Demand Classes Research Articles

Dynamic inventory rationing with mixed backorders and lost sales

Customers may react differently when stockouts occur. In this paper we investigate the rationing policy for an inventory system with a mixture of demand classes of backorder type and lost sales type. Since the penalty cost of backorders varies with time, the priorities of demand classes also alter with time. This totally changes the problem structure compared with the classic rationing models. A dynamic rationing policy is studied in this paper by considering the dynamics of demand priorities. A Markov decision model is developed to obtain the optimal dynamic rationing levels for multiple demand classes. The results indicate that between the priority switching points, rationing levels often exhibit different patterns. For lost sales demand classes, the rationing levels always decrease as the remaining time approaches to zero. For backorder demand classes, the rationing levels increase in some parts due to declining of the priorities. The rationing levels of all demand classes finally decline to zero to reduce the inventory holding cost. The application of dynamic rationing is further extended from a single period model to a multi-period (S,T) model where unit cost has to be included. The optimal ordering policy is proved to be a myopic base stock policy and the dynamic rationing policy in the single period model can still be applied with modified time-independent penalty costs for lost sales classes. To overcome the computational complexity, a heuristic dynamic rationing policy is introduced. Due to its good outcome, implementing such a heuristic dynamic rationing policy can be a practical solution for inventory system with mixed backorders and lost sales, in order to enhance the system performance.

Risk assessment of interruption times affecting domestic and non-domestic electricity customers

Legislation defined to protect domestic and non-domestic customers from long durations of interruptions includes additional requirements to system’s reliability-related performance that distribution network operators (DNOs) must consider in planning the operation and maintenance process of power supply systems. DNOs are required to restore the supply to interrupted customers that fall into “unprotected” customer class within a given period of time, otherwise penalties are applied. In order to meet these requirements, comprehensive strategies must be defined based on upfront analyses. Accordingly, this paper proposes a deterministic algorithm for estimating DNOs’ risk of experiencing interruptions with durations above imposed targets. Besides the Regulator-defined legislation, security of supply requirements are engaged in the development of the proposed methodology. Failure analysis of network components is used to identify interrupted customers that are grouped into power demand classes such that the duration of interruptions can be addressed following the security of supply requirements. Moreover, the penalty times defined by the Energy Regulator are engaged in the analysis and used as thresholds to quantify the penalty risk that DNOs are exposed to.The proposed methodology is applied to a typical UK distribution system, whose average reliability performance is also considered in the analysis.

Econometric and RBF Neural Network Models for Analyzing Automobile Demand in Iran

Identifying factors having influential impact on automobile demand estimation has become a primary concern for automobile industry. There has been substantial development modeling for automobile demand estimation. The Regression, Time series, CHAID and RBF neural network modeling types are proposed. In this study, automobile demand is classified into three classes. The first issue to be addressed by this study is to selecting the most appropriate modeling types in each class by comparing the actual demand and estimated demand in terms of Root-Mean-Square-Error (RMSE). Results indicate that modeling can be different for different classes of automobile demand. The second aim of this study is to identify the significant indicators for estimating automobile demand in each class of Iranian market.

Stochastic optimization model for order acceptance with multiple demand classes and uncertain demand/supply

This article considers an order acceptance problem in a make-to-stock manufacturing system with multiple demand classes in a finite time horizon. Demands in different periods are random variables and are independent of one another, and replenishments of inventory deviate from the scheduled quantities. The objective of this work is to maximize the expected net profit over the planning horizon by deciding the fraction of the demand that is going to be fulfilled. This article presents a stochastic order acceptance optimization model and analyses the existence of the optimal promising policies. An example of a discrete problem is used to illustrate the policies by applying the dynamic programming method. In order to solve the continuous problems, a heuristic algorithm based on stochastic approximation (HASA) is developed. Finally, the computational results of a case example illustrate the effectiveness and efficiency of the HASA approach, and make the application of the proposed model readily acceptable.

