ON (s,S) inventory policy with/without retrial and interruption of services/production

In this thesis we have developed a few inventory models in which items are served to the customers after a processing time. This leads to a queue of demand even when items are available. In chapter two we have discussed a problem involving search of orbital customers for providing inventory. Retrial of orbital customers was also considered in that chapter; in chapter 5 also we discussed retrial inventory model which is sans orbital search of customers. In the remaining chapters (3, 4 and 6) we did not consider retrial of customers, rather we assumed the waiting room capacity of the system to be arbitrarily large. Though the models in chapters 3 and 4 differ only in that in the former we consider positive lead time for replenishment of inventory and in the latter the same is assumed to be negligible, we arrived at sharper results in chapter 4. In chapter 6 we considered a production inventory model with production time distribution for a single item and that of service time of a customer following distinct Erlang distributions. We also introduced protection of production and service stages and investigated the optimal values of the number of stages to be protected.

Studies On Classical And Retrial Inventory With Positive Service Time

Department of Mathematics, Cochin University of Science and Technology

A new inventory model for aircraft spares

A special inventory problem is presented: aircraft spares that are repaired and returned to spares, called rotable inventory. Rotable inventory is not consumed so does not change in the medium term, but is rotated through operational, maintenance and stock phases. The objective for inventory performance is fleet Service Level (SL), which effects aircraft dispatch performance. A model is proposed where the fleet SL drives combined stock levels such that cost is optimized. By holding greater numbers of lower-cost items and holding lower levels of more expensive items, it is possible to achieve substantial cost savings while maintaining performance. This approach is shown to be an advance over the current literature and is tested with case data, with conclusive results.

Analysis of Some Stochastic Inventory Models with Pooling Retrial of Customers

The thesis deals with analysis of some Stochastic Inventory Models with Pooling/Retrial of Customers.. In the first model we analyze an (s,S) production Inventory system with retrial of customers. Arrival of customers from outside the system form a Poisson process. The inter production times are exponentially distributed with parameter µ. When inventory level reaches zero further arriving demands are sent to the orbit which has capacity M(<∞). Customers, who find the orbit full and inventory level at zero are lost to the system. Demands arising from the orbital customers are exponentially distributed with parameter γ. In the model-II we extend these results to perishable inventory system assuming that the life-time of each item follows exponential with parameter θ. The study deals with an (s,S) production inventory with service times and retrial of unsatisfied customers. Primary demands occur according to a Markovian Arrival Process(MAP). Consider an (s,S)-retrial inventory with service time in which primary demands occur according to a Batch Markovian Arrival Process (BMAP). The inventory is controlled by the (s,S) policy and (s,S) inventory system with service time. Primary demands occur according to Poissson process with parameter λ. The study concentrates two models. In the first model we analyze an (s,S) Inventory system with postponed demands where arrivals of demands form a Poisson process. In the second model, we extend our results to perishable inventory system assuming that the life-time of each item follows exponential distribution with parameter θ. Also it is assumed that when inventory level is zero the arriving demands choose to enter the pool with probability β and with complementary probability (1- β) it is lost for ever. Finally it analyze an (s,S) production inventory system with switching time. A lot of work is reported under the assumption that the switching time is negligible but this is not the case for several real life situation.

Stochastic Inventory with/without Service Time, Reneging and Retrial of Customers

This thesis Entitled Stochastic modelling and analysis.This thesis is divided into six chapters including this introductory chapter. In second chapter, we consider an (s,S) inventory model with service, reneging of customers and finite shortage of items.In the third chapter, we consider an (s,S) inventoiy system with retrial of customers. Arrival of customers forms a Poisson process with rate. When the inventory level depletes to s due to demands, an order for replenishment is placed.In Chapter 4, we analyze and compare three (s,S) inventory systems with positive service time and retrial of customers. In all these systems, arrivals of customers form a Poisson process and service times are exponentially distributed. In chapter 5, we analyze and compare three production inventory systems with positive service time and retrial of customers. In all these systems, arrivals of customers form a Poisson process and service times are exponentially distributed.In chapter 6, we consider a PH /PH /l inventory model with reneging of customers and finite shortage of items.

