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We consider a single-item single-period joint inventory management and pricing problem of a retailer selling an item that has selling price uncertainties. Unlike most of the literature on the newsvendor problem, we assume that price-dependent demand arrives randomly according to a stochastic arrival process whose rate depends on the fluctuating market input price process. The retailer’s problem is to choose the order quantity and a proportional price markup over the input price to maximize the expected profit. This setting is mostly encountered by retailers that trade in different currencies or have to purchase and convert commodities for seasonal sales. For this setting, we characterize both the optimal inventory and markup levels. We present monotonicity properties of the expected profit function with respect to each decision variable. We also show that more volatile input price processes lead to lower expected profits.

In patch foraging tasks, animals must decide whether to remain with a depleting resource or to leave it in search of a potentially better source of reward. In such tasks, animals consistently follow the general predictions of optimal foraging theory (the Marginal Value Theorem; MVT): to leave a patch when the reward rate in the current patch depletes to the average reward rate across patches. Prior studies implicate an important role for the anterior cingulate cortex (ACC) in foraging decisions based on MVT: within single trials, ACC activity increases immediately preceding foraging decisions, and across trials, these dynamics are modulated as the value of staying in the patch depletes to the average reward rate. Here, we test whether these activity patterns reflect dynamic encoding of decision-variables and whether these signals are directly involved in decision-making or serve a more general function such as monitoring task performance or allocating cognitive control. We developed a leaky accumulator model based on the MVT that generates estimates of decision variables within and across trials, and tested model predictions against ACC activity recorded from rats performing a patch foraging task. Model predicted changes in MVT decision variables closely matched rat ACC activity. Next, we pharmacologically inactivated ACC to test the contribution of these signals to decision-making. Despite ACC inactivation, rats still followed the MVT decision rule, suggesting that foraging decision variables represented in the ACC are used for a more general function such as regulating cognitive control or motivation. Significance The ability to make adaptive patch-foraging decisions – to remain with a depleting resource or search for better alternatives – is critical to animal well-being. Previous studies have found that anterior cingulate cortex (ACC) activity is modulated at different points in the foraging decision process, raising questions about whether the ACC guides ongoing decisions or serves a more general purpose of regulating cognitive control. To investigate the function of the ACC in foraging, the present study developed a dynamic model of behavior and neural activity, and tested model predictions using recordings and inactivation of ACC. Findings revealed that ACC continuously signals decision variables but that these signals are more likely used to regulate cognitive control than to guide ongoing decisions.

The correct parameter determination of the photovoltaic module and the solar cell is considered an important phase to deliver a reliable simulation for the PV system characteristics. The triple diode model (TDM) has been examined to model the PVM 752 GaAs thin-film PV solar cell (SC), STM6 PV module, and RTC SC. A set of the measured I-V data at various levels of the weather conditions has been considered for the studied PV solar cell/modules. A new marine predators algorithm (MPA) is used to identify the TDM parameters based on measured datasets. Throughout the optimization procedure, the nine undetermined parameters of TDM are employed as decision variables but the fitness function requires to be least is the RMSE between the experimental and calculated datasets. The achieved results by MPA are compared with different algorithms. The comparison confirmed the superiority of MPA.

Car ferry services constitute an important part of the transportation network in several parts of the world, especially in areas with limited alternative modes of transport. A central problem facing decision makers is the socially optimal capacity of ferry services. However, the literature has not examined all the decision variables the are relevant to decision makers in a simultaneous framework, only partially. We add to the literature by treating all the relevant decisions variables in a simultaneous framework, which enables a more complete representation of optimal capacity, than partial frameworks. Our proposed methodology also includes the cost of not being able to board the first arriving departure, which is an essential cost in the case of car ferries with too low capacity. We apply the methodology to a case study of three major ferry crossings in Norway. Results indicate that a too large capacity is provided. Thus, local policy makers should consider revising the current service levels. Other policy makers may enact better decisions based on the findings we provide. Sensitivity test suggests that the method used to estimate the number of users not being able to board due to capacity concerns may be improved. This, however, does not alter our main conclusion.

