A Single-Product Inventory Model for Multiple Demand Classes

We consider a single-product inventory system that serves multiple demand classes, which differ in their shortage costs or service level requirements. We assume a critical-level control policy, and show the equivalence between this inventory system and a serial inventory system. Based on this equivalence, we develop a model for cost evaluation and optimization, under the assumptions of Poisson demand, deterministic replenishment lead-time, and a continuous-review (Q, R) policy with rationing. We propose a computationally-efficient heuristic and develop a bound on its performance. We provide a numerical experiment to show the effectiveness of the heuristic and the value from a rationing policy. Finally, we describe how to extend the model to permit service times, and to embed within a multi-echelon setting

On stock rationing policies for continuous review inventory systems

Cataloged from PDF version of article.Rationing is an inventory policy that allows prioritization of different demand classes. In this thesis, we analyze the stock rationing policies for continuous review systems. We clarify some of the ambiguities present in the current literature. Then, we propose a new method for the exact analysis of lot-for-lot inventory systems with backorders under rationing policy. We show that if such an inventory system is sampled at multiples of supply leadtime, the state of the system evolves according to a Markov chain. We provide a recursive procedure to generate the transition probabilities of the embedded Markov chain. It is possible to obtain the steady-state probabilities of interest with desired accuracy by considering a truncated version of the chain. Finally, we propose a dynamic rationing policy, which makes use of the information on the status of the outstanding replenishment orders. We conduct a simulation study to evaluate the performance of the proposed policy.Bulut, ÖnderM.S

Using imperfect advance demand information in ordering and rationing decisions

Cataloged from PDF version of article.In this paper, we consider an inventory problem with two demand classes having different priorities. The appropriate policy of rationing the available stock, i.e. reserving some stock for meeting prospective future demand of preferred customers at the expense of deliberately losing some of the currently materialized demand of lower demand class(es), relies on the estimation of the future demand. Utilizing current signals on future demand, which we refer to as imperfect advance demand information (ADI), decreases uncertainty on future demand and may help to make better decisions on when to start rejecting lower class demand. We develop a model that incorporates imperfect ADI with inventory ordering (replenishment) decision and rationing available stock. In a two-period setting, we show some structural properties, solve the rationing problem, and propose solution methods based on Monte Carlo simulation for the ordering problem. We conduct numerical tests to measure the impact of system parameters on the expected value of imperfect ADI, and provide useful managerial insights. (C) 2009 Elsevier B.V. All rights reserved

E-Fulfillment and Multi-Channel Distribution – A Review

This review addresses the specific supply chain management issues of Internet fulfillment in a multi-channel environment. It provides a systematic overview of managerial planning tasks and reviews corresponding quantitative models. In this way, we aim to enhance the understanding of multi-channel e-fulfillment and to identify gaps between relevant managerial issues and academic literature, thereby indicating directions for future research. One of the recurrent patterns in today’s e-commerce operations is the combination of ‘bricks-and-clicks’, the integration of e-fulfillment into a portfolio of multiple alternative distribution channels. From a supply chain management perspective, multi-channel distribution provides opportunities for serving different customer segments, creating synergies, and exploiting economies of scale. However, in order to successfully exploit these opportunities companies need to master novel challenges. In particular, the design of a multi-channel distribution system requires a constant trade-off between process integration and separation across multiple channels. In addition, sales and operations decisions are ever more tightly intertwined as delivery and after-sales services are becoming key components of the product offering.Distribution;E-fulfillment;Literature Review;Online Retailing