Analysis of Some Stochastic Inventory Models with Pooling/ Retrial of Customers

In this thesis we have presented several inventory models of utility. Of these inventory with retrial of unsatisfied demands and inventory with postponed work are quite recently introduced concepts, the latt~~ being introduced for the first time. Inventory with service time is relatively new with a handful of research work reported. The di lficuity encoLlntered in inventory with service, unlike the queueing process, is that even the simplest case needs a 2-dimensional process for its description. Only in certain specific cases we can introduce generating function • to solve for the system state distribution. However numerical procedures can be developed for solving these problem.

Retrial Queues with Orbital Search

Queueing system in which arriving customers who find all servers and waiting positions (if any) occupied many retry for service after a period of time are retrial queues or queues with repeated attempts. This study deals with two objectives one is to introduce orbital search in retrial queueing models which allows to minimize the idle time of the server. If the holding costs and cost of using the search of customers will be introduced, the results we obtained can be used for the optimal tuning of the parameters of the search mechanism. The second one is to provide insight of the link between the corresponding retrial queue and the classical queue. At the end we observe that when the search probability Pj = 1 for all j, the model reduces to the classical queue and when Pj = 0 for all j, the model becomes the retrial queue. It discusses the performance evaluation of single-server retrial queue. It was determined by using Poisson process. Then it discuss the structure of the busy period and its analysis interms of Laplace transforms and also provides a direct method of evaluation for the first and second moments of the busy period. Then it discusses the M/ PH/1 retrial queue with disaster to the unit in service and orbital search, and a multi-server retrial queueing model (MAP/M/c) with search of customers from the orbit. MAP is convenient tool to model both renewal and non-renewal arrivals. Finally the present model deals with back and forth movement between classical queue and retrial queue. In this model when orbit size increases, retrial rate also correspondingly increases thereby reducing the idle time of the server between services

Stochastic processes and their applications semi-markov analysis of some inventory and queuing problems

This thesis analyses certain problems in Inventories and Queues. There are many situations in real-life where we encounter models as described in this thesis. It analyses in depth various models which can be applied to production, storag¢, telephone traffic, road traffic, economics, business administration, serving of customers, operations of particle counters and others. Certain models described here is not a complete representation of the true situation in all its complexity, but a simplified version amenable to analysis. While discussing the models, we show how a dependence structure can be suitably introduced in some problems of Inventories and Queues. Continuous review, single commodity inventory systems with Markov dependence structure introduced in the demand quantities, replenishment quantities and reordering levels are considered separately. Lead time is assumed to be zero in these models. An inventory model involving random lead time is also considered (Chapter-4). Further finite capacity single server queueing systems with single/bulk arrival, single/bulk services are also discussed. In some models the server is assumed to go on vacation (Chapters 7 and 8). In chapters 5 and 6 a sort of dependence is introduced in the service pattern in some queuing models.

Design and management of a supply chain: a joint location-inventory problem under uncertainty (Part A)

In this paper, a joint location-inventory model is proposed that simultaneously optimises strategic supply chain design decisions such as facility location and customer allocation to facilities, and tactical-operational inventory management and production scheduling decisions. All this is analysed in a context of demand uncertainty and supply uncertainty. While demand uncertainty stems from potential fluctuations in customer demands over time, supply-side uncertainty is associated with the risk of “disruption” to which facilities may be subject. The latter is caused by external factors such as natural disasters, strikes, changes of ownership and information technology security incidents. The proposed model is formulated as a non-linear mixed integer programming problem to minimise the expected total cost, which includes four basic cost items: the fixed cost of locating facilities at candidate sites, the cost of transport from facilities to customers, the cost of working inventory, and the cost of safety stock. Next, since the optimisation problem is very complex and the number of evaluable instances is very low, a "matheuristic" solution is presented. This approach has a twofold objective: on the one hand, it considers a larger number of facilities and customers within the network in order to reproduce a supply chain configuration that more closely reflects a real-world context; on the other hand, it serves to generate a starting solution and perform a series of iterations to try to improve it. Thanks to this algorithm, it was possible to obtain a solution characterised by a lower total system cost than that observed for the initial solution. The study concludes with some reflections and the description of possible future insights.