We study an Inventory Routing Problem at the tactical planning level, where the initial inventory levels at the supplier and at the customers are decision variables and not given data. Since the total inventory level is constant over time, the final inventory levels are equal to the initial ones, making this problem periodic. We propose a class of matheuristics, in which a route-based formulation of the problem is solved to optimality with a given subset of routes. Our goal is to show how to design effective subsets of routes. For some of them, we prove effectiveness in the worst case, i.e., we provide a finite worst-case performance bound for the corresponding matheuristic. Moreover, we show they are also effective on average, in a large set of instances, when some additional routes are added to this subset of routes. These solutions significantly dominate, both in terms of cost and computational time, the best solutions obtained by applying a branch-and-cut algorithm we design to solve a flow–based formulation of the problem.

Innumerable rumors spread quickly through social networks and how to fast control the spread of rumors is crucial. An efficient way is to take different measures for users with different influence extent by rumors, but the costs of these measures vary. In this paper, we try to minimize the spread (termination) time of rumors considering the controlling cost. To solve this problem, we creatively design five different measures to control rumors. First, we propose a contact coefficient to quantify the influence weight for each user. Second, we classify the users to different groups based on their influence weights so that the rumors can be controlled by the measures accordingly. Thus, the controlling of rumors can be formulated into an optimization problem, in which decision variables based on contact coefficients are used to classify users. Then an approximation algorithm named WB-GA is designed to classify different users, ensuring that rumors can be controlled as fast as possible within given costs. The experimental results on real online networks show that our algorithm is highly efficient and effective.

In many real-world problems, one may encounter uncertainty in the input data. The fuzzy set theory fits well to handle such situations. However, it is not always possible to determine with full satisfaction the membership and non-membership degrees associated with an element of the fuzzy set. The intuitionistic fuzzy sets play a key role in dealing with the hesitation factor along-with the uncertainty involved in the problem and hence, provides more flexibility in the decision-making process. In this article, we introduce a new ordering on the set of intuitionistic fuzzy numbers and propose a simple approach for solving the fully intuitionistic fuzzy linear programming problems with mixed constraints and unrestricted variables where the parameters and decision variables of the problem are represented by intuitionistic fuzzy numbers. The proposed method converts the problem into a crisp non-linear programming problem and further finds the intuitionistic fuzzy optimal solution to the problem. Some of the key significance of the proposed study are also pointed out along-with the limitations of the existing studies. The approach is illustrated step-by-step with the help of a numerical example and further, a production planning problem is also demonstrated to show the applicability of the study in practical situations. Finally, the efficiency of the proposed algorithm is analyzed with the existing studies based on various computational parameters.

In this paper, we develop a branch and bounds algorithm to solve bound-construction bi-objective optimization problem. The proposed algorithm allows to determine an approximation of the Pareto optimal solutions sets in both spaces: decisions and objectives ones. By running α -dense space filling curves, we convert a multidimensional bi-objective optimization problem into a one-dimensional one. Hence it gets possible the implementation of the proposed algorithm when objectives depend on more than one decision variable. The proposed algorithm was applied on an engineering problem to find the working space of a robotic manipulator and the obtained results are promising.

This paper introduces an interactive approach to support multi-criteria decision analysis of project portfolios. In high-scale strategic decision domains, scientific studies suggest that the Decision Maker (DM) can find help by using many-objective optimisation methods, which are supposed to provide values in the decision variables that generate high-quality solutions. Even so, DMs usually wish to explore the possibility of reaching some levels of benefits in some objectives. Consequently, they should repeatedly run the optimisation method. However, this approach cannot perform well – in an interactive way – for large instances under the presence of many objective functions. We present a mathematical model that is based on compromise programming and fuzzy outranking to aid DMs in analysing multi-criteria project portfolios on the fly. This approach allows relaxing the problem of rapidly optimising portfolios while preserving the beneficial properties of the DM’s preferences expressed by outranking relations. Our model supports the decision analysis on two instance benchmarks: for the first one, a better compromise solution was generated 84% of the runs; for the second one, this ranged from 93% to 97%. Our model was also applied to a real-world problem involving social projects, obtaining satisfactory results.

