Continuous Review Perishable Inventory System Research Articles

Two-commodity perishable inventory system with partial backlog demands.

This article examines a two-commodity continuous review perishable inventory system. The demands are arrived at for each product by independent Markovian arrival processes (MAP). Lifetimes follow an exponential distribution. The commodities are assumed to be substitutable. If both commodities have reached zero, demand is backlogged up to predetermined levels. This article’s novelty has been a local purchase, which is made to clear the backlog instantaneously when demand reaches a predetermined level. In the steady-state, the joint probability distribution of inventory levels of both commodities is obtained. Several metrics of system performance in steady-state are derived and also provided as numerical examples to explain the optimum values of the system’s parameters.

A MAP/PH/1 Perishable Inventory System with Dependent Retrial Loss

This paper considers a continuous review perishable inventory system with an infinite orbit. The replenishment of items in the inventory is governed by (s, Q) policy. The Markovian Arrival Process characterizes the arrival pattern of primary customers and the service time follows phase-type distribution. Inventoried items are subject to decay with some preassigned linear rate. The items are purchased from an outside source and lead time is exponentially distributed. An unsatisfied primary customer may enter an orbit or exit the system with a predetermined probability. The retrial customers, those who entered into the orbit, try to access the idle server with a linear rate. An unsatisfied retrial customer may enter or exit the orbit with prefixed probability based on the inventory level. Stationary probability vectors are obtained using the Matrix Analytic method. Numerical optimization of the profit function is carried out for different parameter values.

Optimal service rates of a perishable inventory system with service facility

This paper studies a continuous-review perishable inventory system with service facility. We consider a finite capacity inventory system with Markovian arrivals and exponentially distributed service times. The inventory is replenished according to an (s, S) policy and the lead times follow phase type distribution. The life time of each item is assumed to be exponential. By controlling the service rate at each instance of time, we can minimise the total expected cost rate. We formulate this model as a semi Markov decision problem. The stationary optimal policy is computed using linear programming algorithm and the results are illustrated numerically.

QMCD approach for perishability models: The (S, s) control policy with lead time

We consider cost minimization for an (S, s) continuous-review perishable inventory system with random lead times and times to perishability, and a state-dependent Poisson demand. We derive the stationary distributions for the inventory level using the Queueing and Markov Chain Decomposition (QMCD) methodology. Applying QMCD, we develop an intuitive approach to characterizing the distribution of the residual time for the next event in different states of the system. We provide comprehensive analysis of two main models. The first model assumes a general random lifetime and an exponential distributed lead time. The second model assumes an exponential distributed lifetime and a general lead time. Each model is analyzed under both backordering and lost sales assumptions. We consider a fixed cost for each order, a purchase cost, a holding cost, a cost for perished items, and a penalty cost in the case of shortage. Numerical examples are provided and show that variability of lead time is more costly than that of perishability time. Therefore, after reducing lead time and increasing perishability time, managers should focus on reducing variability of lead time.

A stochastic inventory system with replacement of perishable items

This article presents a continuous review perishable inventory system in which the perished items will be replaced by the supplier at a later time. Demands occur according to a Markov arrival process. The items in the inventory have exponential life times and these perished items are stored in a place, called pool for replacement. The (s, S) ordering policy is adopted. At the time of placing an order, the ordering quantity is adjusted with number of items in the pool. The lead time is assumed to have phase type distribution. The joint probability distribution of the inventory level and the number of pooled items is obtained in the steady state case using the matrix-geometric methods. Various system performance measures in the steady state are derived and the total expected cost rate is calculated under a prefixed cost structure. The results derived in this work are numerically illustrated.

Optimal Service Rates of a perishable Inventory System with Service Facility

This paper studies a continuous-review perishable inventory system with service facility. We consider a finite capacity inventory system with Markovian arrivals and exponentially distributed service times. The inventory is replenished according to an (s, S) policy and the lead times follow phase type distribution. The life time of each item is assumed to be exponential. By controlling the service rate at each instance of time, we can minimise the total expected cost rate. We formulate this model as a semi Markov decision problem. The stationary optimal policy is computed using linear programming algorithm and the results are illustrated numerically.

Perishable inventory model with Markovian arrival process, retrial demands and multiple working vacations

In this paper, we consider a continuous review perishable inventory system in which two types of customers, positive and negative, arrive according to a Markovian arrival process. The life time of an item and the lead time of reorder are exponentially distributed. Demands that occur during stock out period or busy period either enter an orbit of size N or are lost. The orbital demands compete their service with an exponential rate depending on the number of demands in the orbit. The waiting demands in the orbit may renege the system after an exponentially distributed amount of time. The server takes multiple working vacations at zero inventory. The steady state joint probability distribution of the number of customers in the orbit and the inventory level is obtained. Various performance measures and cost analysis are shown with numerical results.

