A NUMERICAL APPROACH TO THE CONTACT OF NOMINALLY FLAT SURFACES

Machined surfaces can be described by heights and wavelengths of the surface asperities that show a statistical variation. Considering that a regular wavy surface with a sinusoidal profile is the crudest model for a rough surface, studying the contact of regular wavy surfaces is a good approximation for the contact of nominally flat surfaces. Such contact problems exhibit periodicity that can be simulated with the aid of computational techniques derived for contact mechanics in the frequency domain. The displacement calculation, which is a necessary step in the resolution of the contact problem, is mathematically a convolution product that can be calculated in the frequency domain with increased computational efficiency. The displacement induced by a unit surface load can be expressed in the frequency domain by the frequency response functions, which are counterparts of the space domain solutions to half-space fundamental problems such as the Boussinesq problem. The displacement induced by a periodic pressure distribution can be computed by executing the convolution product between the frequency response function and pressure on a single period. It should be noted that the convolution calculation in the spectral domain implies that the contributions of all neighbouring pressure periods are accounted for. The need to treat numerically only a single period results in remarkable computational efficiency, allowing for high density meshes that can capture the essential features of any textured real surface. The displacement calculation promotes the solution of the contact problem by an iterative approach. The advanced method is benchmarked against existing analytical solutions for the 3D contact of surfaces possessing two-dimensional waviness. This essentially deterministic model, supported by a direct numerical solution that can be obtained for samples of real rough surfaces, presents itself as a worthy alternative to the existing statistical models for rough contact interaction.

Effective Online Order Acceptance Policies for Omnichannel Fulfillment

Problem definition: Omnichannel retailing has led to the use of traditional stores as fulfillment centers for online orders. Omnichannel fulfillment problems have two components: (1) accepting a certain number of online orders prior to seeing store demands and (2) satisfying (or filling) some of these accepted online demands as efficiently as possible with any leftover inventory after store demands have been met. Hence, there is a fundamental trade-off between store cancellations of accepted online orders and potentially increased profits because of more acceptances of online orders. We study this joint problem of online order acceptance and fulfillment (including cancellations) to minimize total costs, including shipping charges and cancellation penalties in single-period and limited multiperiod settings. Academic/practical relevance: Despite the growing importance of omnichannel fulfillment via online orders, our work provides the first study incorporating cancellation penalties along with fulfillment costs. Methodology: We build a two-stage stochastic model. In the first stage, the retailer sets a policy specifying which online orders it will accept. The second stage represents the process of fulfilling online orders after the uncertain quantities of in-store purchases are revealed. We analyze threshold policies that accept online orders as long as the inventories are above a global threshold, a local threshold per region, or a hybrid. Results: For a single period, total costs are unimodal as a function of the global threshold and unimodal as a function of a single local threshold holding all other local thresholds at constant values, motivating a gradient search algorithm. Reformulating as an appropriate linear program with network flow structure, we estimate the derivative (using infinitesimal perturbation analysis) of the total cost as a function of the thresholds. We validate the performance of the threshold policies empirically using data from a high-end North American retailer. Our two-location experiments demonstrate that local thresholds perform better than global thresholds in a wide variety of settings. Conversely, in a narrow region with negatively correlated online demand between locations and very low shipping costs, global threshold outperforms local thresholds. A hybrid policy only marginally improves on the better of the two. In multiple periods, we study one- and two-location models and provide insights into effective solution methods for the general case. Managerial implications: Our methods provide effective algorithms to manage fulfillment costs for online orders, demonstrating a significant reduction over policies that treat each location separately and reflecting the significant advantage of incorporating shipping in computing thresholds. Numerical studies provide insights as to why local thresholds perform well in a wide variety of situations.

A Single-period OPF-based Strategy to Manage Distributed Energy Resources with Intertemporal Constraints in Low-voltage Grids

10 pages, 9 figures, 6 tables.

A Single-period OPF-based Strategy to Manage Distributed Energy Resources with Intertemporal Constraints in Low-voltage Grids

10 pages, 9 figures, 6 tables.