A heuristic for rationing inventory in two demand classes with backlog costs and a service constraint

We study the rationing policy in an inventory system with two demand classes and different service criteria for backorders. Due to the difference of customer values, system performance sometimes has to be measured with a mixture of penalty cost and service level in managing inventory. With a continuous review (r,Q) system, we develop a critical level rationing policy in which a threshold mechanism is adopted to allocate backorders when multiple outstanding orders exist. Due to the complexity of the problem, a heuristic is developed based on the principle that both demand classes are served with respective target service levels. We also introduce bounds so that the search ranges of decision variables become restrictive. The numerical examples indicate an excellent performance of our heuristic. In addition, when ordering cost is medium or high, the threshold clearing mechanism has the same results as the optimal one. When ordering cost is small (set to zero), different clearing mechanisms should be used depending on the priorities of demand classes. Further analysis indicates that transforming the service constraint into a cost parameter and then applying the existing algorithm will not be a good approach for this problem with mixed performance criteria. It either increases the costs or violates the service constraint. This study also shows the importance of applying rationing policy when high priority class has a low demand volume, target service levels between two classes have a large gap, or replenishment lead time is long. The results of this study should enhance our understanding of how to implement rationing policies in practice.

Cost analysis of an (S−1,S) inventory system with two demand classes and rationing

In this paper we analyze a continuous review, lost sales (S−1,S) inventory system with two demand classes—high priority and low priority. We compare two different policies—one where the two classes of customers are treated exactly alike and the other where a threshold rationing policy is used. We prove that under certain conditions there is a sub-optimal rationing policy which yields a lower cost for the supplier and higher service levels for both the high priority and low priority customers than the optimal policy where the two customers are treated alike.

An ant colony system for transportation user equilibrium analysis in congested networks

In this paper we present Ant Colony System for Traffic Assignment (ACS-TA) for the solution of deterministic and stochastic user equilibria (DUE and SUE, respectively) problems. DUE and SUE are two well known transportation problems where the transportation demand has to be assigned to an underlying network (supply in transportation terminology) according to single user satisfaction rather than aiming at some global optimum. ACS-TA turns the classic ACS meta-heuristic for discrete optimization into a technique for equilibrium computation. ACS-TA can be easily adapted to take into account all aspects characterizing the traffic assignment problem: multiple origin-destination pairs, link congestion, non-separable cost link functions, elasticity of demand, multiple classes of demand and different user cost models including stochastic cost perception. Applications to different networks, including a non-separable costs case study and the standard Sioux Falls benchmark, are reported. Results show good performance and wider applicability with respect to conventional approaches especially for stochastic user equilibrium computation.

Anticipated rationing policy for two demand classes under service level constraints

This paper considers a periodic-review, infinite-horizon, backorder inventory model with two demand classes, where a base-stock policy controls replenishment. We propose an easy-to-use rationing policy, which reserves inventory for future high priority demands by taking the coming delivery of the next period into consideration, hence called anticipated rationing policy. By applying a multidimensional Markov chain approach, we are able to evaluate system performance exactly. We also derive structural results and find optimal solutions for both α-service level and γ-service level constraint problems. A numerical comparison study demonstrates the effectiveness of anticipated rationing policy, where the well-known constant level rationing policy serves as the benchmark.

Use of advance demand information in multi-stage production-inventory systems with multiple demand classes

This paper considers three-stage production-inventory systems serving two customer classes, where only one class provides advance demand information and early order fulfilment is acceptable. We propose a new approach for production replenishment and order fulfilment in such systems that uses advance demand information for performance improvement. The approach combines the benefits of early fulfilment and Kanban-based pull systems. Simulation is used to establish the performance of the resulting policy vs. two existing policies, for a variety of production scenarios and cost structures. A lower bound on total cost is also established using a simulation-based procedure. In general, early fulfilment with one-for-one replenishment is shown to provide greater benefit than making items to order. Neither of the existing policies, however, was found to use advance demand information as effectively as the proposed approach, which outperformed the existing policies in every case considered. Additionally, the proposed policy has the advantage of both retaining its benefit at high levels of system utilisation and increasing benefit up to the maximum level of advance demand information provided.

