A k-hop Collaborate Game Model: Extended to Community Budgets and Adaptive Non-Submodularity

Revenue maximization (RM) is one of the most important problems on online social networks (OSNs), which attempts to find a small subset of users in OSNs that makes the expected revenue maximized. It has been researched intensively before. However, most of exsiting literatures were based on non-adaptive seeding strategy and on simple information diffusion model, such as IC/LT-model. It considered the single influenced user as a measurement unit to quantify the revenue. Until Collaborate Game model appeared, it considered activity as a basic object to compute the revenue. An activity initiated by a user can only influence those users whose distance are within k-hop from the initiator. Based on that, we adopt adaptive seed strategy and formulate the Revenue Maximization under the Size Budget (RMSB) problem. If taking into account the product's promotion, we extend RMSB to the Revenue Maximization under the Community Budget (RMCB) problem, where the influence can be distributed over the whole network. The objective function of RMSB and RMCB is adatpive monotone and not adaptive submodular, but in some special cases, it is adaptive submodular. We study the RMSB and RMCB problem under both the speical submodular cases and general non-submodular cases, and propose RMSBSolver and RMCBSolver to solve them with strong theoretical guarantees, respectively. Especially, we give a data-dependent approximation ratio for RMSB problem under the general non-submodular cases. Finally, we evaluate our proposed algorithms by conducting experiments on real datasets, and show the effectiveness and accuracy of our solutions

The effect of discount coupons on lead time driven cancellations

학위논문(석사) -- 서울대학교대학원 : 경영대학 경영학과, 2021.8. 양홍석.생산 운영 관리에서 배송은 성공의 핵심적인 요인으로 작용한다. 하지만, 완벽한 운영 체계를 가지고 있지 않은 회사들은 제품의 인기로 인한 갑작스러운 주문 폭주를 감당할 수 없어 고객에게 제때 배송을 할 수 없는 경우가 발생한다. 이로 인해 고객은 기다리다 지쳐 주문을 취소할 수 있으면 이는 회사의 이익 손실과 직결된다. 따라서 본 논문에서는 인센티브의 일종인 쿠폰 (판촉)을 제공하여 기업의 손실을 최소화하고자 한다. 본 연구의 목적은 다음과 같다. 1) 쿠폰 도입이 주문 취소가 발생하는 상황에서 기업 이익에 얼마나 도움이 되는지 2) 최적의 쿠폰 할인 수준을 어떻게 결정해야하는지 3) 기업이 쿠폰을 도입해야 하는 시기가 어떻게 되는지 알아볼 것이다. 본 연구를 진행하기 위해서 비동질적인 포아송 과정(nonhomogeneous Poisson process)을 통하여 예측된 주문 취소 양과 쿠폰을 받아들일지에 대한 확률 함수를 이용하여 이익 함수를 구조화한다. 다음 최적의 쿠폰 레벨 변화 추이를 살펴볼 것이다. 결론적으로 고객에게 쿠폰을 제공하는 것은 기업의 이익 손실을 최소화하는데 도움이 된다. 그러나 제품의 인기 기간이 늘어나고 제품의 인기가 증가 함수를 따르면, 어느 특정한 시점부터는 쿠폰의 효율을 감소되고 심지어 무용지물이 된다. 본 연구는 길어진 리드 타임으로 인한 주문 취소가 발생하는 상황에서 기업 관리자들이 기업의 이익을 극대화하기 위해 쿠폰 도입을 고려하여 어떻게 대처해야 하는지에 대한 통찰력을 제공하고 학문적인 부분에서는 쿠폰과 리드 타임으로 인한 주문 취소를 같이 고려하여 이익을 극대화하는 연구 분야를 확장하는데 의미를 지니고 있다.Delivery is one of the key success factors in operations management. However, firms may be difficult to deliver products to customers on time because of meagre production system if there is an increase of orders due to popularity. This may cause customers to cancel their orders, which are a loss in profit. Therefore, this paper by providing discount coupon, tries to minimize firms’ loss. The aims of this study are: 1) to examine how helpful coupon is to the profit in order cancellation situation; 2) to determine the optimal level of discount coupon; and 3) when should firms introduce coupons. This paper, therefore, first find the expected number of order cancellations by using nonhomogeneous Poisson process. Second, by introducing discount coupon with multivariate probability function, profit function will be structured. Then, analysis on the optimal level of discount coupon and point when to introduce discount coupon will be carried out. In addition, by numerical analysis, a trend of optimal level change by time period will be looked. In conclusion, offering coupon to the customers helps a firm to minimize its loss of profit. However, if popularity does not settle down, discount coupon loses its advantage because lead time keep increasing. This paper gives insight of how managers should respond to the situation where order cancellations occur due to the long lead time by considering discount coupon to maximize their profit. For academic insight, this paper offers a broader research on profit maximization by jointly thinking coupon and order cancellations due to lead time.1.Introduction 1 2.Literature Review 3 2.1 History of discount coupon 3 2.2 Order cancellation and lead time related studies 5 3.Model Development 9 3.1 Case dealing in the model 9 3.1.1 Notation 11 3.1.2 Assumption 12 3.2 Basic profit function 13 3.3 Loss of profit due to order cancellation 13 3.4 Profit change due to introduction of coupon 15 4.Model Analysis 19 4.1 Optimal level of , which maximizes 19 4.2 Decision to adopt coupon 21 4.3 Numerical analysis 23 4.3.1 Settings 24 4.3.2 Results 25 5.Conclusion 27 6.Discussion 29 References 32 Abstract in Korean 36석

Adaptive Multi-Feature Budgeted Profit Maximization in Social Networks

Online social network has been one of the most important platforms for viral marketing. Most of existing researches about diffusion of adoptions of new products on networks are about one diffusion. That is, only one piece of information about the product is spread on the network. However, in fact, one product may have multiple features and the information about different features may spread independently in social network. When a user would like to purchase the product, he would consider all of the features of the product comprehensively not just consider one. Based on this, we propose a novel problem, multi-feature budgeted profit maximization (MBPM) problem, which first considers budgeted profit maximization under multiple features propagation of one product. Given a social network with each node having an activation cost and a profit, MBPM problem seeks for a seed set with expected cost no more than the budget to make the total expected profit as large as possible. We consider MBPM problem under the adaptive setting, where seeds are chosen iteratively and next seed is selected according to current diffusion results. We study adaptive MBPM problem under two models, oracle model and noise model. The oracle model assumes conditional expected marginal profit of any node could be obtained in O(1) time and a (1-1/e) expected approximation policy is proposed. Under the noise model, we estimate conditional expected marginal profit of a node by modifying the EPIC algorithm and propose an efficient policy, which could return a (1-exp({\epsilon}-1)) expected approximation ratio. Several experiments are conducted on six realistic datasets to compare our proposed policies with their corresponding non-adaptive algorithms and some heuristic adaptive policies. Experimental results show efficiencies and superiorities of our policies.Comment: 12 pages, 6 figure