Partial Demand Information Research Articles

Distributionally robust newsvendor problem with partial demand information under carbon emission regulations

Carbon emission schemes are widely adopted and implemented in practice to control greenhouse gas emissions. However, a firm restricted by carbon emission schemes with only partial demand information may face greater challenges. In this paper, we investigate an ordering and pricing newsvendor problem with partial demand information, which considers carbon emissions generated from the processes of ordering and disposing of the excess inventory. We propose three distributionally robust models to maximize the worst-case profit under different carbon emission regulations: carbon tax, cap-and-trade and carbon cap, respectively. We derive the implicit solution under the carbon tax scheme and design heuristic algorithms based on Lagrangian relaxation under the cap-and-trade and carbon cap regulations. Numerical analysis indicates: (i) all three regulations are effective in reducing carbon emissions; (ii) the implementation of carbon schemes leads to higher optimal pricing and lower optimal ordering quantity, both carbon tax and carbon cap regulations will always lead to lower profit, while the retailer may benefit from the cap-and-trade regulation by selling out the carbon credit; (iii) the proposed approach performs well under different distribution specific scenarios.

Humanitarian relief network design: Responsiveness maximization and a case study of Typhoon Rammasun

In this article, we study a humanitarian relief network design problem, where the demand for relief supplies in each affected area is uncertain and can be met by more than one relief facility. Given a certain cost budget, we simultaneously optimize the decisions of relief facility location, inventory pre-positioning, and relief facility to affected area assignment so as to maximize the responsiveness. The problem is formulated as a chance-constrained stochastic programming model in which a joint chance constraint is utilized to measure the responsiveness of the humanitarian relief network. We approximate the proposed model by another model with chance constraints, which can be solved based on two settings of the demand information in each affected area: (i) the demand distribution is given; and (ii) the partial demand information, e.g., the mean, the variance, and the support, is given. We use a case study of the 2014 Typhoon Rammasun to illustrate the application of the model. Computational results demonstrate the effectiveness of the solution approaches and show that the chance-constrained stochastic programming models are superior to the deterministic model for humanitarian relief network design.

Robust decisions for regulated sustainable manufacturing with partial demand information: Mandatory emission capacity versus emission tax

While emission tax and mandatory emission capacity regulations are widely implemented to control greenhouse gas emissions, it remains unclear which will lead to better performance in an uncertain environment. Furthermore, a regulated sustainable manufacturer with only partial demand information may be challenged by more uncertainties than a manufacturer would be in a free market without regulation. These factors motivate us to examine the effects of two types of emission reduction regulations on the optimal production decisions of a manufacturer facing stochastic demand with partial distribution information. Based on distributionally robust newsvendor models, we use the Hurwicz decision criterion to build robust optimization models for a regulated sustainable manufacturer. We first solve the closed-form expressions of the optimal production quantities for two optimization models; then, we compare their expected profits and carbon emissions. The comparisons show that an emission tax may be more favorable than mandatory emission capacity regulation in terms of the manufacturer’s environmental performance. A numerical study with a Taguchi experiment is performed to compare the two policies and to test the robustness. We find interesting insights: For manufacturers, a decision maker with an optimistic attitude to demand uncertainty, can gain higher profits and emit less carbon, which differs from the results of some previous research. For regulators, with a large carbon cap, mandatory emission capacity regulation can lead manufacturers to gain higher profits and emit more carbon than those achieved under emission tax regulation, which provides new insights for policy makers.

A hierarchical MPC and sliding mode based two-level control for freeway traffic systems with partial demand information

In this paper a hierarchical two-level control scheme is proposed in order to solve a ramp metering problem in freeway traffic systems. The proposal combines a Model Predictive Control (MPC) based supervisor with decentralized low-level Sliding Mode Controllers (SMCs). The considered freeway METANET model describes the traffic system, which is naturally affected by uncertainties since the mainstream inflow, the traffic demands on the on-ramps, and the flows exiting the off-ramps are not a priori known. In the proposed scheme, two control loops are present. A centralized MPC computes the optimal control inputs by minimizing the total time spent by the vehicles in the traffic system on the basis of a nominal model of the considered freeway stretch. The computed optimal inputs are used to generate the corresponding density references for the low-level on-ramp controllers, which rely on a saturated version of the Suboptimal Second-Order Sliding Mode (SSOSM) control algorithm. SSOSM controllers allow to regulate the density error to zero in a finite time, thus reducing the mismatch between the controlled traffic system dynamics and the model used by the MPC supervisor during the optimization. A simulation study encompassing several realistic scenarios is reported to assess the validity of the proposed approach also in comparison with other classical traffic control strategies. As confirmed by simulation, in spite of the uncertainties, the proposed control scheme produces satisfactory performance in terms of both total time spent minimization and capacity drop alleviation.

