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This paper is devoted to the performance analysis and optimization of blood testing procedures. We present a queueing model of two queues in series, representing the two stages of a blood-testing procedure. Service (testing) in stage 1 is performed in batches, whereas it is done individually in stage 2. Since particular elements of blood can only be stored and used within a finite time window, the sojourn time of blood units in the system of two queues in series is an important performance measure, which we study in detail. We also introduce a profit objective function, taking into account blood acquisition and screening costs as well as profits for blood units, which were found uncontaminated and were tested fast enough. We optimize that profit objective function w.r.t. the batch size and the length of the time window.

We consider a continuous review (s, S) model of perishable items with lost sales. Once items are perished the entire inventory drops instantaneously to zero. The total cost includes the cost of: ordering, unsatisfied demand, units destroyed, holding, and fixed cost of perishability. Both the time to perishability and the lead times are assumed to be exponentially distributed while two cases of demand distribution are considered: Poisson and compound Poisson with general demand sizes. We study the average cost criterion and provide computational results on the problem of finding the optimal re-order level, s, and order up-to level, S. None of the known work on the subject is as general as the model presented here. Our analysis leads to several insights on the optimal (s, S) policies for perishable items in the presence of lead times. For example, we demonstrate that the effectiveness of a heuristic that ignores perishability (and is also analyzed here) decreases with the demand variability and that the cost may either increase or decrease with this variability.

We consider a production–inventory control model with two reflecting boundaries, representing the finite storage capacity and the finite maximum backlog. Demands arrive at the inventory according to a Poisson process, their i.i.d. sizes having a common phase-type distribution. The inventory is filled by a production process, which alternates between two prespecified production rates ρ1 and ρ2: as long as the content level is positive, ρ1 is applied while the production follows ρ2 during time intervals of backlog (i.e., negative content). We derive in closed form the various cost functionals of this model for the discounted case as well as under the long-run-average criterion. The analysis is based on a martingale of the Kella–Whitt type and results for fluid flow models due to Ahn and Ramaswami.

We study a stochastic fluid EOQ-type model operating in a Markovian random environment of alternating good and bad periods determining the demand rate. We deal with the classical problem of “when to place an order” and “how big it should be,” leading to the trade-off between the setup cost and the holding cost. The key functionals are the steady-state mean of the content level, the expected cycle length (which is the time between two large orders), and the expected number of orders in a cycle. These performance measures are derived in closed form by using the level crossing approach in an intricate way. We also present numerical examples and carry out a sensitivity analysis.

We consider control policies for perishable inventory systems with random input whose purpose is to mitigate the effects of unavailability. In the basic uncontrolled system, the arrival times of the items to be stored and the ones of the demands for those items form independent Poisson processes. The shelf lifetime of every item is finite and deterministic. Every demand is for a single item and is satisfied by the oldest item on the shelf, if available. The first controlled model excludes the possibility of unsatisfied demands by introducing a second source of fresh items that is completely reliable and delivers without delay whenever the system becomes empty. In the second model, there is no additional ordering option by outsourcing. However, to avoid the most adverse effects of unavailability, the demands are classified into different categories of urgency. An incoming demand is satisfied or not according to its category and the current state of the system. For both models, we determine the steady-state distribution of the virtual outdating process, which is then used to derive the relevant cost functionals: the steady-state distribution and expected value of the number of items in the system, the rate of outdatings, as well as, for model 1, the rate of special orders from the external source and, for model 2, the rate of unsatisfied demands.

We consider a storage model that can be on or off. When on, the content increases at some state-dependent rate and the system can switch to the off state at a state-dependent rate as well. When off, the content decreases at some state-dependent rate (unless it is at zero) and the system can switch to the on position at a state-dependent rate. This process is a special case of a piecewise deterministic Markov process. We identify the stationary distribution and conditions for its existence and uniqueness.

The aim of this article is to derive the income and cost functionals required to determine the actuarial value of certain types of perishable inventory system. In the basic model, the arrival times of the items to be stored and the ones of the demands for those items form independent Poisson processes. The shelf lifetime of every item is finite and deterministic. Every demand is for a single item and is satisfied by the oldest item on the shelf, if available. The price of an item depends on its shelf age. For an actuarial valuation, it is important to know the distribution of the total value of the items in the system and the expected (discounted) total income and cost generated by the system when in steady state. All of these functionals are determined explicitly. As extensions of the original model, we also deal with the case of batch arrivals and general renewal interdemand times; in both cases, closed-form solutions are obtained.

We consider a stochastic input–output system with additional total clearings at certain random times determined by its own evolution (and specified by a controller). Between two clearings, the stock level process is a superposition of a Brownian motion with drift and a compound Poisson process with positive jumps, reflected at zero. We introduce meaningful cost functionals for this system and determine them explicitly under several (classical and new) clearing policies.

