Loss systems in a random environment

We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service process is completely blocked: Service is interrupted and newly arriving customers are lost. We prove an if-and-only-if-condition for a product form steady state distribution of the joint queueing-environment process. A consequence is a strong insensitivity property for such systems. We discuss several applications, e.g. from inventory theory and reliability theory, and show that our result extends and generalizes several theorems found in the literature, e.g. of queueing-inventory processes. We investigate further classical loss systems, where due to finite waiting room loss of customers occurs. In connection with loss of customers due to blocking by the environment and service interruptions new phenomena arise. We further investigate the embedded Markov chains at departure epochs and show that the behaviour of the embedded Markov chain is often considerably different from that of the continuous time Markov process. This is different from the behaviour of the standard M/G/1, where the steady state of the embedded Markov chain and the continuous time process coincide. For exponential queueing systems we show that there is a product form equilibrium of the embedded Markov chain under rather general conditions. For systems with non-exponential service times more restrictive constraints are needed, which we prove by a counter example where the environment represents an inventory attached to an M/D/1 queue. Such integrated queueing-inventory systems are dealt with in the literature previously, and are revisited here in detail

A periodic review policy with quality improvement, setup cost reduction, backorder price discount, and controllable lead time

This paper explores a periodic review inventory model under stochastic demand. The setup (or ordering) cost and the lead time are controllable. The model considers an imperfect production process, whose quality can be improved by means of an investment. A backorder price discount to motivate customers to wait for backorders is included. The demand in the protection interval is first assumed Gaussian; then, the distribution-free approach is adopted. The objective is to determine the review period, the setup cost, the quality level, the backorder price discount, and the length of lead time that minimize the long-run expected total cost per time unit. A solution method for each case is presented. Numerical experiments show that substantial savings can be achieved if the quality level, the setup cost and the lead time are controlled, and if a backorder price discount is applied. A sensitivity analysis is finally carried out

Assessment of joint inventory replenishment: a cooperative games approach

This research deals with the design of a logistics strategy with a collaborative approach between non-competing companies, who through joint coordination of the replenishment of their inventories reduce their costs thanks to the exploitation of economies of scale. The collaboration scope includes sharing logistic resources with limited capacities; transport units, warehouses, and management processes. These elements conform a novel extension of the Joint Replenishment Problem (JRP) named the Schochastic Collaborative Joint replenishment Problem (S-CJRP). The introduction of this model helps to increase practical elements into the inventory replenishment problem and to assess to what extent collaboration in inventory replenishment and logistics resources sharing might reduce the inventory costs. Overall, results showed that the proposed model could be a viable alternative to reduce logistics costs and demonstrated how the model can be a financially preferred alternative than individual investments to leverage resources capacity expansions. Furthermore, for a practical instance, the work shows the potential of JRP models to help decision-makers to better understand the impacts of fleet renewal and inventory replenishment decisions over the cost and CO2 emissions.DoctoradoDoctor en Ingeniería Industria

Service Inventory Management : Solution techniques for inventory systems without backorders

Koole, G.M. [Promotor]Vis, I.F.A. [Copromotor

Start-up manufacturing firms: operations for survival

Start-up firms play an important role in the economy. Statistics show that a large percent of start-up firms fail after few years of establishment. Raising capital, which is crucial to success, is one of the difficulties start-up firms face. This Ph.D thesis aims to draw suggestions for start-up firm survival from mathematical models and numerical investigations. Instead of the commonly held profi t maximizing objective, this thesis assumes that a start-up firm aims to maximize its survival probability during the planning horizon. A firm fails if it runs out of capital at a solvency check. Inventory management in manufacturing start-up firms is discussed further with mathematical theories and numerical illustrations, to gain insight of the policies for start-up firms. These models consider specific inventory problems with total lost sales, partial backorders and joint inventory-advertising decisions. The models consider general cost functions and stochastic demand, with both lead time zero and one cases. The research in this thesis provides quantitative analysis on start-up firm survival, which is new to the literature. From the results, a threshold exists on the initial capital requirement to start-up firms, above which the increase of capital has little effect on survival probability. Start-up firms are often risk-averse and cautious about spending. Entering the right niche market increases their chance of survival, where the demand is more predictable, and start-ups can obtain higher backorder rates and product price. Sensitivity tests show that selling price, purchasing price and overhead cost have the most impact on survival probability. Lead time has a negative effect on start-up firms, which can be offset by increasing the order frequent. Advertising, as an investment in goodwill, can increase start-up firms' survival. The advertising strategies vary according to both goodwill and inventory levels, and the policy is more flexible in start-up firms. Externally, a slightly less frequency solvency check gives start-up firms more room for fund raising and/or operation adjustment, and can increase the survival probability. The problems are modelled using Markov decision processes, and numerical illustrations are implemented in Java

Models for Retail Inventory Management with Demand Learning

Matching supply with demand is key to success in the volatile and competitive retail business. To this end, retailers seek to improve their inventory decisions by learning demand from various sources. More interestingly, retailers' inventory decisions may in turn obscure the demand information they observe. This dissertation examines three problems in retail contexts that involve interactions between inventory management and demand learning. First, motivated by the unprecedented adverse impact of the 2008 financial crisis on retailers, we consider the inventory control problem of a firm experiencing potential demand shifts whose timings are known but whose impacts are not known. We establish structural results about the optimal policies, construct novel cost lower bounds based on particular information relaxations, and propose near-optimal heuristic policies derived from those bounds. We then consider the optimal allocation of a limited inventory for fashion retailers to conduct "merchandise tests" prior to the main selling season as a demand learning approach. We identity a key tradeoff between the quantity and quality of demand observations. We also find that the visibility into the timing of each sales transaction has a pivotal impact on the optimal allocation decisions and the value of merchandise tests. Finally, we consider a retailer selling an experiential product to consumers who learn product quality from reviews generated by previous buyers. The retailer maximizes profit by choosing whether to offer the product for sale to each arriving customer. We characterize the optimal product offering policies to be of threshold type. Interestingly, we find that it can be optimal for the firm to withhold inventory and not to offer the product even if an arriving customer is willing to buy for sure. We numerically demonstrate that personalized offering is most valuable when the price is high and customers are optimistic but uncertain about product quality.Doctor of Philosoph