Supply Chain Replenishment Decision for Newsvendor Products with Multiple Periods and a Short Life Cycle

Traditionally, the newsvendor problem is a single-period model for a retailer and can be applied in the replenishment decision for a product with a short life cycle. However, many fashionable commodities are seasonal; not all of these products must be sold within a single period of a selling season, and they can be replenished once in each cycle. This study develops a novel multi-period model to determine multiple ordering replenishment decisions for a product over a short selling season. This study not only demonstrates the profit function for a retailer, but also provides those for both the manufacturer and the entire channel in a supply chain problem. The proposed multi-period ordering model provides explicit insights into how the ordering decisions of the retailer are affected in a specific period by considering unsold inventory or unsatisfied demand from a previous period. A numerical analysis and the simulation results illustrate the feasibility of the proposed model.

Dynamic climate clubs: On the effectiveness of incentives in global climate agreements

A proposal to combat free riding in international climate agreements is the establishment of a climate club—a coalition of countries in a structure to encourage high levels of participation. Empirical models of climate clubs in the early stages relied on the analysis of single-period coalition formation. The earlier results suggested that there were limits to the potential strength of clubs and that it would be difficult to have deep abatement strategies in the club framework. The current study extends the single-period approach to many periods and develops an approach analyzing “supportable policies” to analyze multiperiod clubs. The major element of the present study is the interaction between club effectiveness and rapid technological change. Neither alone will produce incentive-compatible policies that can attain the ambitious objectives of international climate policy. The trade sanctions without rapid technological decarbonization will be too costly to produce deep abatement; similarly, rapid technological decarbonization by itself will not induce deep abatement because of country free riding. However, the two together can achieve international climate objectives.

Time-Varying Vibration Compensation Based on Segmented Interference for Triangular FMCW LiDAR Signals

Frequency modulation continuous wave (FMCW) light detection and ranging (LiDAR) 3D imaging system may suffer from time-varying vibrations which will affect the accuracy of ranging and imaging of a target. The system uses only a single-period FMCW LiDAR signal to measure the range of each spot; however, traditional methods may not work well to compensate for the time-varying vibrations in a single period because they generally assume the vibration velocity is constant. To solve this problem, we propose a time-varying vibration compensation method based on segmented interference. We first derive the impact of time-varying vibrations on the range measurement of the FMCW LiDAR system, in which we divide the time-varying vibration errors into primary errors caused by the vibrations with a constant velocity and quadratic errors. Second, we estimate the coefficients of quadratic vibration errors by using a segmented interference method and build a quadratic compensation filter to eliminate the quadratic vibration errors from the original signals. Finally, we use the symmetrical relations of signals in a triangular FMCW period to estimate the vibration velocity and establish a primary compensation filter to eliminate the primary vibration errors. Numerical tests verify the applicability of this method in eliminating time-varying vibration errors with only a one-period triangular FMCW signal and its superiority over traditional methods.

Single-Period Capacity and Demand Allocation Decision Making under Uncertainty

The newsvendor model deals with a single-period capacity allocation problem under uncertainty. The real world examples include perishable products (e.g., fish, vegetable), holiday-related products (e.g., Easter, Christmas, Halloween), seasonal products (e.g., fashion), and promotional products. This section addresses three newsvendor models: traditional newsvendor, inverse newsvendor, and sequential newsvendor models. The main decision under the traditional newsvendor setting is capacity allocation (i.e., how much to order), whereas the main decision under the inverse newsvendor setting is demand allocation (i.e., how many customers to be served) under the fixed capacity. This section demonstrates how to compare profit maximization approach to customer-oriented approach under the traditional newsvendor. The inverse newsvendor applies to revenue management for the hospitality industry. The sequential newsvendor model determines the optimal sequence when the number of customers to be served (determined by the inverse newsvendor model) is given. Normal distribution is considered for analytical solution and numerical studies. In addition, a discrete distribution is considered for numerical studies.