Xue-Ming Yuan

Stability of Data Networks: Stationary and Bursty Models

This paper studies stability of network models that capture macroscopic features of data communication networks, including the Internet. The network model consists of a set of links and a set of possible routes that are fixed subsets of links. A connection is dynamically established along one of the routes to transmit data as requested and is terminated after the transmission is over. The transmission bandwidth of a link is dynamically allocated, according to specific bandwidth allocation policy, to ongoing connections that traverse the link. A network model is said to be stable under a given bandwidth allocation policy if, roughly, the number of ongoing connections in the network will not blow up over time. We consider a stationary and a bursty network model; the former assumes stochastically stationary arrival processes of connections as did many theoretical studies, while the latter allows more realistic bursty and correlated arrival processes. For both models under a necessary stability condition (i.e., the average offered transmission load on each link is within its bandwidth capacity), we show that the proportionally fair, the minimum potential delay, the max-min fair, and a class of utility-maximizing bandwidth allocation policies ensure network model stability, while some priority-oriented and maximum throughput policies do not. Interestingly, the bandwidth allocation policy that maximizes the arctan(·) utility ensures the stability of the stationary model butnot the bursty model. This raises a serious concern about the current practice in the Internet protocol design, since such a policy is thought of as a good approximation of one of the most widely used TCP in the Internet.

Modeling returns of merchandise in an inventory system

Returns of merchandise occur commonly in the retail and rental businesses. This paper presents a new continuous review (s, S) inventory system with returns. The system is fairly complicated as its performance is a function of important factors such as demand rate, return time, return rate and replenishment frequency. Based on a Markovian approach, we derive essential operating characteristics of the system, and propose an algorithm to search for the optimal replenishment parameters. The results enable us to obtain valuable insights into the rental system, such as the impact of partial returns.ZusammenfassungSowohl im Einzelhandel als auch im Leasinggeschäft kommen Rückgaben von Gütern häufig vor. Diese Arbeit stellt ein (s, S)-Lagerhaltungssystem mit kontinuierlicher Bestandsüberwachung und solchen Rückflüssen vor. Das System ist relativ kompliziert, da sein Verhalten von vielen Einflußfaktoren wie Nachfragerate, Rückgabezeit, Rückflußrate und Wiederbeschaffungshäufigkeit abhängt. Unter Verwendung eines Markov-Ansatzes werden wesentliche Kenngrößen des Systems abgeleitet und ein Algorithmus zur Bestimmung der optimalen Dispositionsparameter vorgeschlagen. Die Ergebnisse ermöglichen wertvolle Einblicke in das Sytem wie z.B. in Hinblick auf den Einfluß partieller Rückgaben.

Optimal inventory policy with supply uncertainty and demand cancellation

We consider a periodic review model where the firm manages its inventory under supply uncertainty and demand cancellation. We show that because of supply uncertainty, the optimal inventory policy has the structure of re-order point type. That is, we order if the initial inventory falls below this re-order point, otherwise we do not order. This is in contrast to the work of Yuan and Cheung (2003) who prove the optimality of an order up to policy in the absence of supply uncertainty. We also investigate the impact of supply uncertainty and demand cancellation on the performance of the supply chain. Using our model, we are able to quantify the importance of reducing the variance of either the distribution of yield or the distribution of demand cancellation. The single, multiple periods and the infinite horizon models are studied.

Optimal warranty policies for systems with imperfect repair

We investigate a system whose basic warranty coverage is minimal repair up to a specified warranty length. An additional service is offered whereby first failure is restored up to the consumers chosen level of repair. The problem is studied under two system replacement strategies: periodic maintenance before and after warranty. It turns out that our model generalizes the model of Rinsaka and Sandoh [K. Rinsaka, H. Sandoh, A stochastic model with an additional warranty contract, Computers and Mathematics with Applications 51 (2006) 179-188] and the model of Yeh et al. [R.H. Yeh, M.Y. Chen, C.Y. Lin, Optimal periodic replacement policy for repairable products under free-repair warranty, European Journal of Operational Research 176 (2007) 1678-1686]. We derive the optimal maintenance period and optimal level of repair based on the structures of the cost function and failure rate function. We show that under certain assumptions, the optimal repair level for additional service is an increasing function of the replacement time. We provide numerical studies to verify some of our results.

