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

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

Dynamic inventory rationing for systems with multiple demand classes

Ph.DDOCTOR OF PHILOSOPH

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

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 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

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%

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