Weber and Stidham (1987) used submodularity to establish transition monotonicity (a service completion at one station cannot reduce the service rate at another station) for Markovian queueing networks that meet certain regularity conditions and are controlled to minimize service and queueing costs. We give an extension of monotonicity to other directions in the state space, such as arrival transitions, and to arrival routing problems. The conditions used to establish monotonicity, which deal with the boundary of the state space, are easily verified for many queueing systems. We also show that, without service costs, transition-monotone controls can be described by simple control regions and switching functions, extending earlier results. The theory is applied to production/inventory systems with holding costs at each stage and finished goods backorder costs.

Weber and Stidham (1987) used submodularity to establish transition monotonicity (a service completion at one station cannot reduce the service rate at another station) for Markovian queueing networks that meet certain regularity conditions and are controlled to minimize service and queueing costs. We give an extension of monotonicity to other directions in the state space, such as arrival transitions, and to arrival routing problems. The conditions used to establish monotonicity, which deal with the boundary of the state space, are easily verified for many queueing systems. We also show that, without service costs, transition-monotone controls can be described by simple control regions and switching functions, extending earlier results. The theory is applied to production/inventory systems with holding costs at each stage and finished goods backorder costs.

In this research, we consider production/inventory management decisions of a rmthat sells its product in two market segments during a nite planning horizon. In thebeginning of each period, the rm makes a decision on how much to produce basedon the production capacity and the current on-hand inventory available. After theproduction is made at the beginning of the period, the rm rst satises the stochasticdemand from customers in its primary market. Any primary market demand thatcannot be satised is lost. After satisfying the demand from the primary market, ifthere is still inventory on hand, all or part of the remaining products can be sold ina secondary market with ample demand at a lower price. Hence, the second decisionthat the rm makes in each period is how much to sell in the secondary market, orequivalently, how much inventory to carry to the next period.The objective is to maximize the expected net revenue during a nite planninghorizon by determining the optimal production quantity in each period, and theoptimal inventory amount to carry to the next period after the sales in primary andsecondary markets. We term the optimal inventory amount to be carried to the nextperiod as \economic retention quantity". We model this problem as a nite horizonstochastic dynamic program. Our focus is to characterize the structure of the optimalpolicy and to analyze the system under dierent parameter settings. Conditioning on given parameter set, we establish lower and upper bounds on the optimal policyparameters. Furthermore, we provide computational tools to determine the optimalpolicy parameters. Results of the numerical analysis are used to provide furtherinsights into the problem from a managerial perspective.

In this research, we consider production/inventory management decisions of a rmthat sells its product in two market segments during a nite planning horizon. In thebeginning of each period, the rm makes a decision on how much to produce basedon the production capacity and the current on-hand inventory available. After theproduction is made at the beginning of the period, the rm rst satises the stochasticdemand from customers in its primary market. Any primary market demand thatcannot be satised is lost. After satisfying the demand from the primary market, ifthere is still inventory on hand, all or part of the remaining products can be sold ina secondary market with ample demand at a lower price. Hence, the second decisionthat the rm makes in each period is how much to sell in the secondary market, orequivalently, how much inventory to carry to the next period.The objective is to maximize the expected net revenue during a nite planninghorizon by determining the optimal production quantity in each period, and theoptimal inventory amount to carry to the next period after the sales in primary andsecondary markets. We term the optimal inventory amount to be carried to the nextperiod as \economic retention quantity". We model this problem as a nite horizonstochastic dynamic program. Our focus is to characterize the structure of the optimalpolicy and to analyze the system under dierent parameter settings. Conditioning on given parameter set, we establish lower and upper bounds on the optimal policyparameters. Furthermore, we provide computational tools to determine the optimalpolicy parameters. Results of the numerical analysis are used to provide furtherinsights into the problem from a managerial perspective.

