비선형 고객 보상프로그램에 대한 소비자 반응

박상준(Park, Sang-June),변지연(Byun, Ji-Yeon) 한국마케팅학회 2015 마케팅연구 Vol.30 No.3

고객 보상프로그램은 일반적으로 제품 구매에 따라 구매 단위당 일정 포인트(또는 마일리지)를 적립해 주고, 적립된 포인트가 일정 수준을 넘어서면 보상물(제품 또는 할인)을 제공해 주는 고객 인센티브 제도로 운영되고 있다. 본 연구에서는 고객 보상프로그램을 누적 구매량에 관계없이 구매단위당 동일한 포인트를 적립해주는 ‘선형고객 보상프로그램’과 누적 구매량에 따라 구매단위당 포인트를 다르게 적립해 주는 ‘비선형 고객 보상프로그램’으로 구분하고, 이들에 대한 소비자 반응 차이를 분석하고 있다. 실증연구 결과는 고객 보상프로그램의 운영비가 동일하게 설계된 ‘선형 고객 보상프로그램’과 ‘비선형 고객 보상프로그램’의 비교를 통해 ‘비선형 고객 보상프로그램’이 보다 긍정적인 소비자 반응(선호도, 소비 적극성, 소비 감정)을 이끌어 낼 수 있음을 보여주고 있다. 고객보상프로그램 운영에 따른 비용의 차이가 없으면서도 고객의 반응을 제고할 수 있는 고객 보상프로그램의 설계는 기업의 수익과 직결된다는 측면에서, ‘비선형 고객 보상프로그램’에 대한 본 연구는 보상프로그램을 운영하는 마케팅 관리자들에게 보다 효율적인 고객 보상프로그램 개발에 관한 시사점을 제공할 것으로 기대된다. A customer compensation program enforced as the additional service is widely used in various industries (for example, aviation industry). We classify customer compensation programs into ‘linear compensation program’ and ‘non-linear compensation program’, and analyze a consumer’s differential reactions to the two different types of the compensation programs. In the ‘linear compensation program’, customers get some points (or mileages) depending on the amounts of their purchases after joining the compensation program. In the ‘non-linear compensation program, on the other hand, they get a fixed sum of points just after a consumer joins a compensation program, and then gets additional points depending on the amounts of their purchases. If a ‘linear compensation program’ and a ‘non-linear compensation program’ ask the identical points to be compensated, the financial (or operation) costs of the both programs are identical, however, customers’ attitudes on the both programs may be different. This paper provides some insights on customer compensation programs from the empirical studies. First, consumers prefer a ‘non-linear consumer compensation program’ to a ‘linear consumer compensation program’. Second, their activeness of consumption behaviors in a ‘non-linear compensation program’ is higher than in a ‘linear compensation program’. Third, consumers feel more positive consumption emotion in a ‘non-linear customer compensation program’ than in a ‘linear customer compensation program’. Almost companies use a ‘linear compensation program’ as a customer compensation program, however, this study demonstrates that a ‘non-linear compensation program’ may be more effective in deriving positive customers’ responses than a ‘linear compensation program’ even though the identical operation cost is expected in the both programs.

선형계획법을 이용한 한국 성인의 최적 식품섭취패턴 설계 (Ⅱ) : 단계적 나트륨 목표섭취량 설정에 따른 최적 식품섭취패턴 조정

아사노가나(Kana Asano),양홍석(Hongsuk Yang),이영미(Youngmi Lee),김미영(Meeyoung Kim),윤지현(Jihyun Yoon) 한국영양학회 2019 Journal of Nutrition and Health Vol.52 No.4