We consider two model variants of a production-inventory system. The system is characterized by a producing machine which is susceptible to failure following which it must be repaired to make it operative again. The machine's production can also be stopped deliberately because of stocking capacity limitations. During ON periods the input into the buffer is continuous and uniform (until a threshold is reached), whereas during OFF periods the output from the buffer is a compound Poisson process. We are interested in computing the equilibrium content level process under the assumption that full backlogging is allowed. In the first model, variant OFF periods are independent of the demand process, and in the second variant, they are determined and controlled in accordance with a certain level crossing stopping rule.

We consider a reflected independent superposition of a Brownian motion and a compound Poisson process with positive and negative jumps, which can be interpreted as a model for the content process of a storage system with different types of customers under heavy traffic. The distributions of the duration of a busy cycle and the maximum content during a cycle are determined in closed form.

We present the production version of two EOQ-type models in heavy traffic. The output is interpreted by random demand and the input by a deterministic production plus random returns. In the ON part of the cycle, the inventory content is a reflected Brownian motion, and in the OFF part, it is a Brownian motion with a negative drift. The ON/OFF periods generate an alternative renewal process and the content-level process is a regenerative process. Two control policies are considered. In one policy that is natural under conditions of continuous review, production is stopped when the content level in the ON period reaches a predetermined level q. In the other policy, which resembles periodic review, production is stopped when the ON time reaches a predetermined time t0.

We consider a fluid system in which during off-times the buffer content increases as a piecewise linear process according to some general semi-Markov process, and during on-times, it decreases with a state-dependent rate (or remains at zero). The lengths of off-times are exponentially distributed. We show that such a system has a stationary distribution which satisfies a decomposition property where one component in the decomposition is associated with some dam process and the other with a clearing process. For the cases of constant and linear decrease rates, the steady-state Laplace–Stieltjes transform and moments of the buffer content are computed explicitly.

This paper is devoted to the analysis of a fluid queue with a buffer content that varies linearly during periods that are governed by a three-state semi-Markov process. Two cases are being distinguished: (i) two upward slopes and one downward slope, and (ii) one upward slope and two downward slopes. In both cases, at least one of the period distributions is allowed to be completely general. We obtain exact results for the buffer content distribution, the busy period distribution, and the distribution of the maximal buffer content during a busy period. The results are obtained by establishing relations between the fluid queues and ordinary queues with instantaneous input and by using level crossing theory.

The blood bank system is a typical example of a perishable inventory system. The commodity arrival and customer demand processes are stochastic. However, the stored items have a constant lifetime. In this study, we introduce a diffusion approximation to this system. The stock level is represented by the amount of items arriving during the age of the oldest item; it is assumed to fluctuate as an alternating two-sided regulated Brownian motion between barriers 0 and 1. Hittings of level 0 are outdatings and hittings of level 1 are unsatisfied demands. Also, there are two predetermined switchover levels, a and b, with 0 ≤ a < b ≤ 1. Whenever the stock level process upcrosses level b, the controller generates a switch in the drift from γ = γ0 to γ = γ1, while downcrossings of level a generate switches from γ1 to γ0. A useful martingale is introduced for analyzing the stationary law of the controlled process as well as the total expected discounted cost.

We consider a dam model with a compound Poisson input having positive jumps in which the release rule can be dynamically controlled between two release functions, r1 and r2. The dam process has two switchover levels, a and b, 0 < a < b < ∞, which are prescribed to switch the release rule from r2 to r1 only when the dam downcrosses levels and switch from r1 to r2 only when the dam upcrosses level b. We derive integral equations whose solutions determine the stationary distribution of the dam content and demonstrate such a determination explicitly for the case of exponential jumps. We also compute an expression for the average number of switches from r1 to r2, and vice versa; consider an approximation to the general case (with b − a being sufficiently large with respect to r1 and r2 and the jump sizes), which allows the use of asymptotic results from renewal theory; and study the wet period analysis for the case of exponential jumps.

Two classes of inventory systems are considered, and modeled under a control policy of the bang-bang type. For the first, items and demands for those items arrive independently and singly at a system. Unsatisfied demands are lost, and items staying on the shelf too long are considered unsuitable for use and are rejected. For the second, items are produced continuously over time with fixed rate in a storage/production system with capacity k, in which demands of exponential size arrive according to a Poisson process, and no backorders are allowed. The problem of controlling the demand rate in the first model is shown to be equivalent to the problem of controlling the production rate in the second model. Optimization methods are then considered for both models employing discounted cost and averaged cost rate criteria for the optimal selection of switchover levels for arrival and demand rates.