A Stochastic Dynamic Programming Approach to Revenue Management in a Make-to-Stock Production System

In this paper, we consider a make-to-stock production system with known exogenous replenishments and multiple customer classes. The objective is to maximize profit over the planning horizon by deciding whether to accept or reject a given order, in anticipation of more profitable future orders. What distinguishes this setup from classical airline revenue management problems is the explicit consideration of past and future replenishments and the integration of inventory holding and backlogging costs. If stock is on-hand, orders can be fulfilled immediately, backlogged or rejected. In shortage situations, orders can be either rejected or backlogged to be fulfilled from future arriving supply. The described decision problem occurs in many practical settings, notably in make-to-stock production systems, in which production planning is performed on a mid-term level, based on aggregated demand forecasts. In the short term, acceptance decisions about incoming orders are then made according to stock on-hand and scheduled production quantities. We model this problem as a stochastic dynamic program and characterize its optimal policy. It turns out that the optimal fulfillment policy has a relatively simple structure and is easy to implement. We evaluate this policy numerically and find that it systematically outperforms common current fulfillment policies, such as first-come-first-served and deterministic optimization.revenue management;advanced planning systems;make-to-stock production;order fulfillment

Optimal Structural Results for Assemble-to-Order Generalized M-Systmes

Cataloged from PDF version of article.We consider an assemble-to-order generalized M-system with multiple components and multiple products, batch ordering of components, random lead times, and lost sales. We model the system as an in nite-horizon Markov decision process and seek an optimal control policy, which speci es when a batch of components should be produced and whether an arriving demand for each product should be satis ed. To facilitate our analysis, we introduce new functional characterizations for convexity and submodularity with respect to certain non-unitary directions. These help us characterize optimal inventory replenishment and allocation policies under a mild condition on component batch sizes via a new type of policy: lattice-dependent base-stock and lattice-dependent rationing

A Stochastic Dynamic Programming Approach to Revenue Management in a Make-to-Stock Production System

In this paper, we consider a make-to-stock production system with known exogenous replenishments and multiple customer classes. The objective is to maximize profit over the planning horizon by deciding whether to accept or reject a given order, in anticipation of more profitable future orders. What distinguishes this setup from classical airline revenue management problems is the explicit consideration of past and future replenishments and the integration of inventory holding and backlogging costs. If stock is on-hand, orders can be fulfilled immediately, backlogged or rejected. In shortage situations, orders can be either rejected or backlogged to be fulfilled from future arriving supply. The described decision problem occurs in many practical settings, notably in make-to-stock production systems, in which production planning is performed on a mid-term level, based on aggregated demand forecasts. In the short term, acceptance decisions about incoming orders are then made according to stock on-hand and scheduled production quantities. We model this problem as a stochastic dynamic program and characterize its optimal policy. It turns out that the optimal fulfillment policy has a relatively simple structure and is easy to implement. We evaluate this policy numerically and find that it systematically outperforms common current fulfillment policies, such as first-come-first-served and deterministic optimization

Admission control for a capacitated supply system with real-time replenishment information

Control towers can provide real-time information on logistic processes to support decision making. The question however, is how to make use of it and how much it may save. We consider this issue for a company supplying expensive spare parts and which has limited production capacity. Besides deciding on base stock levels, it can accept or reject customers. The real-time status information is captured by a k-Erlang distributed replenishment lead time. First we model the problem with patient customers as an infinite-horizon Markov decision process and minimize the total expected discounted cost. We prove that the optimal policy can be characterized using two thresholds: a base work storage level that determines when ordering takes place and an acceptance work storage level that determines when demand of customers should be accepted. In a numerical study, we show that using real-time status information on the replenishment item and adopting admission control can lead to significant cost savings. The cost savings are highest when the optimal admission threshold is a work storage level with a replenishment item halfway in process. This finding is different from the literature, where it is stated that the cost increase of ignoring real-time information is negligible under either the lost sales or the backordering case. Next we study the problem where customers are of limited patience. We find that the optimal admission policy is not always of threshold type. This is different from the literature which assumes an exponential production lead time.</p

A dynamic rationing policy for continuous-review inventory systems

Stock rationing is an inventory policy that allows differential treatment of customer classes without using separate inventories. In this paper, we propose a dynamic rationing policy for continuous-review inventory systems, which utilizes the information on the status of the outstanding replenishment orders. For both backordering and lost sales environments, we conduct simulation studies to compare the performance of the dynamic policy with the static critical level and the common stock policies and quantify the gain obtained. We propose two new bounds on the optimum dynamic rationing policy that enables us to tell how much of the potential gain the proposed dynamic policy realizes. We discuss the conditions under which stock rationing - both dynamic and static - is beneficial and assess the value of the dynamic policy. © 2009 Elsevier B.V. All rights reserved

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

Dynamic shipments of inventories in shared warehouse and transportation networks

In shared warehouse and transportation networks, dynamic shipments of inventories are carried out based on up-to-date inventory information. This paper studies the effect of network structures on optimal decision-making. We propose a discrete time modeling framework with stochastic demand, capturing a wide variety of network structures. Using Markov decision processes, we obtain optimal order and dynamic shipment decisions for small networks. We compare optimal solutions of different four-node network structures. Results indicate product characteristics significantly influence the effectiveness of network structures. Surprisingly, two-echelon networks are occasionally costlier than any other network. Moreover, dynamic shipments yield considerable gains over static shipments

Dynamic inventory rationing for systems with multiple demand classes

Ph.DDOCTOR OF PHILOSOPH