본 연구는 선형계획법을 이용하여 나트륨의 제약조건 변화에 따른 최적 식품섭취패턴 변화를 살펴보고 보다 실현성이 높은 나트륨의 목표섭취량을 구하고, 이를 나트륨의 제약조건으로 최적 식품섭취패턴을 설계하는 것을 목적으로 수행되었다. 주요 결과는 다음과 같다. 나트륨의 제약조건 (2,000 mg)을 100 mg 단위로 증가시키면서 선형계획법을 이용하여 조미료의 최적섭취량을 성 및 연령별 여덟 집단에 대해 산출하였다. 조미료의 최적섭취량이 조미료의 실제섭취량의 25<SUP>th</SUP> 백분위수에 가장 가까운 경우의 나트륨 양은 남성 19 ~ 29세, 30 ~ 49세, 50 ~ 64세, 65세 이상에서 각각 3,600 mg, 4,500 mg, 4,200 mg, 3,400 mg, 여성 19 ~ 29세, 30 ~ 49세, 50 ~ 64세, 65세 이상에서 각각 2,800 mg, 3,100 mg, 3,100 mg, 2,500 mg으로 산출되었다. 이를 나트륨의 제약조건으로 하였을 때 성 및 연령별 여덟 집단의 최적 식품섭취패턴이 선형계획법을 이용하여 수학적으로 설계되었다. 결론적으로 나트륨의 제약조건을 2,000 mg으로부터 500 ~ 2,500 mg 정도 성 및 연령별로 상향 조정하였을 때 실현성이 높은 최적 식품섭취패턴이 설계되었다. 이 최적 식품섭취패턴에서는 여덟 집단 모두 공통적으로 채소류, 여성에서 우유 · 유제품류, 50 ~ 64세를 제외한 여성에서 과일류의 섭취량을 현재보다 더 늘릴 필요가 있는 것으로 나타났다. Purpose: The Dietary Reference Intakes for Koreans (KDRIs) suggest that the goal for the intake of sodium should be less than 2,000 mg, which is thought to be infeasible to achieve when eating the typical Korean diet. This study aimed to obtain the new intake goals for sodium with improved feasibility to achieve, and also to design optimized food intake patterns for Korean adults by performing linear programming. Methods: The data from a one day 24-hour dietary recall of the 2010 ~ 2014 Korea National Health and Nutrition Survey were used to quantify food items that Korean adults usually consumed. These food items were categorized into seven groups and 24 subgroups. The mean intakes and intake distributions of the food groups and the food subgroups were calculated for eight age (19 ~ 29, 30 ~ 49, 50 ~ 64, and over 65 years old) and gender (male and female) groups. A linear programming model was constructed to minimize the difference between the optimized intakes and the mean intakes of the food subgroups while meeting KDRIs for energy and 13 nutrients, and not exceeding the typical quantities of each of the food subgroups consumed by the respective age and gender groups. As an initial solution of the linear programming, the optimized intake of seasonings, including salt, was calculated as 0 g for all the age and gender groups when the sodium constraint was inserted not to exceed 2,000 mg. Therefore, the sodium constraint was progressively increased by 100 mg until the optimized intake of seasoning was obtained as the values closest to the 25<SUP>th</SUP> percentile of the intake distribution of seasonings for the respective age and gender groups. Results: The optimized food intake patterns were mathematically obtained by performing linear programming when the sodium constraint values were 3,600 mg, 4,500 mg, 4,200 mg, 3,400 mg, 2,800 mg, 3,100 mg, 3,100 mg, and 2,500 mg for the eight age and gender groups. Conclusion: The optimized food intake patterns for Korean adults were designed by performing linear programming after increasing the sodium constraint values from 2,000 mg to 2500 ~ 4,500 mg according to the age and gender groups. The resulting patterns suggest that current diets should be modified to increase the intake of vegetables for all the groups, milk/dairy products for the female groups, and fruits for the female groups except for the females aged 50 ~ 64 years.