Pooling and polling : creation of pooling in inventory and queueing models

The subject of the present monograph is the ‘Creation of Pooling in Inventory and Queueing Models’. This research consists of the study of sharing a scarce resource (such as inventory, server capacity, or production capacity) between multiple customer classes. This is called pooling, where the goal is to achieve cost or waiting time reductions. For the queueing and inventory models studied, both theoretical, scientific insights, are generated, as well as strategies which are applicable in practice. This monograph consists of two parts: pooling and polling. In both research streams, a scarce resource (inventory or server capacity, respectively production capacity) has to be shared between multiple users. In the first part of the thesis, pooling is applied to multi-location inventory models. It is studied how cost reduction can be achieved by the use of stock transfers between local warehouses, so-called lateral transshipments. In this way, stock is pooled between the warehouses. The setting is motivated by a spare parts inventory network, where critical components of technically advanced machines are kept on stock, to reduce down time durations. We create insights into the question when lateral transshipments lead to cost reductions, by studying several models. Firstly, a system with two stock points is studied, for which we completely characterize the structure of the optimal policy, using dynamic programming. For this, we formulate the model as a Markov decision process. We also derived conditions under which simple, easy to implement, policies are always optimal, such as a hold back policy and a complete pooling policy. Furthermore, we identified the parameter settings under which cost savings can be achieved. Secondly, we characterize the optimal policy structure for a multi-location model where only one stock point issues lateral transshipments, a so-called quick response warehouse. Thirdly, we apply the insights generated to the general multi-location model with lateral transshipments. We propose the use of a hold back policy, and construct a new approximation algorithm for deriving the performance characteristics. It is based on the use of interrupted Poisson processes. The algorithm is shown to be very accurate, and can be used for the optimization of the hold back levels, the parameters of this class of policies. Also, we study related inventory models, where a single stock point servers multiple customers classes. Furthermore, the pooling of server capacity is studied. For a two queue model where the head-of-line processor sharing discipline is applied, we derive the optimal control policy for dividing the servers attention, as well as for accepting customers. Also, a server farm with an infinite number of servers is studied, where servers can be turned off after a service completion in order to save costs. We characterize the optimal policy for this model. In the second part of the thesis polling models are studied, which are queueing systems where multiple queues are served by a single server. An application is the production of multiple types of products on a single machine. In this way, the production capacity is pooled between the product types. For the classical polling model, we derive a closedform approximation for the mean waiting time at each of the queues. The approximation is based on the interpolation of light and heavy traffic results. Also, we study a system with so-called smart customers, where the arrival rate at a queue depends on the position of the server. Finally, we invent two new service disciplines (the gated/exhaustive and the ??-gated discipline) for polling models, designed to yield ’fairness and efficiency’ in the mean waiting times. That is, they result in almost equal mean waiting times at each of the queues, without increasing the weighted sum of the mean waiting times too much

Continuous time control of make-to-stock production systems

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 2010.Thesis (Ph. D.) -- Bilkent University, 2010.Includes bibliographical references leaves 117-120.We consider the problem of production control and stock rationing in a make-tostock production system with multiple servers –parallel production channels--, and several customer classes that generate independent Poisson demands. At decision epochs, in conjunction with the stock allocation decision, the control specifies whether to increase the number of operational servers or not. Previously placed production orders cannot be cancelled. We both study the cases of exponential and Erlangian processing times and model the respective systems as M /M /s and M /Ek /s make-to-stock queues. We characterize properties of the optimal cost function, and of the optimal production and rationing policies. We show that the optimal production policy is a state-dependent base-stock policy, and the optimal rationing policy is of state-dependent threshold type. For the M /M /s model, we also prove that the optimal ordering policy transforms into a bang-bang type policy when we relax the model by allowing order cancellations. Another model with partial ordercancellation flexibility is provided to fill the gap between the no-flexibility and the full-flexibility models. Furthermore, we propose a dynamic rationing policy for the systems with uncapacitated replenishment channels, i.e., exogenous supply systems. Such systems can be modeled by letting s --the number of replenishment channels-- go to infinity. The proposed policy utilizes the information on the status of the outstanding replenishment orders. This work constitutes a significant extension of the literature in the area of control of make-to-stock queues, which considers only a single server. We consider an arbitrary number of servers that makes it possible to cover the spectrum of the cases from the single server to the infinite servers. Hence, our work achieves to analyze both the exogenous and endogenous supply leadtimes.Bulut, ÖnderPh.D