Consider a channel whose the input alphabet set $\mathbb {X}=\{x_{1},x_{2}, {\dots },x_{K}\}$ contains $K$ discrete symbols modeled as a discrete random variable $X$ having a probability mass function $\mathbf {p}(\mathbf {x}) = [p(x_{1}), p(x_{2}), {\dots }, p(x_{K})]$ and the received signal $Y$ being a continuous random variable. $Y$ is a distorted version of $X$ caused by a channel distortion, characterized by the conditional densities $p(y|x_{i})=\phi _{i}(y)$ , $i=1,2, {\dots },K$ . To recover $X$ , a quantizer $Q$ is used to quantize $Y$ back to a discrete output $\mathbb {Z} =\{z_{1}, z_{2}, {\dots }, z_{N}\}$ corresponding to a random variable $Z$ with a probability mass function $\mathbf {p}(\mathbf {z}) = [p(z_{1}), p(z_{2}), {\dots }, p(z_{N})]$ such that the mutual information $I(X;Z)$ is maximized subject to an arbitrary constraint on $\mathbf {p}(\mathbf {z})$ . Formally, we are interested in designing an optimal quantizer $Q^{*}$ that maximizes $\beta I(X;Z) - C(Z)$ where $\beta $ is a positive number that controls the trade-off between maximizing $I(X;Z)$ and minimizing an arbitrary cost function $C(Z)$ . Let $\mathbf {p}(\mathbf {x}|y)=[p(x_{1}|y),p(x_{2}|y), {\dots },p(x_{K}|y)]$ be the posterior distribution of $X$ for a given value of $y$ , we show that for any arbitrary cost function $C(.)$ , the optimal quantizer $Q^{*}$ separates the vectors $\mathbf {p}(\mathbf {x}|y)$ into convex regions. Using this result, a method is proposed to determine an upper bound on the number of thresholds (decision variables on $y$ ) which is used to speed up the algorithm for finding an optimal quantizer. Numerical results are presented to validate the findings.

Passenger Vehicle Type Choice (PVTC) has an undeniable impact on crash severity and costs. To estimate that, one must carefully consider subjective factors as well as objective ones. Ignoring the role of subjective variables can cause bias in the estimation of the effective variables' coefficients. The present paper investigates the impact of safety attitude, transportation attitude, and lifestyle on PVTC in a bi-level structure. To do so, we used the data from 633 face-to-face interviews conducted in Iran. The passenger vehicles investigated in this study are divided into five categories according to their weight and safety performance: mini, compact, medium, large, and sport utility vehicles (SUVs). In the analysis of the mentioned structure, the Integrated Choice and Latent Variables (ICLV) approach is utilized. One of the important findings of the current study the significant influence of subjective variables on PVTC. Since subjective variables have an indirect effect on the decision variable, ignoring them will lead to biased estimates. For instance, aging in consumers increases the need for larger and more comfortable vehicles and reduces the tendency for high speeds. These two effects together neutralize the effect of age on the choice of large vehicles and SUVs. The effect of age on the choice of large vehicles could not be explained by solely relying on the objective variables.

Dopamine potently regulates forebrain physiology that underlies reward learning and behavioral flexibility. A detailed accounting of how cellular and circuit interactions come to impact reinforcement learning continues to be refined at multiple levels of analysis. This review provides a brief summary of our current understanding of quantitative decision variables relayed by dopamine dynamics in striatal targets, circuit substrates that support specific dopaminergic computations, and how different behavioral task-demands leverage these specializations to afford adaptive behaviors. Moreover, we motivate the revision of a longstanding hypothesis for globally broadcast dopamine prediction error signals, and instead, make the case for regionally specialized forebrain dopamine dynamics tailored to local computational needs.

Penelitian ini bertujuan untuk mengetahui dan menguji apakah Komunikasi Word Of Mouth dan Place berpengaruh terhadap Keputusan Pembelian pada usaha Susu Kambing Etawa Mulia Jaya di Desa Melati II Kecamatan Perbaungan. Sampel yang digunakan dalam penelitian ini adalah konsumen yang sedang mengkomsumsi produk Susu Kambing Etawa Mulia Jaya dengan jumlah 87 konsumen yang diambil selama 3 bulan. Hasil penelitian menggunakan uji t (parsial) menunjukkan bahwa Komunikasi Word Of Mouth berpengaruh secara signifikan terhadap Keputusan Pembelian dengan nilai thitung sebesar 4,051 > ttabel 1,988 dan taraf signifikan 0,000 < 0,05 dan bahwa Place berpengaruh secara signifikan terhadap Keputusan Pembelian dengan nilai thitung sebesar 3,455 > ttabel 1,988 dengan taraf signifikan 0,001 < 0,05. Hasil penelitian menggunakan uji F (Simultan) menunjukkan bahwa Komuniaksi Word Of Mouth dan Place secara serentak berpengaruh signifikan terhadap Keputusan Pembelian dengan nilai Fhitung sebesar 42,856 > Ftabel 3,11 dengan taraf signifikan sebesar 0,000 < 0,05. Berdasarkan perhitungan menggunakan koefisien determinasi diperoleh nilai Adjusted R Square sebesar 0,493 menunjukkan sekitar 49,3% variabel Keputusan Pembelian dapat dijelaskan oleh variabel Komunikasi Word Of Mouth dan Place.