A Perishable Inventory System with Postponed Demands and Finite

In this article, we consider a continuous review perishable inventory system with a finite number of homogeneous sources generating demands. The demand time points form quasi random process and demand is for single item. The maximum storage capacity is assumed to be The life time of each item is assumed to have exponential distribution. The order policy is policy, that is, whenever the inventory level drops to a prefixed level an order for items is placed. The ordered items are received after a random time which is distributed as exponential. We assume that the demands that occur during the stock out periods either enter a pool or leave the system which is according to a Bernoulli trial. The demands in the pool are selected one by one, while the stock is above the level with interval time between any two successive selections is distributed as exponential. The joint probability distribution of the number of customers in the pool and the inventory level is obtained in the steady state case. Various system performance measures are derived to compute the total expected cost per unit time in the steady state. The optimal cost function and the optimal are studied numerically.

Perishable inventory system with service interruptions, retrial demands and negative customers

In this paper, we consider a continuous review perishable inventory system wherein demands arrive according to the Poisson process, each demanding exactly one unit of inventory item and the life time of each item is assumed to be exponential. The operating policy is (s, S) policy, i.e., whenever the inventory level drops to s, an order for Q(=S − s) items is placed. The ordered items are received after a random time which is distributed as exponential. The service may be interrupted according to the Poisson process in which case it restarts after an exponentially distributed time. The demands that occur during the server breakdown period or stock-out period may turn out to be ordinary or a negative demand and then they enter into the orbit of infinite size. These orbiting demands send out a signal to compete for their demand which is distributed as exponential. The matrix analytic method is used for the steady state distribution of the model. Various performance measures and cost analysis are shown with numerical results.

A perishable inventory system with service facility and feedback customers

In this article, we consider a continuous review perishable inventory system with service facility consisting of finite waiting hall and a single server. The primary customers arrive according to a Markovian arrival process. An arriving customer, who finds the waiting hall is full, is considered to be lost. The individual customer’s unit demand is satisfied after a random time of service which is distributed as exponential. The life time of each item is assumed to be exponentially distributed. The items are replenished based on variable ordering policy. The lead time is assumed to have phase type distribution. After the service completion, the primary customer may decide either to join the secondary (feedback) queue, which is of infinite size, or leave the system according to a Bernoulli trial and the server decides to serve either for primary or feedback customer according to a Bernoulli trail. The primary and secondary service are at different counters. The service time for feedback customers is assumed to be independent exponential distribution. After the service completion for feedback customer, the server starts immediately for primary customer’s service, whenever the inventory level and the primary customer level is positive, otherwise the server becomes idle for an exponential duration. If the primary customer level and inventory level becomes positive during the server idle period then he starts service for primary customer immediately. After completing his idle period, the server goes to secondary counter to serve for feedback customer, if any. The joint probability distribution of the system is obtained in the steady state. Important system performance measures are derived and the long-run total expected cost rate is also calculated. The results are illustrated numerically.

Perishable Inventory System with (S, Q) Policy in Supply Chain

In this paper we consider a continuous review perishable inventory system in Multi-echelon system, which is a building block for supply chain. A (s, Q) type perishable inventory system with Poisson demand and exponential distributed lead times for items are assumed at DC (middle echelon). A one-for- one type inventory policy is assumed at retailer node (lower echelon). Demands occurring during the stock out periods are assumed to be lost. The DC replenishes their stocks with exponential distributed lead times from warehouse (upper echelon) has abundant supply source. The items are supplied to the DC in packs of Q (= S-s) items from the warehouse. The steady state probability distribution and the operating characteristics are obtained explicitly. The required algorithm is derived and it is implemented using Mat lab. The measures of system performance in the steady state are obtained.

Analysis of Two-Echelon Perishable Inventory System with Direct and Retrial demands

In this paper, we consider a continuous review perishable inventory system with Markovian demand. The operating policies are (s, S) and (0,M). The life time of an item has an exponential distribution. The ordered items are received after a random time which is assumed to be exponential distribution. The demands that occur directly to the distribution centre are called direct demands. The arrival process for the direct demand follows Poisson process. The demand process to the retailer node is independent to the direct demand process and follows Poisson process. The demands that occur during stock out period are enter into the orbit of finite size. These orbiting demands retry for their demand after a random time, which is assumed to be exponential distribution. The joint probability distribution of the inventory level at lower echelon, higher echelon and the number of customer in the orbit is obtained in the steady state case. Various system performance measures in the steady state are derived and the long run total expected cost rate is calculated.

Transient behaviour and entropy measures on an inventory system with two demand classes

This article considers a continuous review perishable inventory system that consists of a single server. The customers arriving to the service station belong to any one of two types, that is, type-1 and type-2. The demands from each type of customer arrive according to two independent Poisson processes with different parameters. The life time of each item is assumed to be independently distributed as an exponential. The probability distribution of the inventory level is obtained for both transient and steady-state cases. An entropy-based uncertainty metric for measuring the operating performance is presented. The proposed method offers a practical measure to establish the quality (i.e., dependability) of long-run results for a stocking facility. Various system performance measures are derived, and the total expected cost rate is computed under a suitable cost structure.