Distribution center consolidation games

We study the location-inventory model as introduced by Teo et al. (2001) to analyze the impact of consolidation of distribution centers on facility and inventory costs. We extend their result on profitability of consolidation. We associate a cooperative game with each location-inventory situation and prove that this game has a non-empty core for identical and independent demand processes. This illustrates that consolidation does not only lower joint costs (which was shown by Teo et al. (2001)), but it allows for a stable division of the minimal costs as well.

Elinkaaripohjaiseen ABC-analyysiin perustuva päätöksenteontukijärjestelmä

Yritysten vaihto-omaisuudenhallinnasta löytyy usein selviä puutteita. Yksi selkeä syy tähän on perinteisen ABC-analyysin riittämättömyys, joka pohjautuu puhtaasti historiatietoihin. ABC-analyysia oikein tulkitsemalla, voi siitä kuitenkin saada erinomaisen työkalun varastonhallintaan. Tämä edellyttää tuotteen elinkaarenvaiheen huomioimista. Tätä elinkaarenvaiheet huomioivaa ABC-analyysia kutsutaan elinkaaripohjaiseksi ABC-analyysiksi. Koska nykyisissä toiminnanohjausjärjestelmissä ei kuitenkaan ole mahdollista luokitella tuotteita tämän uuden menetelmän mukaisesti, syntyy tarve tukijärjestelmälle. Tukijärjestelmän tarkoituksena on sekä luokitella tuotteet elinkaaripohjaisen ABC-analyysin avulla että antaa tuotteille varastonohjaussuositukset Salmivuori Consulting Oy:n käyttämän ohjausmenetelmän mukaisesti. Varastotasojen määrittämistä helpottamaan luotiin järjestelmän yhteyteen vielä erillinen ohjaustyökalu. Lisäksi työssä on havainnollistettu keskimääräistä varaston arvoa sekä puutekustannuksia minimoivien varastotasojen valintaa case-esimerkin avulla. Järjestelmän luomien tuoteluokkien sekä varastonohjaussuositusten avulla, päätöksentekijällä on mahdollisuudet tehostaa yrityksen vaihto-omaisuudenhallintaa.

Toimittajavarastointi teollisuusyrityksen kilpailuetuna sekä sen aiheuttamien kustannusten tarkastelu

Työn tavoitteena on tutkia toimittajavarastointia sekä siitä aiheutuvia kus-tannuksia. Työssä perehdytään tarkemmin toimitusketjun eri osapuolien väliseen yhteistyömalliin sekä tarkastellaan varastoinnin aiheuttamia kus-tannuksia yleisellä tasolla, sekä toimittajavarastointimallin mukanaan tuo-mien erillisten kustannuserien käsittelyä. Lisäksi tutkitaan, miten toimitta-javarastointimalli tuo lisähyötyä toimittajan toimintaan kilpailijoihin nähden. Tutkimus sisältää teoriaosuuden ja empiirisen osuuden, joissa esitellään aiheeseen liittyviä lainalaisuuksia ja erään teollisuusyrityksen toimittajavarastointia kahden esimerkkiasiakkaan kesken, sekä näiden asiakkaiden toimittajavarastoinnista esimerkkiyritykselle aiheutuvia kustannuksia. Teoriaosuudessa selvitetään toimittajavarastointiin liittyviä teoreettisia lähtökohtia ja sen vaikutuksia yritysten toimintaan. Kyseessä on kvalitatiivinen tapaustutkimus, jossa empiirinen aineisto ke-rättiin havainnoinnin, haastattelujen ja valmiiden dokumenttien perusteella sekä esimerkkiyrityksen tietokannoista. Teoriaosuuden lähteenä käytettiin aikaisempaa alan kirjallisuutta sekä artikkeleita. Tuloksena esitetään kustannusten laskentamalli, jonka avulla voidaan selvittää toimittajavarastoinnista aiheutuvat kustannukset ja niiden ositusperusteet.

