Continuous Review Inventory System Research Articles

A Continuous Review Inventory System with Retrial Customers and Two-Stage Service

A Continuous Review Inventory System with Retrial Customers and Two-Stage Service

A Continuous Review Inventory System with Lost Sales and Emergency Orders

We analyze a continuous review lost sales inventory system with two types of orders—regular and emergency. The regular order has a stochastic lead time and is placed with the cheapest acceptable supplier. The emergency order has a deterministic lead time is placed with a local supplier who has a higher price. The emergency order is not always filled since the supplier may not have the ability to provide the order on an emergency basis at all times. This emergency order has a higher cost per item and has a known probability of being filled. The total costs for this system are compared to a system without emergency placement of orders. This paper provides managers with a tool to assess when dual sourcing is cost optimal by comparing the single sourcing and dual sourcing models.

An inventory system with two heterogeneous servers and orbital search for feedback customers

This model deals a continuous review (s, S) inventory system with two heterogeneous servers (server-1 and server-2). Server-1 serves for primary and feedback customers. The primary customers arrival according to a MAP. Service time for both servers, lead time and feedback customers service have exponential distribution. The Primary customers, who finds either two servers are busy or no item is in stock, waits in the finite waiting hall. If the waiting hall is full, then the arriving customer consider to be lost. After the completion of service, the primary customer will decide either to join the orbit (infinite size) for additional service or leaves the system according to a Bernoulli trial. These orbiting customers compete for their service according to a constant retrial policy. Orbital search for server-2 follows a Bernoulli trial. The results are illustrated numerically.

An inventory system with two heterogeneous servers and orbital search for feedback customers

This model deals a continuous review (s, S) inventory system with two heterogeneous servers (server-1 and server-2). Server-1 serves for primary and feedback customers. The primary customers arrival according to a MAP. Service time for both servers, lead time and feedback customers service have exponential distribution. The Primary customers, who finds either two servers are busy or no item is in stock, waits in the finite waiting hall. If the waiting hall is full, then the arriving customer consider to be lost. After the completion of service, the primary customer will decide either to join the orbit (infinite size) for additional service or leaves the system according to a Bernoulli trial. These orbiting customers compete for their service according to a constant retrial policy. Orbital search for server-2 follows a Bernoulli trial. The results are illustrated numerically.

Multi-objective optimisation of continuous review inventory system under mixture of lost sales and backorders within different constraints

Multi-objective optimisation of continuous review inventory system under mixture of lost sales and backorders within different constraints

Performance Analysis of Substitutable Perishable Inventory System with Direct Demand in Supply Chain

This paper presents continuous review inventory systems in a simple chain with two different substitutable items in stock. The demand for the products follows independent Poisson with rates λ1 and λ2 respectively for product and A and B. The common demand for both products at distributor follows Poisson distribution with rate λd .The operating policy at the lower echelon for the products are (si, Si) that is whenever the inventory level drops to ‘si’ on order for Qi = (Si-si) items is placed, the ordered items are received after a random time which is distributed as exponential. We assume that the demands accruing during the stock-out period are lost. The retailer replenishes the stock of products from the supplier which adopts (0,M) policy. The joint probability disruption of the inventory levels of the products, at retailer and the products at supplier are obtained in the steady state case. Various system performance measures are derived and the long run total expected inventory cost rate is calculated.

Multi-objective optimisation of continuous review inventory system under mixture of lost sales and backorders within different constraints

This paper presents a continuous review stochastic inventory control system. The demand of each product assumed stochastic. In inventory models, it is common to assume that unsatisfied demand is backordered. We considered mixture of lost sales and backorders for shortages. We optimised inventory system with finding fraction of demand backordered. Also, we considered service level in model to improve customer satisfaction and compete better in retail environment. We considered two conflicting objectives: 1) minimising the total cost; 2) maximising the service level. The goal is to generate more diverse and better non-dominated solutions of reorder point, order size and fraction of demand backordered such that the total inventory cost is minimised and the service level is maximised. We considered constraints such as warehouse space, order quantity and restriction on available budget. Constraints are stochastic and follow normal distribution. Two multi-objective optimiser multi-objective particle swarm optimisation (MOPSO) and non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the problem. We compared the performance of two proposed algorithms with TOPSIS and statistical method. In this comparison, the optimum values of the NSGA-II parameters were obtained using regression analysis.