Cost-Profit Trade-Off for Optimally Locating Automotive Service Firms Under Uncertainty

This work investigates the problem of optimally locating an automotive service firm (ASF) subject to stochastic customer demands, varying setup cost and regional constraints. The goal is to minimize the transportation cost while maintaining the specified profit of the ASF. This work studies two variants of the problem: ASF location with known demand probability distributions and with partial demand information, i.e., only the support and mean of the customer demands are known. For the former, a chance-constrained program is formulated that improves an existing model, and then an equivalent deterministic nonlinear program is constructed based on our property analysis results. For the latter, a novel distribution-free model is developed. The proposed models are solved by solver LINGO. Computational results on the benchmark examples show that: i) for the first variant, the proposed approach outperforms the existing one; ii) for the second one, the proposed distribution-free model can effectively handle stochastic customer demands without complete probability distributions; and iii) the results of the distribution-free model are slightly worse than those of the deterministic nonlinear one, but the former is more cost-efficient for the practical ASF location as it is less expensive in obtaining demand information. Moreover, the proposed models and approaches are extended to address a multi-ASF location allocation under demand uncertainty.

Greening and price differentiation coordination in a supply chain with partial demand information and cannibalization

In this paper, a supply chain coordination problem for a single manufacturer and retailer for a single selling period is analyzed. The retailer in the supply chain offers two products, an inaugural green and a regular product at different prices. These products are procured at distinct wholesale prices through a single distribution channel. The inaugural green product is offered by the manufacturer along with the existing regular product and sold at a higher price compared to the regular product. This price differentiation divides the market into two segments where the demand in each segment can be controlled using a differentiation price. However, this segmentation resulted via price differentiation is often imperfect owing to which the retailer experiences cannibalization. Cannibalization is perceived as demand leakages between the two segments. This study proposes mathematical models for single channel coordination that integrate price differentiation and demand leakage aspects for the two-product case of green and regular products. Coordination is modeled for both integrated and decentralized channels. In an integrated channel, the decisions are centralized in a monopoly, whereas, in the decentralized channel, manufacturer and retailer decisions are coordinated in a leader-follower game theoretic setting. The coordination models are developed not only for deterministic demand and stochastic demand with full demand information but also for stochastic demand with partial demand information. For each of the demand situations, analytical (closed-form) solutions for pricing, inventory, and greening effort investment decisions in the supply chain are developed. A detailed numerical study is proposed to illustrate the proposed models. We show that selling green and regular products at differentiated prices can significantly improve the profitability of both the manufacturer and retailer, however, an increased demand leakage can considerably limit the profitability gains. Whereas, manufacturer's decision on price differentiation can be used to mitigate the adverse effects of demand leakages.

Partial Demand Information and Commitment in Dynamic Transportation Procurement

This paper analyzes a decision process of planning transportation procurement for a distribution lane given limited information regarding future demand for transportation services and a specified commitment horizon for procurement contracts. In contrast to variants in which either full demand information or no demand information is known over the planning horizon, our work considers the value of demand visibility for a short horizon in the future (i.e., the value of partial information). Our work also considers a commitment horizon that is much shorter than the planning horizon. We show that the availability of partial information fundamentally changes the contracting policies in the presence of such commitment horizons, and if used optimally, this information can be highly valuable. Partial visibility of demand can increase the willingness of the decision maker to commit to contracts and expand the range of capacity levels selected in settings where the capacity level of a contract is a decision variable. We also identify settings in which the value of partial information is negligible, reducing the incentive of managers to acquire additional demand information for future periods. Finally, we show that with seasonal demand, information is leveraged by properly coordinating with expected demand shocks (e.g., Black Friday) using tailored strategies.

Distribution-Free Model for Ambulance Location Problem with Ambiguous Demand

Ambulance location problem is a key issue in Emergency Medical Service (EMS) system, which is to determine where to locate ambulances such that the emergency calls can be responded efficiently. Most related researches focus on deterministic problems or assume that the probability distribution of demand can be estimated. In practice, however, it is difficult to obtain perfect information on probability distribution. This paper investigates the ambulance location problem with partial demand information; i.e., only the mean and covariance matrix of the demands are known. The problem consists of determining base locations and the employment of ambulances, to minimize the total cost. A new distribution-free chance constrained model is proposed. Then two approximated mixed integer programming (MIP) formulations are developed to solve it. Finally, numerical experiments on benchmarks (Nickel et al., 2016) and 120 randomly generated instances are conducted, and computational results show that our proposed two formulations can ensure a high service level in a short time. Specifically, the second formulation takes less cost while guaranteeing an appropriate service level.

Supply chain coordination under a revenue-sharing contract with corporate social responsibility and partial demand information

Corporate social responsibility is among the most desired features of global operations in supply chains. Despite there is a societal urge for socially responsible supply chains, yet the supply chain players (manufactures, and retailers) may only be motivated being socially responsible given it warrants them improved performance and profitability. In this paper, we have proposed supply chain coordination schemes for pricing inventory, and corporate social responsibility investments decisions for a single manufacturer-retailer supply chain. We developed quantitative models for joint pricing, inventory (order quantity), and investment for socially responsible decisions for a supply chain. Models are formulated for both the price-and-CSR investment dependent deterministic and price-and-CSR investment dependent stochastic demand situations. We also explore when the price-and-CSR investment dependent stochastic demand information is only be partially known in a supply chain, and players may have to anticipate the worst possible demand. It is assumed the demand distribution is unknown, and a distribution-free approach is utilized. We have presented various game-theoretic settings that analyze the decentralized, centralized, and a revenue sharing agreement through bargaining for each of three demand situations. We developed analytical (closed-form) solutions for the control decisions for the players. In a detailed numerical study, the significance of each model, and how the societal responsiveness impacts the supply chain performance and the players' decision under varied game-theoretic settings is highlighted. The study also emphasizes the use of distribution-free approach to minimize the adverse impact of demand information distortion in a supply chain.