Inventory Rationing Based on Different Shortage Cost: A Stable Inventory Demand Case

Abstract This paper discusses an inventory rationing system with a threshold in a relatively stable inventory demand environment. There are two different demand classes in this inventory system, prior demand and secondary demand, distinguished by different shortage cost. The inventory system functions as follow. When the inventory level is above the threshold, demands come from both classes are filled. Once the inventory level falls below the threshold, all demands come from secondary demand class are backordered, only prior demand would be served. Heuristic approach was used to solve the model in this paper, and the optimal order quantity, single inventory cycle time and inventory threshold were given. Compare between inventory system with and without inventory threshold shows the cost advantage of the first system. Sensitivity analysis was performed to give a better understanding of two crucial parameter, inventory threshold and cost saving rate.

Asymptotically Optimal Dynamic Pricing for Network Revenue Management

A dynamic pricing problem that arises in a revenue management context is considered, involving several resources and several demand classes, each of which uses a particular subset of the resources. The arrival rates of demand are determined by prices, which can be dynamically controlled. When a demand arrives, it pays the posted price for its class and consumes a quantity of each resource commensurate with its class. The time horizon is finite: at time T the demands cease, and a terminal reward (possibly negative) is received that depends on the unsold capacity of each resource. The problem is to choose a dynamic pricing policy to maximize the expected total reward. When viewed in diffusion scale, the problem gives rise to a diffusion control problem whose solution is a Brownian bridge on the time interval [0, T]. We prove diffusion-scale asymptotic optimality of a dynamic pricing policy that mimics the behavior of the Brownian bridge. The ‘target point’ of the Brownian bridge is obtained as the solution of a finite dimensional optimization problem whose structure depends on the terminal reward. We show that, in an airline revenue management problem with no-shows and overbooking, under a realistic assumption on the resource usage of the classes, this finite dimensional optimization problem reduces to a set of newsvendor problems, one for each resource.

A possibilistic multiple objective pricing and lot-sizing model with multiple demand classes

We address an inventory-marketing system to determine the production lot size, marketing expenditure and selling prices where a firm faces demand from two or more market segments in which the firm can set different prices. Considering pricing, marketing and lot-sizing decisions simultaneously, the model maximizes the profit and return on inventory investment under multiple time varying demand classes. The model is formulated as a fuzzy non-linear multi-objective one where some parameters are ill-known and modeled by fuzzy numbers. A hybrid possibilistic-flexible programming approach is proposed to handle imprecise data and soft constraints concurrently. After transforming the original model into an equivalent multi-objective crisp model, it is then converted to a classical mono-objective one by a fuzzy goal programming method. An efficient solution procedure using particle swarm optimization (PSO) is also provided to solve the resulting non-linear problem.

Dynamic inventory rationing for systems with multiple demand classes and general demand processes

We consider the dynamic rationing problem for inventory systems with multiple demand classes and general demand processes. We assume that backorders are allowed. Our aim is to find the threshold values for this dynamic rationing policy. For single period systems, dynamic critical level policy is developed and the detailed cost approximation subject to this policy is derived. For multiperiod systems, a dynamic rationing policy with periodic review is proposed. The numerical study shows that our dynamic critical level policies are close to being optimal for various parameter settings.