This thesis presents a study of stochastic models of continuous review of inventory systems of perishable and non-perishable products, as well as inventory systems operating in random environment. It contains five chapters. The first chapter is introductory in nature, containing the motivation for the study and the techniques required for the analysis of respective models described in the remaining chapters. Chapter 2 provides a model of perishable product inventory system operating in a random environment. For the sake of simplicity, the stochastic environment is considered to alternate randomly over time between two states 0 and 1 according to an alternating renewal process. When the environment is in state k, the items in inventory have a perishable rate ìk, the demand rate is ëk and the replenishment cost is CRk. The performance of various measures of the system evolution are obtained, assuming instantaneous replenishment at the epoch of the first demand after the stock-out and associating a Markov renewal process with the inventory level. In Chapter 3, a continuous review single product perishable inventory model is considered. Items deteriorate in two phases and then perish. Independent demands occur at constant rates for items in phase I and in phase II. Demand that occurs for an item in phase I during its stock-out period is satisfied by an item in phase II with some probability. However a demand for an item in phase II occurring during its stock-out period is lost. The reordering policy is an adjustable (S,s) policy with the lead-time following an arbitrary distribution. Identifying the stochastic process as a renewal process, the probability distribution of the inventory level at any arbitrary instant of time is obtained. The expressions for the mean stationary rates of demands lost, demands substituted, perished units and scrapped units are also derived. A numerical example is considered to highlight the results obtained. Chapter 4 is a study of a two-commodity inventory system under continuous review. The maximum storage capacity for the i-th item is Si (i=1, 2). The demand points for each commodity are assumed to form an independent Poisson process, with unit demand for one item and bulk demand for the other. The order level is fixed as si for the i-th commodity (i=1, 2) and the ordering policy is to place an order for Qi (= Si – si , i = 1,2) items for the i-the commodity when both the inventory levels are less than or equal to their respective reorder levels. The lead-time is assumed to be exponential. The joint probability distribution for both commodities is obtained in both transient and steady state cases. Various measures of systems performance and the total expected cost rate in the steady state are derived. The results are illustrated with numerical examples. Chapter 5 provides an analysis of a continuous review of two-product system with two types of demands and with individual (S,s) ordering policy. The lead-time distribution of product 1 is arbitrary and that of product 2 exponential. Two types of demands occur at constant rates either for both products or for product 2 alone. Expressions for the stationary distribution of the inventory level are obtained by identifying the underlying stochastic processes as a semi-regenerative process. The mean stationary rates of the lost demands, the demands that are satisfied and the number of reorders are obtained and these measures are used to provide an expression for the cost rate. The main objective of this thesis is to improve the state of art of continuous review inventory systems. The salient features of the thesis are summarized below: <ul>(a) Consideration of</ul> <ul>(i) The impact of the stochastic environment on inventory systems;</ul> <ul>(ii) The interactions existing among the products in multi-product systems;</ul> <ul>(iii) Individual and joint-ordering policies;</ul> <ul>(b) Discussion of inventory systems with perishable products; </ul> <ul>(c) Effective use of the regeneration point technique to derive expressions for various system measures;</ul> <ul>(d) Illustration of the various results by extensive numerical work;</ul> <ul>(e) Relevant optimization problems</ul> / Thesis (PhD (Industrial Engineering))--University of Pretoria, 2006. / Industrial and Systems Engineering / unrestricted

Submitted by ÁLVARO DE MARTINO LOURENÇÃO null (alvarodml@yahoo.com.br) on 2016-09-01T02:29:53Z No. of bitstreams: 1 dissertação final.pdf: 1977900 bytes, checksum: f021d291c786b9596621fda8c29bfa24 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-09-01T19:40:32Z (GMT) No. of bitstreams: 1 lourencao_am_me_bauru.pdf: 1977900 bytes, checksum: f021d291c786b9596621fda8c29bfa24 (MD5) / Made available in DSpace on 2016-09-01T19:40:32Z (GMT). No. of bitstreams: 1 lourencao_am_me_bauru.pdf: 1977900 bytes, checksum: f021d291c786b9596621fda8c29bfa24 (MD5) Previous issue date: 2016-07-04 / A gestão de estoque pode ser considerada como um dos principais componentes do planejamento e controle da produção. Na literatura acadêmica, inúmeros modelos matemáticos são apresentados para a gestão de estoque, os quais se referem a diferentes aspectos relacionados a essa gestão. O desenvolvimento de modelos de estoque eficientes e a adoção de métodos de otimização adequados para resolução desses modelos são necessários para o suporte à tomada de decisão. Neste trabalho, propõe-se um novo modelo de estoque que considera múltiplos produtos e múltiplas restrições de recursos, explorando o conceito de ponto de reposição e revisão periódica. Este problema é formulado como um problema de otimização não linear inteiro misto. Explora-se para a resolução deste modelo, uma abordagem baseada no método de Branch and Bound com o método de pontos interiores para a resolução dos problemas da árvore de busca. Testes computacionais são realizados com o modelo proposto e o método de resolução adotado. Os resultados obtidos evidenciam os seus potenciais para trabalhar com sistemas de estoque multiprodutos com múltiplas restrições. / Inventory management can be considered as one of the main components of planning and production control. In the academic literature, numerous mathematical models are presented for the inventory management, which refer to different aspects related to such a management. The development of efficient inventory models and the adoption of appropriate optimization methods for solving these models are needed to support decision-making. In this work, we propose a new inventory model that considers multiple products and multiple resource constraints, exploring the concept of replacement point and periodic review. This problem is formulated as a mixed integer non-linear optimization problem. For solving this model, an approach based on Branch and Bound method with interior point method for solving the search tree problems is explored. Computational tests are performed with the proposed model and the resolution method adopted. The obtained results show their potential to work with multiproduct inventory systems with multiple constraints.

