Base-stock policies with reservations

All intensively studied and widely applied inventory control policies satisfy demand in accordance with the First-Come-First-Served (FCFS) rule, whether this demand is in backorder or not. Interestingly, this rule is sub-optimal when the fill-rate is constrained or when the backorder cost structure includes fixed costs per backorder and costs per backorder per unit time. In this paper we study the degree of sub-optimality of the FCFS rule for inventory systems controlled by the well-known base-stock policy. As an alternative to the FCFS rule, we propose and analyze a class of generalized base-stock policies that reserve some maximum number of items in stock for future demands, even if backorders exist. Our analytic results and numerical investigations show that such alternative stock reservation policies are indeed very simple and considerably improve either the fillrate or reduce the total cost, without having much effect on the backorder level

The selective use of emergency shipments for service-contract differentiation

Suppliers of capital goods increasingly offer performance-based service contracts with customer-specific service levels. We use selective emergency shipments of spare parts to differentiate logistic performance: We apply emergency shipments in out-of-stock situations for combinations of parts and customer classes that yield service levels close to the class-specific targets. We develop two heuristics to solve this problem. An extensive numerical experiment reveals average cost savings of 4.4% compared to the one-size-fits-all approach that is often used in practice. It is best to combine our policy with critical levels, which yields an average cost saving of 13.9%

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

Optimal control policies for make-to-stock production systems with several production rates and demand classes

Master'sMASTER OF ENGINEERIN

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