Reservation and allocation policies for influenza vaccines

This research investigates the impact of alternative allocation mechanisms that can be employed in the context of vaccine inventory rationing. Available vaccine inventory can be allocated to arrivals from high priority (target groups such as healthcare professionals) and low priority (non-target groups) demand classes using Partitioned Allocation (PA), Standard Nesting (SN), and Theft Nesting (TN). In any one of the mechanisms, a part of the available inventory is reserved for the exclusive use of the high priority demand class. They differ, however, in how the unreserved portion of the inventory is utilized: Under PA, demand from the high (low) priority class consumes only the reserved (unreserved) quantity. Under SN, demand from the high priority class first consumes the reserved quantity; once and if this quantity is exhausted, high priority demand competes with low priority demand for the remaining inventory. Under TN the sequence of allocation is reversed: both demand classes first compete for the unreserved inventory. Once this portion of inventory is exhausted, high priority demand is fulfilled from the reserved inventory and low priority demand is rejected. We develop service level (probability of fulfilling the entire demand) and fill rate (fraction of demand fulfilled) expressions for all three allocation mechanisms. Based on these expressions, numerical analyses are conducted to illustrate which allocation mechanism a health planner should choose depending on the availability of vaccines, and how the health planner should set the reserved quantity for the high priority class. We observe that (1) there exist certain conditions under which one of the allocation mechanisms outperforms the others and (2) this effect is determined by the decision maker’s choice of the performance measure.

Inventory rationing with multiple demand classes: The case of group buying

Web-based group buying is practised in many businesses nowadays. Noting that the group-buying mechanism is often used with traditional selling methods, this paper develops models in which sellers provide customers with a group-buying option and a regular spot-selling option. We prove the optimality of a threshold rationing policy. Our findings help those sellers who offer multiple selling options in designing and implementing an efficient demand and inventory management system.

Ad-Valorem Platform Fees and Efficient Price Discrimination

This paper investigates a puzzle and possible policy concern: Why do platforms such as eBay and Visa that enable the trade of goods of different unobserved costs and values rely predominantly on linear ad-valorem fees, that is, fees that increase in proportion to the sale price of the trades that they enable? Under a broad class of demand functions, we show that a linear ad-valorem fee schedule enables a platform to maximize its profit as if it could actually observe the costs and values of the goods traded and set a different optimal fee for each good. Surprisingly, we find for this class of demands, allowing the platform to set ad-valorem fees (i.e. price discriminate) increases social welfare, both when the platform is regulated to recover costs and when the platform is unregulated.

Asymptotically optimal dynamic pricing for network revenue management