Coordinated replenishments in inventory systems with correlated demands

Abstract Demand correlation among different inventory items is common in real-life multi-item inventory systems. However, this phenomenon has not received sufficient attention in the existing inventory literature. In this paper, we construct a Markovian model for a two-item inventory system with correlated demands and coordinated replenishments. We obtain an expression for the long-run total cost per unit of time under the can-order replenishment policy. For the scenario with independent replenishments, the explicit formula for the long-run total cost per time unit can be derived, which leads to analytical solutions for the optimal policies. We then present numerical examples of the optimal can-order policies and discuss some managerial insights regarding demand correlation and replenishment coordination. Our numerical results also suggest a possible heuristic method for obtaining can-order replenishment policies for multi-item systems.

Performance analysis of assembly systems with unreliable machines and finite buffers

Abstract An unreliable assembly system is studied in which different types of components are processed by two separate work centers before merging to an assembly station with random breakdown. Blocking at the work centers and starvation at the assembly station may occur because of finite buffer sizes and uncertainties in job arriving times and processing/assembly times. We derive the system stability condition, and obtain formulas for the system state probabilities, blocking probabilities, starvation probability, stockout probability, system availability in the steady state. We also obtain the distributions of blocking times and first failure times, respectively. Through numerical examples, we elaborate on the monotonous properties of the performance measures, and draw the insights into the impacts of the system parameters on its various performance indices, which provide important guidance for design of assembly systems.

Analysis of a software focused products and service supply chain

In this paper, we study a software-focused products and service supply chain based on the practice of two leading electronic manufacturing services providers in the world and their major corporate clients. We discuss the common and unique issues that a software-focused supply chain has compared with a traditional supply chain. We also indicate the research challenges and opportunities for a software-focused supply chain

Optimal Inventory Policy for Systems with Demand Cancellations

We analyze a periodic review inventory model in which all demands have to be reserved with a one-period leadtime. During the reservation period, some of the reservations may be cancelled. As a result, the reservation information is not perfectly reliable. Our objective is to determine the optimal replenishment policy for this inventory model. We show that the cost function is convex and the optimal policy is a reorder-up-to type of policy. This policy stipulates that unless the initial on-hand inventory is lower than the reorder-up-to level, an order should be made to raise the inventory level to the reorder-up-to level. Furthermore, this reorder-up-to level is a function of the amount of reserved demand. The single- and multiple-period cases are studied. Finally, we consider the infinite-horizon case and show that results from the finite-horizon case converge to the infinite-horizon case. The expression for solving the optimal policy parameter is also derived.

Throughput, flow times, and service level in an unreliable assembly system

Abstract This paper considers an unreliable assembly network where different types of components are processed by two separate work centers before being merged at an assembly station. The operation complexity of the system is a result of finite inter-station buffers, uncertain service times, and random breakdowns that lead to blocking at the work centers and starvation at the assembly station. The objective of this study is to gain an understanding of the behavior of such systems so that we can find a way to maximize the system throughput while maintaining the required customer service level. By constructing appropriate Markov processes, we obtain the probability distribution of the production flow time and derive formulas for throughput, the loss probability of type-2 workpieces, and the mean flow time. We present expressions for average work-in-process (WIP) and study their monotone properties. Using the distribution of the flow time, a customer service level can be defined and computed. We then formulate a system optimization model that can be used to maximize the throughput while maintaining an acceptable service level.

A network prototype for integrated production-distribution planning with non-multi-functional plants

This paper proposes a two-echelon network prototype for integrated production and distribution planning where non-multi-functional plants supply multiple types of products with limited quantities to the customers via capacitated warehouses. Four variations of the prototype, formulated as individual mixed integer programming models, are solved using the branch and bound algorithms by numerical experiments to examine the cost implications of production-distribution strategies involving single-sourcing constraints on different levels of the supply chain. Further discussions on the practicality and versatility of the proposed prototype (i.e. its ability to consider different facility locations, specialised capabilities of individual plants, safety stock levels and demand characteristics) illustrate the usefulness of the prototype to industry practitioners when making strategic and/or tactical decisions.