Optimal Pricing Strategies and Customers’ Equilibrium Behavior in an Unobservable M/M/1 Queueing System with Negative Customers and Repair

This work investigates the optimal pricing strategies of a server and the equilibrium behavior of customers in an unobservable M/M/1 queueing system with negative customers and repair. In this work, we consider two pricing schemes. The first is termed the ex-post payment scheme, where the server charges a price that is proportional to the time spent by a customer in the system. The second scheme is the ex-ante payment scheme, where the server charges a flat rate for all services. Based on the reward-cost structure, the server (or system manager) should make optimal pricing decisions in order to maximize its expected profit per time unit in each payment scheme. This study also investigates equilibrium joining/balking behavior under the server’s optimal pricing strategies in the two pricing schemes. We show, given a customer’s equilibrium, that the two pricing schemes are perfectly identical from an economic point of view. Finally, we illustrate the effect of several system parameters on the optimal joining probabilities, the optimal price, and the equilibrium behavior via numerical examples

Essays in competition with product differentiation and bargaining in markets

The fourth essay uses bargaining theory and compares the outcome of a negotiation in two differently organized markets. In the first market, sellers simultaneously offer their good or service for sale. In the second market, sellers queue and offer their good or service sequentially for sale. Relevant markets are the taxi market and the inland waterways transport markets.

Stability Problems for Stochastic Models: Theory and Applications II

Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

Strategic behaviour in queueing systems in alternating environment

Σε αυτήν την εργασία μελετάμε τη στρατηγική συμπεριφορά πελατών που φθάνουν σε ένα σύστημα αναμονής το οποίο εξελίσσεται σε εναλλασσόμενο περιβάλλον, δηλαδή σε ένα σύστημα που ο ρυθμός άφιξης πελατών αλλά και ο ρυθμός εξυπηρέτησης μεταβάλλεται. Εισάγοντας μια δομή αμοιβής-κόστους στο σύστημα, εξετάζουμε τη συμπεριφορά των πελατών όταν τους επιτρέπεται να αποφασίσουν για τις ενέργειές τους μέσα στο σύστημα. Χρησιμοποιώντας εργαλεία από τη θεωρία παιγνίων και τη θεωρία ουρών μελετάμε τρία συστήματα αναμονής που εξελίσσονται σε εναλλασσόμενο περιβάλλον με σκοπό την εύρεση στρατηγικών ισορροπίας και κοινωνικά βέλτιστων στρατηγικών.In this essay we study the behaviour of customers in a queueing system in alternating environment, where the arrival and the service rate are alternating between two or more states. By inserting a reward-cost structure in the system we examine the arriving customers behaviour while they are free to decide their actions in the system. Using tools from game theory an queueing theory we study three queueing systems in alternating environment in order to find equillibrium and socially optimal strategies

On Production and Subcontracting Strategies for Manufacturers with Limited Capacity and Backlog-Dependent Demand

We study a manufacturing firm that builds a product to stock to meet a random demand. If there is a positive surplus of finished goods, the customers make their purchases without delay and leave. If there is a backlog, the customers are sensitive to the quoted lead time and some choose not to order if they feel that the lead time is excessive. A set of subcontractors, who have different costs and capacities, are available to supplement the firm's own production capacity. We derive a feedback policy that determines the production rate and the rate at which the subcontractors are requested to deliver products. The performance of the system when it is managed according to this policy is evaluated. The subcontractors represent a set of capacity options, and we calculate the values of these options

Capacity flexibility of a maintenance service provider in specialized and commoditized system environments