This thesis studies the problem of modeling life-limited spare units in a steady-state scenario. This means that units that have a predefined lifespan are to be modeled in a scenario where all conditions are kept constant and all transients have faded out. OPUS10 is a spare parts optimization software developed by Systecon AB. There is no way to explicitly model the life-limited units in OPUS10, although there are different approximate models that are built on adjustments of the failure rate and repair fraction or the definition of preventive maintenance. The objective of this thesis is to analyze the usage of life-limited items in real life and to investigate what approximated models different OPUS10 users will utilize in their modeling of life-limited units. Furthermore, the objective is to analyze the consequences of the approximated models and to investigate the possibility of an improved model. The results show that the main interest when choosing which approximated model to use is the type of life limit. There are three different types of operating time life limits investigated. Either the unit is discarded immediately after the life limit is reached, or it is instead discarded at the next failure. There is also the possibility of resetting of the life limit timer at each maintenance. In all three cases, it is shown that if choosing the most fitting approximate model, the results are very accurate. If the life limit is instead measured in calendar time, even the best approximation will give an under-estimation of the expected number of backorders. It is also shown that most of the OPUS10 users model life-limited units as preventive maintenance with discard, which is not the best approximation in any of the types of life limits.

No description available.

We have not been able to find a lot of research that defines and categorises different kinds of inventory systems. This thesis expands on what makes an inventory system what it is and how different active inventory systems differ from each other. There’s a lack of non-generic language both in research and everyday discussions between friends that we aim to alleviate. We adapt and make use of an existing pattern creation method as well as an immersive-participatory method to play and analyse nine games that all make use of inventory systems in very different ways. Through this method we created three game design patterns that describe the differences in limitation and presentation within active inventory systems; allocated inventories, numerical inventories and spatial inventories.

In this thesis we analyze the procurement process of buyers and supply decisions of manufacturers. Companies are looking for ways to decrease their procurement costs, which account for a large percentage of the supply chain costs. We study the effects of demand aggregation and collaborative procurement on buyers' profitability. First, we make a high-level analysis and consider a market with multiple buyers and suppliers where multi-unit transactions for multiple items take place. The procurement costs are effected by economies of scale in the suppliers' production costs and by economies of scope in transportation. We design buyer strategies that model different collaboration levels and assess the role of collaboration under varying market conditions. Next, we analyze the procurement process at a lower level and identify benefits of inter-firm collaboration among buyers who are potential competitors in the end market. We adopt a game-theoretic approach to explore the economics of the basic mechanism underlying collaborative procurement, and determine the conditions that makes it beneficial for the participants. Besides low procurement costs, important considerations in supplier selection are responsiveness and the reliability of the suppliers in meeting demand. Hence, manufacturers face the pressure for quoting short and reliable lead times. We cover several aspects of the manufacturer's problem, such as quoting reliable due-dates based on current workload in the system, maximizing profit considering the lateness cost incurred due to late deliveries, and deciding on the level of inventory to increase responsiveness. We employ a model where demand arrival and manufacturing processes are stochastic, and obtain insights on the optimal due-date quotation policy and on the optimal inventory level.