Effects of emission reduction and partial demand information on operational decisions of a newsvendor problem

Abstract This paper analyzes a newsvendor problem with partial demand information under two kinds of carbon emission regulations, in which only the mean and variance of the demand distribution are known. Under the carbon cap and cap-and-trade regulations, two distributionally robust models are formulated to determine the optimal order quantities to maximize the worst-case expected profits. We derive the closed-form expression of the optimal order quantity and show that the cap-and-trade regulation can lead to higher profit and lower carbon emissions. Numerical examples are provided to illustrate the theoretical results and develop the robustness of system parameters via the robust parameter design technique. The results indicate that compared with carbon emission parameters, the demand information parameters have more effect on the optimal worst-case expected profit and less effect on carbon emissions under carbon cap regulation. And the demand information parameters except for the variance of demand have more effect on both the optimal worst-case expected profit and carbon emissions under cap-and-trade regulation.

Newsvendor problems with sequentially revealed demand information

AbstractThis article analyzes a capacity/inventory planning problem with a one‐time uncertain demand. There is a long procurement leadtime, but as some partial demand information is revealed, the firm is allowed to cancel some of the original capacity reservation at a certain fee or sell off some inventory at a lower price. The problem can be viewed as a generalization of the classic newsvendor problem and can be found in many applications. One key observation of the analysis is that the dynamic programming formulation of the problem is closely related to a recursion that arises in the study of a far more complex system, a series inventory system with stochastic demand over an infinite horizon. Using this equivalence, we characterize the optimal policy and assess the value of the additional demand information. We also extend the analysis to a richer model of information. Here, demand is driven by an underlying Markov process, representing economic conditions, weather, market competition, and other environmental factors. Interestingly, under this more general model, the connection to the series inventory system is different. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 2012

Monopoly Pricing with Limited Demand Information

Traditional monopoly pricing models assume that firms have full information about the market demand and consumer preferences. In this paper we study a prototypical monopoly pricing problem for a seller with limited market information and different levels of demand learning capability under relative performance criterion of the competitive ratio. We provide closed-form solutions for the optimal pricing policies for each case and highlight several important structural insights. We note the following: a) From the firm's viewpoint the worst-case operating conditions are when it faces a homogeneous market where all customers value the product equally, but where the specific valuation is unknown. In cases with partial demand information, the worst case cumulative willingness-to-pay distribution becomes piecewise-uniform as opposed to a point mass. b) Dynamic (skimming) pricing arises naturally as a hedging mechanism for the firm against the two principal risks that it faces: first, the risk of foregoing revenue from pricing too low, and second, the risk of foregoing sales from pricing too high. And, c) even limited learning, e.g., market information at a few price points, leads to significant performance gains.

Stochastic integrated vendor–buyer model with unstable lead time and setup cost

This paper presents a new vendor-buyer system where there are different objectives for both sides. The proposed method of this paper is different from the other previously published works since it considers different objectives for both sides. In this paper, the vendor’s emphasis is on the crashing of the setup cost, which not only helps him compete in the market but also provides better services to his customers; and the buyer’s aim is to reduce the lead time, which not only facilitates the buyer to fulfill the customers’ demand on time but also enables him to earn a good reputation in the market or vice versa. In the light of the above stated facts, an integrated vendor-buyer stochastic inventory model is also developed. The propsed model considers two cases for demand during lead time: Case (i) Complete demand information, Case (ii) Partial demand information. The proposed model jointly optimizes the buyer’s ordered quantity and lead time along with vendor’s setup cost and the number of shipments. The results are demonstrated with the help of numerical examples.

Monopoly pricing with limited demand information

Traditional monopoly pricing models assume that firms have full information about the market demand and consumer preferences. In this article, we study a prototypical monopoly pricing problem for a seller with limited market information and different levels of demand learning capability under relative performance criterion of the competitive ratio (CR). We provide closed-form solutions for the optimal pricing policies for each case and highlight several important structural insights. We note the following: (1) From the firm's viewpoint the worst-case operating conditions are when it faces a homogeneous market where all customers value the product equally, but where the specific valuation is unknown. In cases with partial demand information, the worse case cumulative willingness-to-pay distribution becomes piecewise-uniform as opposed to a point mass. (2) Dynamic (skimming) pricing arises naturally as a hedging mechanism for the firm against the two principal risks that it faces: first, the risk of foregoing revenue from pricing too low, and second, the risk of foregoing sales from pricing too high. And, (3) even limited learning, for example market information at a few price points, leads to significant performance gains.