Strategies for a centralized single product multiclass M/G/1 make-to-stock queue

Make-to-stock queues are typically investigated in the M/M/1 settings. For centralized single-item systems with backlogs, the multilevel rationing (MR) policy is established as optimal and the strict priority (SP) policy is a practical compromise, balancing cost and ease of implementation. However, the optimal policy is unknown when service time is general, i.e., for M/G/1 queues. Dynamic programming, the tool commonly used to investigate the MR policy in make-to-stock queues, is less practical when service time is general. In this paper we focus on customer composition: the proportion of customers of each class to the total number of customers in the queue. We do so because the number of customers in M/G/1 queues is invariant for any nonidling and nonanticipating policy. To characterize customer composition, we consider a series of two-priority M/G/1 queues where the first service time in each busy period is different from standard service times, i.e., this first service time is exceptional. We characterize the required exceptional first service times and the exact solution of such queues. From our results, we derive the optimal cost and control for the MR and SP policies for M/G/1 make-to-stock queues

Priority allocation decisions in large scale MTO/MTS multi-product manufacturing systems : Technical report

In this paper, the authors consider a single stage multi-product manufacturing facility producing a large number of end-products for delivery within a service constraint for the customer lead-time. The manufacturing facility is modeled as a multi-product, multi-priority queuing system. In order to reduce inventory costs, an e±cient priority allocation between items consists in producing some items according to a Make-To-Stock (MTS) policy and others according to a Make-To-Order (MTO)policy epending on their features (costs, required lead-time, demand rates). The authors propose a general optimization procedure that gives a near-optimal °ow control (MTO or MTS) to associate with each product and the corresponding near-optimal priority strategy. We illustrate e±ciency of our procedure via several examples and by a numerical analysis. In addition, we show numerically that a small number of priority classes is su±cient to obtain near-optimal performances.Make-to-Stock (MTS); Make-to-Order (MTO); Priority allocation; Scheduling rule; Heterogeneous multi-product queuing system

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

Revenue Management and Demand Fulfillment: Matching Applications, Models, and Software

Recent years have seen great successes of revenue management, notably in the airline, hotel, and car rental business. Currently, an increasing number of industries, including manufacturers and retailers, are exploring ways to adopt similar concepts. Software companies are taking an active role in promoting the broadening range of applications. Also technological advances, including smart shelves and radio frequency identification (RFID), are removing many of the barriers to extended revenue management. The rapid developments in Supply Chain Planning and Revenue Management software solutions, scientific models, and industry applications have created a complex picture, which appears not yet to be well understood. It is not evident which scientific models fit which industry applications and which aspects are still missing. The relation between available software solutions and applications as well as scientific models appears equally unclear. The goal of this paper is to help overcome this confusion. To this end, we structure and review three dimensions, namely applications, models, and software. Subsequently, we relate these dimensions to each other and highlight commonalities and discrepancies. This comparison also provides a basis for identifying future research needs.Manufacturing;Revenue Management;Software;Advanced Planning Systems;Demand Fulfillment

Revenue management models in the manufacturing industry

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2005.Includes bibliographical references (p. 107-110).In recent years, many manufacturing companies have started exploring innovative revenue management technologies in an effort to improve their operations and ultimately their bottom lines. Methods such as differentiating customers based on their sensitivity to price and delays are employed by firms to increase their profits. These developments call for models that have the potential to radically improve supply chain efficiencies in much the same way that revenue management has changed the airline industry. In this dissertation, we study revenue management models where customers can be separated into different classes depending on their sensitivity to price, lead time, and service. Specifically, we focus on identifying effective models to coordinate production, inventory and admission controls in face of multiple classes of demand and time- varying parameters. We start with a single-class-customer problem with both backlogged and discretionary sales. Demand may be fulfilled no later than N periods with price discounts if the inventory is not available. If profitable, demand may be rejected even if the inventory is still available.(cont.) For this problem we analyze the structure of the optimal policy and show that it is characterized by three state-independent control parameters: the produce-up-to level (S), the reserve-up-to level (R), and the backlog-up-to level (B). At the beginning of each period, the manufacturer will produce to bring the inventory level up to S or to the maximum capacity; during the period, s/he will set aside R units of inventory for the next period, and satisfy some customers with the remaining inventory, if expected future profit is higher; otherwise, s/he will satisfy customers with the inventory and backlog up to B units of demands. Then, we analyze a single-product, two-class-customer model in which demanding (high priority) customers would like to receive products immediately, while other customers are willing to wait in order to pay lower prices. For this model, we provide a heuristic policy characterized by three threshold levels: S, R, B.(cont.) In this policy, during each period, the manufacturer will set aside R units of inventory for the next period, and satisfy some high priority customers with the remaining inventory, if expected future profit is higher; otherwise, s/he will satisfy as many of the high priority customers as possible and backlog up to B units of lower priority customers. Finally, we examine production, rationing, and admission control policies in manufacturing systems with both make-to-stock(MTS) and make-to-order(MTO) products. Two models are analyzed. In the first model, which is motivated by the automobile industry, the make-to-stock product has higher priority than the make-to-order product. In the second model, which is motivated by the PC industry, the manufacturer gives higher priority to the make-to-order product over the make-to-stock product. We characterize the optimal production and order admission policies with linear threshold levels. We also extend those results to problems where low-priority backorders can be canceled by the manufacturer, as well as to problems with multiple types of make-to-order products.by Tieming Liu.Ph.D

Computation of order and volume fill rates for a base stock inventory control system with heterogeneous demand to investigate which customer class gets the best service

We consider a base stock inventory control system serving two customer classes whose demands are generated by two independent compound renewal processes. We show how to derive order and volume fill rates of each class. Based on assumptions about first order stochastic dominance we prove when one customer class will get the best service. That theoretical result is validated through a series of numerical experiments which also reveal that it is quite robust.Base stock policy; service measures; two customer classes; compound renewal processes

An overview of inventory systems with several demand classes

In this chapter we discuss inventory systems where several demand classes may be distinguished. In particular, we focus on single-location inventory systems and we analyse the use of a so-called critical level policy. With this policy some inventory is reserved for high-priority demand. A number of practical examples where several demand classes naturally arise are presented, and the implications and modelling of the critical level policy in distribution systems are discussed. Finally, an overview of the literature on inventory systems with several demand classes is given

Inventory rationing in an (s, Q) inventory model with lost sales a two demand classes

Whenever demand for a single item can be categorized into classes of different priority, an inventory rationing policy should be considered. In this paper we analyse a continuous review (s,Q) model with lost sales and two demand classes. A so-called critical level policy is applied to ration the inventory among the two demand classes. With this policy, low--priority demand is rejected in anticipation of future high--priority demand whenever the inventory level is at or below a prespecified critical level. For Poisson demand and deterministic lead times, we present an exact formulation of the average inventory cost. A simple optimization procedure is presented, and in a numerical study we compare the optimal rationing policy with a policy where no distinction between the demand classes is made. The benefit of the rationing policy is investigated for various cases and the results show that significant cost reductions can be obtained

Finding optimal policies in the (S - 1, S ) lost sales inventory model with multiple demand classes

This paper examines the algorithms proposed in the literature forfinding good critical level policies in the (S-1,S) lost salesinventory model with multiple demand classes. Our main result isthat we establish guaranteed optimality for two of thesealgorithms. This result is extended to different resupplyassumptions, such as a single server queue. As a corollary, weprovide an alternative proof of the optimality of critical levelpolicies among the class of all policies.inventory;customer differentiation;multiple demand classes;rationing lost sales;stochastic dynamic programming