In this essay, I describe 10 critical complicating factors that directly affect the six basic modeling components of problem definition, assumptions, decision variables, objective functions, constraints, and solution approach. The proposed 10 contextual complicating factors are (1) organization, (2) decision-making processes, (3) measures and key performance indicators, (4) rational and irrational biases, (5) decision horizon and interval, (6) data availability, accuracy, fidelity, and latency, (7) legacy and other computer systems, (8) organizational and individual risk tolerance, (9) clarity of model and method, and (10) implementability and sustainability of the approach. I hypothesize that the core analytical problem cannot be adequately described or usefully solved without careful consideration of these factors. I describe detailed examples of these contextual factors’ effects on modeling from six published applied prescriptive analytics projects and provide other examples from the literature. The complicating factors are pervasive in these projects, directly and dramatically affecting basic modeling components over half the time. Further, in the presence of these factors, 23 statistically significant correlations tend to form in three clusters, which I characterize as culture, decision, and project clusters. Unrecognized, these factors would have hampered the implementation and ongoing use of these analytical models; in a sense, the models themselves were wrong, absent consideration of these contextual considerations. With these insights, I hope to help practitioners identify the effects of these common complications and avoid project failure by incorporating these contextual factors into their modeling considerations. Future research could seek to better understand these factors and their effects on modeling.

In this paper, we analyze how sequentially introducing decision variables into an integer program (IP) affects the value function and its level sets. We use a Gilmore-Gomory approach to find parametrized IP value functions over a restricted set of variables. We introduce the notion of maximal connected subsets of level sets - volumes in which changes to the constraint right-hand side have no effect on the value function - and relate these structures to IP value functions and optimal solutions.

This study aims to measure the effectiveness of Hello Decoration's marketing communications in increasing sales through Instagram social media. The method used in this study is descriptive with a quantitative approach that aims to determine the effectiveness of marketing communications implemented by Hello Decoration. While the statistical formula used is the tabulation of the frequency and the average score for each research variable. The population in this study were all followers of @hellodecoration_mks, totalling 685. While the sampling technique in this study was purposive sampling. The results of this study indicate that the statistical value for each variable is on a very effective scale, namely the awareness variable (4.34), interest variable (4.29), desire variable (4.31), decision variable (4.33), and the action variable (4,30). So that the calculation for all variables reaches a value of 4.31 which is on a very effective scale from the scale range of 4.20 to 5.00. These numbers show that Hello Decoration's marketing communications implemented through Instagram social media have proven to be very effective in persuading customers to use Hello Decoration services and customers feel happy so they want to return to using Hello Decoration services.

The purpose of this study is to find out the influence of service quality and price on the decision to purchase UMKM Roti Bakar 97. The variables used in this study were purchase decision variables as dependent variables, while independent variables were the influence of service quality and price. This type of research is descriptive research with quantitative approach. The subject of the study was consumers who had purchased UMKM Roti Bakar 97 products. Primary data was obtained from questionnaires from 58 respondents with purposive sampling. Then the data is analyzed using multiple linear regression analysis. The results of the study on the t test showed that the variable quality of service (X1) had no significant effect on the purchase decision (Y) with a significance value of 0.169 0.05 and a calculated t value of 1,395 t table 2,004; price variable (X2) has no effect on the purchase decision variable (Y) with a significance value of 0.173 0.05 and a calculated t value of 1,381 t table of 2,004. Based on the test results F service quality and price simultaneously influenced the purchase decision indicated by the significance value of 0.00 0.05

Certain products, such as automobiles, typically have warranty policies that incorporate two dimensions, namely time since purchase of the product and usage based on mileage accumulated. If both of these parameters are less than stipulated values in the warranty policy, in case of product failure, the manufacturer replaces or repairs the product free of charge. In many consumer durable goods, while an initial warranty is offered during purchase of the product, options exist to renew the warranty in the event of no product failure during the initial warranty. In this paper we consider such extended warranties in the context of two-dimensional policies. The decision variables in the formulated model are the warranty time and usage in the initial policy, the warranty time and usage in the extended policy, the product price, and the premium to be charged by the manufacturer for extending the warranty. We assume, however, that not all customers will choose to renew the warranty even if the product did not fail during the initial warranty. Customer propensity to renew warranty could be influenced by the unit product price and the customer's threshold price level, above which the customer is motivated to purchase an extended warranty.