Open AccessOpen Access licenseAboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail Go to SectionOpen AccessOpen Access license HomeStochastic SystemsVol. 2, No. 2 Asymptotically Optimal Dynamic Pricing for Network Revenue ManagementRami Atar, Martin I. ReimanRami Atar, Martin I. ReimanPublished Online:21 Sep 2012https://doi.org/10.1287/12-SSY062AbstractA dynamic pricing problem that arises in a revenue management context is considered, involving several resources and several demand classes, each of which uses a particular subset of the resources. The arrival rates of demand are determined by prices, which can be dynamically controlled. When a demand arrives, it pays the posted price for its class and consumes a quantity of each resource commensurate with its class. The time horizon is finite: at time T the demands cease, and a terminal reward (possibly negative) is received that depends on the unsold capacity of each resource. The problem is to choose a dynamic pricing policy to maximize the expected total reward. When viewed in diffusion scale, the problem gives rise to a diffusion control problem whose solution is a Brownian bridge on the time interval [0, T]. We prove diffusion-scale asymptotic optimality of a dynamic pricing policy that mimics the behavior of the Brownian bridge.The ‘target point’ of the Brownian bridge is obtained as the solution of a finite dimensional optimization problem whose structure depends on the terminal reward. We show that, in an airline revenue management problem with no-shows and overbooking, under a realistic assumption on the resource usage of the classes, this finite dimensional optimization problem reduces to a set of newsvendor problems, one for each resource. Back to Top Next FiguresReferencesRelatedInformationCited ByConstant Regret Resolving Heuristics for Price-Based Revenue ManagementYining Wang, He Wang31 January 2022 | Operations Research, Vol. 0, No. 0A Re-Solving Heuristic with Uniformly Bounded Loss for Network Revenue ManagementPornpawee Bumpensanti, He Wang16 March 2020 | Management Science, Vol. 66, No. 7Real-Time Dynamic Pricing for Revenue Management with Reusable Resources, Advance Reservation, and Deterministic Service Time RequirementsYanzhe (Murray) Lei, Stefanus Jasin2 April 2020 | Operations Research, Vol. 68, No. 3Nonparametric Self-Adjusting Control for Joint Learning and Optimization of Multiproduct Pricing with Finite Resource CapacityQi (George) Chen, Stefanus Jasin, Izak Duenyas23 April 2019 | Mathematics of Operations Research, Vol. 44, No. 2Workload-Dependent Dynamic Priority for the Multiclass Queue with RenegingRami Atar, Anat Lev-Ari7 November 2017 | Mathematics of Operations Research, Vol. 43, No. 2Joint Dynamic Pricing and Order Fulfillment for E-commerce RetailersYanzhe (Murray) Lei, Stefanus Jasin, Amitabh Sinha27 March 2018 | Manufacturing & Service Operations Management, Vol. 20, No. 2Real-Time Dynamic Pricing with Minimal and Flexible Price AdjustmentQi (George) Chen, Stefanus Jasin, Izak Duenyas23 November 2015 | Management Science, Vol. 62, No. 8Reoptimization and Self-Adjusting Price Control for Network Revenue ManagementStefanus Jasin13 June 2014 | Operations Research, Vol. 62, No. 5 Volume 2, Issue 2December 2012Pages 232-446 Article Information Metrics Downloaded 133 times in the past 12 months Information Received:January 01, 2012Published Online:September 21, 2012 Copyright © 2012, The author(s)Cite asRami Atar, Martin I. Reiman (2012) Asymptotically Optimal Dynamic Pricing for Network Revenue Management. Stochastic Systems 2(2):232-276. https://doi.org/10.1287/12-SSY062 KeywordsRevenue managementdynamic pricingthe Gallego and Van Ryzin modelfluid optimization problemdiffusion control problemasymptotic optimalityBrownian bridgebridge policyPDF download