In the last decades, after-sales services have become increasingly important since service is a source of differentiation as well as a lucrative business opportunity due to the substantial amount of revenue that can be generated from the products in use throughout their life cycle. Following this trend, many after-sales service providers have emerged in the market or evolved as semi-autonomous units within the OEM (Original Equipment Manufacturer) companies. In this thesis, we focus on the maintenance aspect of after-sales services. We assume that a maintenance service provider (MSP) is running a repair shop in an environment with numerous operating systems that are prone to failure. The MSP is responsible for keeping all systems in an environment up and working. We mainly focus on two types of environments: 1) Specialized System Environment 2) Commoditized System Environment. The systems in the first environment are highly customized. They are designed and built specifically following the owners’ precise requirements. Defense systems, specific lithography systems, mission aircrafts or other advanced/complex, engineer-to-order capital goods are examples of such specialized systems. Due to the diversity of owners’ requirements, each system develops many unique characteristics, which make it hard, if not impossible, to find a substitute for the system, in the market as a whole. In the second environment, the systems are more generic in terms of their functionality. Trucks, cranes, printers, copy machines, forklifts, computer systems, cooling towers, some common medical devices (i.e. anesthesia, x-ray and ultrasound machines, etc…), power systems are examples of such more commoditized systems. Due to the more generic features of the owners’ requirements, it is easier to find a substitute for a system in the market, with more or less the same functionality, for short-term hiring purposes. Upon a system breakdown, the defective unit (system/subsystem) is sent to the repair shop. MSP is responsible for the repair and also liable for the costs related to the down time. In order to alleviate the down-time costs, there are chiefly two different downtime service strategies that the MSP can follow, depending on the environment the repair shop is operating in. In the specialized system environment, the MSP holds a spare unit inventory for the critical subsystem that causes most of the failures. The downtime service related decision in such a case would be the inventory level of the critical spare subsystems. On the other hand, in the commoditized system environment, rather than keeping a spare unit inventory, the MSP hires a substitute system from an agreed rental store/3rd party supplier. The downtime service related decision in this case is the hiring duration. Next to the above downtime service related decisions, repair shop’s capacity level is the other primary determinant of the systems’ uptime/availability. Since maintenance is a labor-intensive industry, the capacity costs constitute a large portion of the total costs. Increasing pressure on profitability and the growing role of External Labor Supplier Agencies motivate service provider firms to scrutinize the prospects and possibilities of capacity flexibility by using contingent workforce. For various reasons, flexible capacity practices in real life are often periodic, and the period length is both a decision parameter and a metric for flexibility. A shorter period length implies more frequent adapting possibilities and a better tailoring of the capacity. On the other hand, the flexible capacity cost per unit time is higher for shorter period lengths due to the compensating wage differentials, which models the relation between the wage rate and the unpleasantness, risk or other undesirable attributes of the job. Certainly, short period length in this context is an undesirable attribute for the flexible capacity resource, as it mandates the resource to switch tasks and to be ready/available more frequently, without the guarantee that s/he will be actually employed. Therefore, we propose several empirically testable functional forms for the cost rate of a flexible capacity unit, which are decreasing with the period length and, in the limit, approaches to the cost rate of a permanent capacity unit from above. In the light of discussions above, we investigate three different capacity modes in this dissertation: ¿ Fixed Capacity Mode: In this mode, all of the capacity is permanent and ready for use in the repair shop. This mode serves as a reference point in order to assess the benefits of other flexible capacity modes. The relevant capacity decision in this mode is the single capacity level of the repair shop. ¿ Periodic Two-Level Capacity Mode: In this mode, we assume two levels of repair shop capacity: permanent and permanent plus contingent capacity levels. The permanent capacity is always available in the system, whereas the deployment of the contingent capacity is decided at the start of each period based on the number of units waiting to be repaired in the shop. The relevant capacity decisions in this mode are the permanent and contingent capacity levels, the period length and the states (in terms of number of defective units waiting) where the contingent capacity is deployed. ¿ Periodic Capacity Sell-Back Mode: In this mode, the failed units are sent to the repair shop at regular intervals in time. Due to this admission structure, when the repair of all the defective units in the repair shop are completed in a period, it is known that no new defective parts will arrive to the shop at least until the start of the next period. This certainty in idle times allows for a contract, where the repair shop capacity is sold at a reduced price to the capacity agency where it is assigned to other tasks until the start of the next period. The original cost of the multi-skilled repair shop capacity per time unit is higher than the permanent capacity cost that is mentioned in previous modes due to the compensation factors such as additional skills, frequent task switching and transportation/transaction costs. Similar to the previous capacity mode, the compensation decreases with the length of the period length. The relevant capacity decisions in this mode are the capacity level and the period length. The primary goal of this thesis is to develop quantitative models and methods for taking optimal capacity decisions for the repair shop in the presence of the capacity modes described above and to integrate these decisions with the other downtime service decisions of the MSP for two different types of system environments (specialized vs. commoditized). After the introduction of the problem, concepts and literature review are given in Chapters 1. In Chapter 2, we focus on the use of capacity flexibility in the repair operations of the MSP in specialized system environment. The capacity related decisions are integrated with the decision on the stock level of the spare unit inventory for all three capacity modes. In Chapter 3 we investigate the same three capacity modes in a (partially) commoditized system environment, where hiring a substitute system for a pre-determined, uniform duration becomes the conventional method upon a failure. In this chapter the decision on the hiring duration is integrated with the other capacity related decisions. Then we provide some preliminary analysis and give the early results on the hybrid strategy where both "keeping stock" and "hire substitute" strategies are followed. Finally in Chapter 4, we summarize our results, give the conclusion and discuss the topics covered in this thesis with a brief exploration on the future research. The numerical results reveal that, in both specialized and commoditized system environments, substantial cost savings (up to 70%) can be achieved under periodic two-level capacity and periodic capacity sell-back modes compared to the fixed capacity mode. However, both period length and the compensation scheme of the capacity resources greatly influence the savings, even in some cost instances, flexible modes (periodic two-level and capacity sell-back) become less economical compared to the fixed capacity mode. Cost parameter instances in which each of the 3 capacity modes becomes cost-optimal, the characteristics of the cost savings and the sensitivity analysis of cost/policy parameters are investigated in both of the system environments in Chapter 2 and Chapter 3, respectively. In the commoditized system environment, under the same cost parameter settings, the hiring substitute from an external supplier for a fixed duration causes a better, more refined and certain control compared to keeping an inventory. Hybrid strategy, in which a substitute is hired after a stock-out instance, is applicable in commoditized as well as commoditizing (previously specialized systems that are in the ongoing commoditization process) system environments. Hybrid strategy outperforms both "only keeping stock" and "only hiring substitute" alternatives; however, in the commoditized system environment, a MSP may still have a proclivity to employ the "hiring substitute" strategy only, because it does not require any initial investment, which is convenient for SMEs. These issues will be explicated further in Chapter 5. We believe that the framework, the design and analysis of the problems addressed as well as the results and the insights obtained in this dissertation can help and motivate other researchers/practitioners to further investigate the cost saving prospects from capacity flexibility in maintenance service operations. We also anticipate that the commoditization framework described in this thesis will be increasingly useful in the future, since the commoditization of the parts/machines will be much more widespread, pushing all the after-sales service providers to compete on the efficiency of their operatio

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn

Stochastic Processes with Applications

Stochastic processes have wide relevance in mathematics both for theoretical aspects and for their numerous real-world applications in various domains. They represent a very active research field which is attracting the growing interest of scientists from a range of disciplines.This Special Issue aims to present a collection of current contributions concerning various topics related to stochastic processes and their applications. In particular, the focus here is on applications of stochastic processes as models of dynamic phenomena in research areas certain to be of interest, such as economics, statistical physics, queuing theory, biology, theoretical neurobiology, and reliability theory. Various contributions dealing with theoretical issues on stochastic processes are also included