Logiciel de génération de nombres aléatoires dans OpenCL

clRNG et clProbdist sont deux interfaces de programmation (APIs) que nous avons développées pour la génération de nombres aléatoires uniformes et non uniformes sur des dispositifs de calculs parallèles en utilisant l’environnement OpenCL. La première interface permet de créer au niveau d’un ordinateur central (hôte) des objets de type stream considérés comme des générateurs virtuels parallèles qui peuvent être utilisés aussi bien sur l’hôte que sur les dispositifs parallèles (unités de traitement graphique, CPU multinoyaux, etc.) pour la génération de séquences de nombres aléatoires. La seconde interface permet aussi de générer au niveau de ces unités des variables aléatoires selon différentes lois de probabilité continues et discrètes. Dans ce mémoire, nous allons rappeler des notions de base sur les générateurs de nombres aléatoires, décrire les systèmes hétérogènes ainsi que les techniques de génération parallèle de nombres aléatoires. Nous présenterons aussi les différents modèles composant l’architecture de l’environnement OpenCL et détaillerons les structures des APIs développées. Nous distinguons pour clRNG les fonctions qui permettent la création des streams, les fonctions qui génèrent les variables aléatoires uniformes ainsi que celles qui manipulent les états des streams. clProbDist contient les fonctions de génération de variables aléatoires non uniformes selon la technique d’inversion ainsi que les fonctions qui permettent de retourner différentes statistiques des lois de distribution implémentées. Nous évaluerons ces interfaces de programmation avec deux simulations qui implémentent un exemple simplifié d’un modèle d’inventaire et un exemple d’une option financière. Enfin, nous fournirons les résultats d’expérimentation sur les performances des générateurs implémentés.

TLC Estados Unidos – Colombia: oportunidades de negocio en el sector cervecero colombiano

El presente trabajo analiza el sector cervecero colombiano y las oportunidades de importación de cerveza artesanal generadas por el TLC Estados Unidos- Colombia. También se describe la relación comercial entre Colombia y Estados Unidos durante el periodo comprendido entre los años 2000 y 2013 junto con la inflación y la tasa de desempleo. Para finalizar se realiza un pronóstico de la demanda y un modelo de inventarios para el posible importador y se brindan sugerencias en cuanto a la distribución de la cerveza.

The effects of uncertainty about the timing of deals on consumer behavior

I examine the effects of uncertainty about the timing of de aIs (i.e. temporary price cuts or sales) on consumer behavior in a dynamic inventory model of consumer choice. I derive implications for purchase behavior and test them empirically, using two years of scanner data for soft drinks. I fmd that loyal consumers' decisions, both about the allocation of their purchases over time and the quantity to be purchased in a particular deal, are affected by the uncertainty about the timing of the deal for the product. Loyal consumers buy a higher fraction of their overall purchases during de ais as the uncertainty decreases. This effect increases with an increase in the product' s share of a given consumer' s purchase in the same category or if the consumer stockpiles (i.e., is a shopper). During a particular deal, loyal shoppers increase the quantity they purchase the more time that has passed since the previous de aI, and the higher the uncertainty about the deals' timing. For the non-Ioyal consumers these effects are not significant. These results hold for products that are frequently purchased, like soft-drinks and yogurt, but do not hold for less frequentIy purchased products, such as laundry detergents. The fmdings suggest that manufacturers and retailers should incorporate the effects of deals' timing on consumers' purchase' decisions when deriving optimal pricing strategies.