool are selected one by one, if the on-hand inventory level is above s+1$s+1$, and the interval time between any two successive selections is assumed to have discrete phase-type distribution. The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady state case. The measures of system performance in the steady state are derived and the total expected cost rate is also calculated. The results are illustrated numerically.     

Uniform distribution of inventory positions in two-echelon periodic review systems with batch-ordering policies and interdependent demands

We consider a two-level inventory system in which there are one supplier and multiple retailers. The retailers face stochastic, interdependent customer demands. Each location employs a periodic-review (R,nQ), or lot-size reorder point, inventory policy. We show that each location's inventory positions are stationary and the stationary distribution is uniform and independent of any other's.     

A two-warehouse production model for deteriorating inventory items with time-dependent demands

A two-warehouse inventory model for deteriorating items with time-dependent demand has been developed. Compared with previous models, the model involves a free form time-dependent demand and a finite replenishment rate within a finite planning horizon. Rather than the heuristic approach of equal production cycle times adopted by Lee and Ma, an approach which permits variation in production cycle times is adopted to determine the number of production cycles and the times for replenishment during a finite planning horizon. Numerical examples are provided to illustrate the application of the model and the results indicate that the performance of the proposed approach is superior to that of the heuristic approach of Lee and Ma.     

Optimal inventory management for a retail chain with diverse store demands

Item demands at individual retail stores in a chain often differ significantly, due to local economic conditions, cultural and demographic differences and variations in store format. Accounting for these variations appropriately in inventory management can significantly improve retailers’ profits. For example, it is shown that having greater differences across the mean store demands leads to a higher expected profit, for a given inventory and total mean demand. If more than one inventory shipment per season is possible, the analysis becomes dynamic by including updated demand forecasts for each store and re-optimizing store inventory policies in midseason. In this paper, we formulate a dynamic stochastic optimization model that determines the total order size and the optimal inventory allocation across nonidentical stores in each period. A generalized Bayesian inference model is used for demands that are partially correlated across the stores and time periods. We also derive a normal approximation for the excess inventory from the previous period, which allows the dynamic programming formulation to be easily solved. We analyze the tradeoffs between obtaining information and profitability, e.g., stocking more stores in period 1 provides more demand information for period 2, but does not necessarily lead to higher total profit. Numerical analyses compare the expected profits of alternative supply chain strategies, as well as the sensitivity to different distributions of demand across the stores. This leads to novel strategic insights that arise from adopting inventory policies that vary by store type.     

Managing inventory and service levels in a safety stock‐based inventory routing system with stochastic retailer demands

The inherent uncertainty in supply chain systems compels managers to be more perceptive to the stochastic nature of the systems' major parameters, such as suppliers' reliability, retailers' demands, and facility production capacities. To deal with the uncertainty inherent to the parameters of the stochastic supply chain optimization problems and to determine optimal or close to optimal policies, many approximate deterministic equivalent models are proposed. In this paper, we consider the stochastic periodic inventory routing problem modeled as chance‐constrained optimization problem. We then propose a safety stock‐based deterministic optimization model to determine near‐optimal solutions to this chance‐constrained optimization problem. We investigate the issue of adequately setting safety stocks at the supplier's warehouse and at the retailers so that the promised service levels to the retailers are guaranteed, while distribution costs as well as inventory throughout the system are optimized. The proposed deterministic models strive to optimize the safety stock levels in line with the planned service levels at the retailers. Different safety stock models are investigated and analyzed, and the results are illustrated on two comprehensively worked out cases. We conclude this analysis with some insights on how safety stocks are to be determined, allocated, and coordinated in stochastic periodic inventory routing problem. Copyright © 2017 John Wiley & Sons, Ltd.     

On priority queues with impatient customers

In this paper, we study three different problems where one class of customers is given priority over the other class. In the first problem, a single server receives two classes of customers with general service time requirements and follows a preemptive-resume policy between them. Both classes are impatient and abandon the system if their wait time is longer than their exponentially distributed patience limits. In the second model, the low-priority class is assumed to be patient and the single server chooses the next customer to serve according to a non-preemptive priority policy in favor of the impatient customers. The third problem involves a multi-server system that can be used to analyze a call center offering a call-back option to its impatient customers. Here, customers requesting to be called back are considered to be the low-priority class. We obtain the steady-state performance measures of each class in the first two problems and those of the high-priority class in the third problem by exploiting the level crossing method. We furthermore adapt an algorithm from the literature to obtain the factorial moments of the low-priority queue length of the multi-server system exactly.      

Lost-sales inventory systems with a service level criterion

Competitive retail environments are characterized by service levels and lost sales in case of excess demand. We contribute to research on lost-sales models with a service level criterion in multiple ways. First, we study the optimal replenishment policy for this type of inventory system as well as base-stock policies and (R, s, S) policies. Furthermore, we derive lower and upper bounds on the order-up-to level, and we propose efficient approximation procedures to determine the order-up-to level. The procedures find values of the inventory control variables that are close to the best (R, s, S) policy and comply to the service level restriction for most of the instances, with an average cost increase of 2.3% and 1.2% for the case without and with fixed order costs, respectively.