Multimodal multiobjective optimization problems (MMOPs) widely exist in real-world applications, which have multiple equivalent Pareto-optimal solutions that are similar in the objective space but totally different in the decision space. While some evolutionary algorithms (EAs) have been developed to find the equivalent Pareto-optimal solutions in recent years, they are ineffective to handle large-scale MMOPs having a large number of variables. This article thus proposes an EA for solving large-scale MMOPs with sparse Pareto-optimal solutions, i.e., most variables in the optimal solutions are 0. The proposed algorithm explores different regions of the decision space via multiple subpopulations and guides the search behavior of the subpopulations via adaptively updated guiding vectors. The guiding vector for each subpopulation not only provides efficient convergence in the huge search space but also differentiates its search direction from others to handle the multimodality. While most existing EAs solve MMOPs with 2-7 decision variables, the proposed algorithm is shown to be effective for benchmark MMOPs with up to 500 decision variables. Moreover, the proposed algorithm also produces a better result than state-of-the-art methods for the neural architecture search.

Decision rules offer a rich and tractable framework for solving certain classes of multistage adaptive optimization problems. Recent literature has shown the promise of using linear and nonlinear decision rules in which wait-and-see decisions are represented as functions, whose parameters are decision variables to be optimized, of the underlying uncertain parameters. Despite this growing success, solving real-world stochastic optimization problems can become computationally prohibitive when using nonlinear decision rules, and in some cases, linear ones. Consequently, decision rules that offer a competitive trade-off between solution quality and computational time become more attractive. Whereas the extant research has always used homogeneous (i.e., either linear or piecewise-linear) decision rules, the major contribution of this paper is a computational exploration of hybrid decision rules combining the benefits of the two classes of decision rules. We first verify empirically that having higher uncertainty resolution or more linear pieces in early stages is more significant than having it in late stages in terms of solution quality. Then, we compare non-increasing and non-decreasing (i.e., higher uncertainty resolution in early and late stages, respectively) hybrid decision rules in a computational study to illustrate the trade-off between solution quality and computational cost. We also demonstrate a case where, unexpectedly, a linear decision rule is superior to a more complex piecewise-linear decision rule within a simulator. This observation bolsters the need to assess the quality of decision rules obtained from a look-ahead model within a simulator rather than just using the optimal look-ahead objective function value.

In this paper, we consider a supply chain with a single manufacturer and two competing retailers. The manufacturer sells his digital goods, which may be pirated, to customers through a traditional and a digital retail channel. It is assumed that the manufacturer takes a leader role and the retailers follow it. We investigate the contracts that the manufacturer offers to the retailers and our goal is to find the optimal pricing and ordering decisions made by retailers and the best contract that includes maximum profit for the supply chain. Also, we study a numerical example and examine the proposed contracts. On the other hand, in the sensitivity analysis section, we analyze the impact of each parameter of the problem, in particular, the impact of piracy on the profit of supply chain members and decision variables.

The energy storage requirement modelling tool outlined here uses an extension of the pinch methodology to quantify the network flexibility required due to greater variable renewable energy (VRE) integration. Quantifying this as the magnitude of energy storage required as a function of storage duration provides improved understanding of the fundamental balancing problem. Identification of the impact that key decision variables, such as location, VRE penetration and VRE that is supplied through wind have on these requirements has been enabled by condensing this dependence within two non-dimensional indices: the storage magnitude index and the storage duration index. These indices, in addition to the size of storage required, have enabled the tipping-points and VRE penetration levels beyond which short-term storage is not sufficient to be identified for the UK and Australian locations considered. In addition to how effective the provision of excess VRE is in the mitigation of the balancing requirements. This analysis shows that seasonal balancing is required at high levels of VRE penetration for all combinations of wind and solar sources, but can be needed with as low as 50% penetration at certain combinations and locations. The tipping-point is highly specific to location and VRE that is supplied through wind, varying between 30% and 50% of VRE penetration.