Modeling and Analysis of Perishable Inventory System with Retrial demands in Supply Chain

In this article, we consider a continuous review perishable inventory system with poisson demands. The maximum storage capacity at lower echelon (retailer) is S and the upper Echelon (Distribution Center) is M (= nQ). The life time of each item is assumed to be exponential. The operating policy is (s, S) policy, that is, whenever the inventory level drops to s, an order for Q = (S - s > s) item is placed. The ordered items are received after a random time which is distributed as exponential. We assume that demands occurring during the stock-out period enter into the orbit. These orbiting demands send out signal to complete for their demand which is distributed as exponential. The joint probability distribution of the inventory level at retailer, inventory level at DC and the number of demands in the orbit are obtained in the steady state case. Various system performance measures are derived and the results are illustrated numerically.

A perishable inventory system with service facility and finite source

In this article, we consider a continuous review (s,S) perishable inventory system with a service facility, wherein the demand of a customer is satisfied only after performing some service on the item which is assumed to be of random duration. We also assume that the demands are generated by a finite homogeneous population. The service time, the lead time are assumed to have Phase type distribution. The life time of the item is assumed to have exponential distributions. The joint distribution of the number of customers in the system and the inventory level is obtained in the steady state case. The Laplace–Stieltjes transform of the waiting time of the tagged customer is derived. Various system performance measures are derived and the total expected cost rate is computed under a suitable cost structure. The results are illustrated numerically.

Dead-time compensation in continuous-review perishable inventory systems with multiple supply alternatives

In this paper, the problem of efficient control of continuous-review perishable inventory systems is addressed. In the considered systems the goods at a distribution center used to fulfill unknown, variable demand are subject to exponential decay. The stock is replenished with delay from multiple supply sources characterized by different latency in procuring orders. A new supply policy which incorporates the Smith predictor to counteract the adverse effects of dead-time is developed. The proposed policy guarantees that the assigned storage space at the distribution center is never exceeded which means that the cost of emergency storage is eliminated. Moreover, it is shown that with appropriately chosen controller parameters all of the demand imposed at the distribution center is realized from the readily available resources. The policy outperforms the classical order-up-to one in terms of higher service level and smaller order-to-demand variance ratio.

Dead-time compensation in continuous-review perishable inventory systems with a remote supply source

Dead-time compensation in continuous-review perishable inventory systems with a remote supply source

A multi-server perishable inventory system with negative customer

In this paper, we consider a continuous review perishable inventory system with multi-server service facility. In such systems the demanded item is delivered to the customer only after performing some service, such as assembly of parts or installation, etc. Compared to many inventory models in which the inventory is depleted at the demand rate, however in this model, it is depleted, at the rate at which the service is completed. We assume that the arrivals of customers are according to a Markovian arrival process (MAP) and that the service time has exponential distribution. The ordering policy is based on (s,S) policy. The lead time is assumed to have exponential distribution. The customer who finds either all servers are busy or no item (excluding those in service) is in the stock, enters into an orbit of infinite size. These orbiting customers send requests at random time points for possible selection of their demands for service. The interval time between two successive request-time points is assumed to have exponential distribution. In addition to the regular customers, a second flow of negative customers following an independent MAP is also considered so that a negative customer will remove one of the customers from the orbit. The joint probability distribution of the number of busy servers, the inventory level and the number of customers in the orbit is obtained in the steady state. Various measures of stationary system performance are computed and the total expected cost per unit time is calculated. The results are illustrated numerically.

A stochastic inventory system with postponed demands

This article considers a continuous review perishable ( s , S ) inventory system in which the demands arrive according to a Markovian arrival process ( MAP ) . The life time of each item in the stock and the lead time of orders are assumed to be independently distributed as exponential. We assume that the demands that occur during stock-out periods either enter a pool of infinite capacity or are lost. The demands in the pool are selected one by one according to FCFS rule when the stock after replenishment is above a prefixed level, say N ( 1 ≤ N ≤ s ) . The interval time between any two successive selections is assumed to be distributed as exponential. In addition to the regular demands, a second flow of negative demands following another MAP is also considered. The negative demand will remove one of the demands waiting in the pool. 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 calculated and the total expected cost is also considered. The results are illustrated numerically.

Analysis of the (s, S) policy for perishables with a random shelf life

A continuous review perishable inventory system operating under the (s,S) policy is considered. Assuming a random shelf life with a general distribution, renewal arrivals and a negligible replenishment lead time, exact expressions for the expected cost rate function for unit and batch demands are derived. For unit demands, it is shown that the average cost rate function is quasi-convex in (s,S). Numerical findings indicate that the loss incurred by ignoring the randomness of the shelf life can be drastic. It is observed that the shape of the shelf life distribution has a significant impact on the costs and a precise estimation of shelf life distribution may result in substantial savings. Based on the presented analytical results, a new heuristic for positive lead times is proposed. Extensive numerical studies show that the proposed heuristic performs better than an existing one suggested for fixed shelf lives in most of the cases studied.