A retrial queueing-inventory system with J-additional options for service and finite source

A continuous review (s; S) inventory system at a service facility with nite homogeneous sources of demands and retrial is analysed. The lifetime of each item is assumed to be exponential. Before items are delivered to the customers, some basic service on the item must be performed. It is known as a regular or main service. The service may get interrupted according to a Poisson process and it restarts after an exponentially distributed time. If the server is idle at the time of arrival of a customer and the inventory level is positive, then the service begins immediately. After the completion of regular service, a customer may either abandon the system forever or demand for a second service from the same server, which is multi-optional. If any arriving customer nds that the server is busy or inventory level is zero, he/she either enters into the orbit with probability p or balks (does not enter) with probability 1 - p. The stationary distribution of the number of customers in the system, server status and the inventory level is obtained by the matrix method. 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. A numerical illustration is given. Key words : (s; S) policy, service interruption, nite source, retrial, repair, essential and optional service.

Optimal Ordering Policy for Inventory Systems with Quantity-Dependent Setup Costs

We consider a continuous-review inventory system in which the setup cost of each order is a general function of the order quantity and the demand process is modeled as a Brownian motion with a positive drift. Assuming the holding and shortage cost to be a convex function of the inventory level, we obtain the optimal ordering policy that minimizes the long-run average cost by a lower bound approach. To tackle some technical issues in the lower bound approach under the quantity-dependent setup cost assumption, we establish a comparison theorem that enables one to prove the global optimality of a policy by examining a tractable subset of admissible policies. Since the smooth pasting technique does not apply to our Brownian inventory model, we also propose a selection procedure for computing optimal policy parameters when the setup cost is a step function.

Closed-Form Approximations for Optimal (r, q) and (S, T) Policies in a Parallel Processing Environment

We consider a single-item continuous-review (r, q) inventory system with a renewal demand process and independent, identically distributed stochastic lead times. Using a stationary marked-point process technique and a heavy-traffic limit, we prove a previous conjecture that inventory position and inventory on-order are asymptotically independent. We also establish closed-form expressions for the optimal policy parameters and system cost in heavy-traffic limit, the first of their kind, to our knowledge. These expressions sharpen our understanding of the key determinants of the optimal policy and their quantitative and qualitative impacts. For example, the results demonstrate that the well-known square-root relationship between the optimal order quantity and demand rate under a sequential processing environment is replaced by the cube root under a stochastic parallel processing environment. We further extend the study to periodic-review (S, T) systems with constant lead times. The electronic companion is available at https://doi.org/10.1287/opre.2017.1623 .

Developing a M/G/C-FCFS queueing model with continuous review (R, Q) inventory system policy in a cement industry

Developing a M/G/C-FCFS queueing model with continuous review (R, Q) inventory system policy in a cement industry

Retrial inventory model with negative customers and multiple working vacations

This paper analyses a continuous review (s, S) inventory system at a service facility, wherein an item demanded by a customer is issued after performing service on the item. Primary arrivals follow a Poisson distribution and they may turn out to be positive or negative and then enter into the orbit. The orbiting demands compete for service according to an exponential distribution. The server takes multiple working vacations at zero inventory. Replenishment times, vacation times, service times during regular busy periods and vacation periods are exponentially distributed. A matrix analytic method is used for the steady-state distribution of the model. Various performance measures and cost analyses are shown with numerical results.

Continuous Review Inventory Systems: Practice Problems

A problem set to review the concepts of continuous review inventory systems. These problems can be assigned for additional practice in calculating order quantities, inventories, and relevant costs. This can be used with the notes Managing Inventories: Determining Order Quantity (UVA-OM-1395) and Managing Inventories: The Reorder Point System (UVA-OM-1394). Excerpt UVA-OM-1489 Rev. Apr. 4, 2014 CONTINUOUS REVIEW INVENTORY SYSTEMS: PRACTICE PROBLEMS 1. Demand for an item is 1,661 units per year. The ordering cost is $ 20 per order. The carrying cost per year (c ´ k) is $ 5.40 per item. On average, how many orders are placed each year, if the economic order quantity (EOQ) is ordered? 2. An office orders stationery from a supplier. The cost of paper is $ 20.51 per ream. The ordering cost is $ 33 per order. The annual cost of carrying the inventory is 0.22 (22%) of the unit cost per ream. The annual demand is 22,013 reams of paper. What is the annual carrying cost of inventory, assuming that the EOQ is ordered? 3. Demand for an item is 9,434 units per year. The ordering cost is $ 21 per order. The carrying cost per year (c ´ k) is $ 18 per item. What is the optimal ordering quantity? . . .