한옥주거단지 사업모델구상 및 타당성 분석

주택에 대한 수요가 다변화되면서 최근 한옥주택 및 한옥주거단지에 대한 사회적 관심이 증대되고 있다. 기존에 한옥이 밀집한 지역을 중심으로한 정비사업 뿐만 아니라, 대규모 택지개발지구등에서도 한옥주택과 주거단지 개발에 대한 시도가 이루어지고 있지만, 본격적인 사업화는 이루어지지 않고 있다. 본 연구는 LH가 공급하는 신도시의 단독주택용지와 특성화용지등을 대상으로 하여 한옥의 잠재적 수요계층을 바탕으로 사업모델을 도출하고 사업모델에 대한 타당성을 검증하여 향후 사업화를 위한 방향을 제안하고자 한다. 기존에 검토되었던 고급형 타운하우스 형태의 한옥주거단지는 입지선정, 수요불일치 등으로 인하여 사업성이 부족한 것으로 분석되었으며, 설문조사 결과등을 바탕으로 계획규모변경, 용도혼합, 필지세분화등의 방법을 통해 사업유형을 6가지로 설정하였다. 사업모델 중에서 가장 사업성이 높은 유형은 블록형 집합주택으로, 이는 규모의 경제법칙(Ecnomy of Scale)에 따른 건축연면적의 증가가 분양수입의 증대로 이어진 것으로 이해할 수 있다. 소규모 한옥과 근생시설이 결합한 공동주택 모델의 타당성도 높게 나타났으며, 블록형 집합주택과 같은 동일한 사업조건을 적용한다면, 한스타일 공동주택의 사업성이 높은 것으로 분석되었다. 그 밖에 블록형 단독주택지내 고급주택 모델은 민간부문이 일반적으로 추진하고 있는 대표적인 사업유형으로서, 1호당 건설비용이 9.1억원으로 가장 많은 비용이 투입되는 것으로 나타났다. 한옥주거단지 사업성 제고를 위해서는 입지선정, 수요계층의 다양화, 주택규모의 적정화, 용도혼합등을 통한 집합화가 필요할 것으로 판단된다. 또한 단독주택용지에 한옥주택을 도입하기 위해서는 기존의 필지계획의 조정과 분할이 필요하며, 한옥형 용지등의 공급을 통해 새로운 수요에 대응하는 전략도 제안될 수 있다. 또한 기존의 획일적인 택지개발방식에서 벗어나 기초인프라(간선도로 및 상하수도)외에 조성되지 않은 자연상태의 토지인 원형지(原形地) 공급을 통한 개발방식도 검토할 수 있으며, 한옥의 지붕 및 가구구조상 1~2층 이상의 건축이 불가능하므로 경사지 형태를 갖는 원형지 공급방식의 단지조성이 토지비절감, 경관효과 등을 감안할 때 적합한 모델로 제안될 수 있다. This study is to derive a project model based on potential demand for Korean-style houses, focusing on new town detached housing sites that LH supplies and to test validity of the derived model and to present the direction and supply methods of the projects. The existing high-class new town Korean-style housing developments that have been considered were found to have little business value due to problems in choice of location and discordance of demand, so 6 types of projects were established through the methods of changes in planned scale, combined use, and subdivision of plot of land based on the results of survey. The type that has the highest business value among the project models was block-type multifamily houses, and this can be interpreted as the increase in total construction area leading to increase inrevenues of allotment sales due to economies of scale. The feasibility of mass housing model in which small-scale Korean-style houses are combined with amenities was found to be high, and if the same project conditions as those of the block-type multifamily houses are applied, the business value of the Korean-style tenement houses was found to be high. Besides, the high-class housing models within block-type detached housing areas are typical projects that the private sector generally promotes, and the construction cost was found to be most expensive with 910 million won per house. In order to enhance the business value of the Korean-style housing development, collectivization such as choice of location, diversification of demand classes, optimization of house sizes, and combination of uses is needed. And in order to adopt Korean-style houses in the detached housing sites, the adjustments and division of the existing planned plots are needed, and the strategies to cope with new demand through supplying Korean-style housing types of sites can be suggested. Also breaking away from the existing uniform residential development methods, the development method through supplying original land that is natural land not yet developed besides basic infrastructures (main roads and water and sewage) can be considered, and as the construction of more than 1~2 stories building is impossible due to the structure of Korean-style house roof and furniture. So it can be suggested that original land in the form of hilly land is considered to be most suitable to large-scale development projects.

Multi-service multi-facility network design under uncertainty

The problem of designing high speed networks using different modules of link capacities, in the same model, in order to meet uncertain demands obtained from different probability distribution functions (PDF) is a very hard and challenging real network design problem. The novelty of the new model, compared to previous ones, is to allow installing more than one module per link having equal or different capacities. Moreover, the scenarios of traffic can be generated, according to practical observations, from the main classes of uncertain demands (multi-service) simulated from different PDFs, including heavy tailed ones. These classes of traffic are considered simultaneously for the scenario generation, different from related works in the literature that use only one probability distribution function to simulate the scenarios of traffic. In this work we present the problem formulation and report computational results using branch-and-bound and L-shaped decomposition solution approaches. We consider in the same model up to three different types of modular capacities (multi-facility), since it seems that using more than this can lead to an intractable model. The objective is to minimize penalty (in case of unmet demands) and investment costs. We obtain confidence intervals (with 95% of covering rate) on the expected optimal solution value for the resulting two-stage stochastic integer-modular problem and discuss when they are meaningful. Numerical experiments show that our model can handle up to medium real size instances.

Network Coding in Node-Constrained Line and Star Networks

Line and star networks with both node and edge constraints are studied in the network coding framework. For line networks, the capacity region of the general multiple multicast problem is established. The coding theorem is based on a binary linear coding scheme, while the converse requires new upper bounds that improve on standard cut-based bounds. For star networks, the multiple unicast problem is examined. Capacity upper bounds are derived and a simple linear coding scheme is proposed which is based on the combinatorial optimization problem of cycle packing in directed graphs. The optimality of this scheme is established for a broad class of demands. The connection of node-constrained network coding in star networks, and index coding with side information is discussed and used to partially characterize the optimal linear code for general rates.