Optimization Models for the Continuous Review Inventory System

Businesses that carry inventory as a means of responding to customer demand must decide when to place inventory orders and how much to order. A model for selecting an optimal order quantity and reorder point in the continuous review system is implemented in spreadsheet software. Historical data on period demand and lead time is processed by performing a statistical test to select a mixture distribution for lead time demand. This distribution is incorporated into an expected shortage calculation and cost model where shortages incur lost sales and/or goodwill costs. The lead time demand distribution selection is evaluated through experiments. In examples, employing an incorrect distribution leads to expenditures between one and eighteen percent higher than those experienced with the correct model. A mismatch of the backorder or lost sales model with the correct underlying assumptions leads to expenses between four and thirteen percent larger than necessary in an example problem.

A Continuous Review Inventory Model with Fuzzy Service Level Constraint and Fuzzy Random Variable Parameters

This paper presents a continuous review inventory system in the presence of fuzziness and randomness in demand and cost parameter. In the realistic situations, determination of the stock-out cost is often difficult. Instead of having stock-out cost term in the objective function, a condition on the service level is established on the model. The model is constructed as a fuzzy stochastic optimization problem, and we developed a methodology to obtain the optimal solutions such that total expected annual cost is minimized in the fuzzy sense. A numerical example is included to illustrate the proposed methodology.

Ergodicity of age-dependent inventory control systems

AbstractWe consider continuous review inventory systems with general doubly stochastic Poisson demand. In this specific case the demand rate, experienced by the system, varies as a function of the age of the oldest unit in the system. It is known that the stationary distributions of the ages in such models often have a strikingly simple form. In particular, they exhibit a typical feature of a Poisson process: given the age of the oldest unit the remaining ages are uniform. The model we treat here generalizes some known inventory models dealing with partial backorders, perishable items, and emergency replenishment. We derive the limiting joint density of the ages of the units in the system by solving partial differential equations. We also answer the question of the uniqueness of the stationary distributions which was not addressed in the related literature.

Closed-Form Approximations for Optimal (r,q) and (S,T) Policies in a Parallel Processing Environment

We consider a single-item continuous-review (r,q) inventory system with a renewal demand process and i.i.d. stochastic leadtimes. Using a stationary marked point process technique and a heavy traffic limit, we prove a previous conjecture that inventory position and inventory on-order are asymptotically independent. We also establish closed-form expressions for the optimal policy parameters and system cost in heavy traffic limit, the first of their kind to our knowledge. These expressions sharpen our understanding of the key determinants of the optimal policy and their quantitative and qualitative impacts. For example, the results demonstrate that the well-known square-root relationship between the optimal order quantity and demand rate under a sequential processing environment is replaced by the cube root under a stochastic parallel processing environment. We further extend the study to periodic-review (S,T) systems with constant leadtimes.

Weibull vs. normal distribution of demand to determine the safety stock level when using the continuous-review (S, s) model without backlogs

Determining safety stock is one of the most critical issues in inventory and logistics management. This paper presents a cost-based analytical model to determine the best safety stock and customer service level for uncertain demand of products during generic replenishment lead times and a continuous-review inventory system. The proposed model uses the Weibull distribution to model the generic stochastic demand. α and β are the scale parameter and the shape parameter, respectively. An experimental analysis based on the assumption of different distributions of demand of product demonstrates the effectiveness of the proposed model compared to the so-called normal-based traditional model. Significantly, the proposed Weibull-based model is a comprehensible and user-friendly tool that can be useful for production system managers and practitioners.

Recent review article on queueing inventory systems

A detailed review on queueing inventory models with various cases like Single server Queueing systems with Inventory, Queueing inventory system with stochastic environment, Queueing systems in Inventory with substitution flexibility, Queuing systems in production-inventory, Queueing system with service inventory, Continuous review inventory systems with server vacation, Inventory system with postponed demands/ customers and Queueing systems with new models of inventory are discussed.

A fuzzy random continuous review inventory model with a mixture of backorders and lost sales under imprecise chance constraint

The article investigates a constrained continuous review inventory system with a mixture of backorders and lost sales. The proposed model is developed with the annual customer demand incorporated as a fuzzy random variable. The lead-time is assumed to be constant while the lead-time demand is assumed to be connected to the annual fuzzy random demand through the length of the lead-time. A budget constraint is imposed on the model in the form of an 'imprecise' chance constraint to present a possible way of quantifying fuzzily defined uncertain information of the constraint. A methodology is proposed to determine the optimal order quantity and the reorder point such that the total cost incurred is minimised subject to the constraint. A numerical example is given to illustrate the proposed methodology.