DYNAMIC PROGRAMMING FOR GENERAL LINEAR QUADRATIC OPTIMAL STOCHASTIC CONTROL WITH RANDOM COEFFICIENTS

( Shan Jian Tang ) 한국금융공학회 2014 한국금융공학회 학술발표회 Vol.2014 No.1

We are concerned with the linear-quadratic optimal stochastic control problem where all the coe_cients of the control system and the running weighting matrices in the cost functional are allowed to be predictable (but essentially bounded) processes and the terminal state-weighting matrix in the cost functional is allowed to be random. Under suitable conditions, we prove that the value field V (t, x, !), (t, x, !) ∈ [0, T] × Rn × , is quadratic in x, and has the following form: V (t, x) = hKtx, xi where K is an essentially bounded nonnegative symmetric matrix-valued adapted processes. Using the dynamic programming principle (DPP), we prove that K is a continuous semimartingale of the form and that (K, L) with L := (L1, ... ,Ld) is a solution to the associated backward stochastic Riccati equation (BSRE), whose generator is highly nonlinear in the unknown pair of processes. The uniqueness is also proved via a localized completion of squares in a self-contained manner for a general BSRE. The existence and uniqueness of adapted solution to a general BSRE was initially proposed by the French mathematician J. M. Bismut [in SIAM J. Control & Optim., 14(1976), pp. 419?444, and in S´eminaire de Probabilit´es XII, Lecture Notes in Math. 649, C. Dellacherie, P. A. Meyer, and M. Weil, eds., Springer-Verlag, Berlin, 1978, pp. 180?264], and subsequently listed by Peng [in Control of Distributed Parameter and Stochastic Systems (Hangzhou, 1998), S. Chen, et al., eds., Kluwer Academic Publishers, Boston, 1999, pp. 265?273] as the first open problem for backward stochastic di_erential equations. It had remained to be open until a general solution by the author [in SIAM J. Control & Optim., 42(2003), pp. 53?75] via the stochastic maximum principle with a viewpoint of stochastic flow for the associated stochastic Hamiltonian system. The present paper is its companion, and gives the second but more comprehensive (seemingly much simpler, but appealing to the advanced tool of Doob-Meyer decomposition theorem, in addition to the DDP) adapted solution to a general BSRE via the DDP. Further extensions to the jump-di_usion control system and to the general nonlinear control system are possible.

선형계획법을 이용한 한국 성인의 최적 식품섭취패턴 설계 (Ⅰ)

아사노가나(Asano, Kana),양홍석(Yang, Hongsuk),이영미(Lee, Youngmi),윤지현(Yoon, Jihyun) 한국영양학회 2018 Journal of Nutrition and Health Vol.51 No.1

본 연구는 선형계획법을 이용하여 현재의 식품섭취패턴에서 크게 벗어나지 않으면서 영양섭취기준을 충족하는 한국 성인의 최적 식품섭취패턴을 설계하였고, 주요 결과는 다음과 같다. 식품품목별 실제섭취량과 최적섭취량을 비교하였을 때 실제섭취량보다 최적섭취량이 높게 나타나 영양섭취기준을 충족하기 위해서 현재보다 섭취량을 더 늘릴 필요가 있는 식품품목으로 모든 집단에서 공통적으로 채소류, 50 ~ 64세 남성을 제외한 집단에서 우유 · 유제품류인 것으로 나타났다. 50 ~ 64세를 제외한 여성에서는 채소류, 우유 · 유제품류 이외에도 과일류도 섭취량을 더 높여야 하는 식품품목으로 나타났다. 모든 남성 집단과 19 ~ 29세를 제외한 여성 집단에서 김치의 최적섭취량이 실제 섭취량보다 낮게 나타나 김치는 덜 섭취해야 하는 식품품목인 것으로 파악되었다. 또한 조미료에 대해서는 모든 집단에서 공통적으로 최적섭취량이 0 g으로 산출되었다. 이에 선형계획법을 이용해서 설계한 최적 식품섭취패턴에서 조미료의 최적섭취량이 실생활에서 실현 불가능한 0 g으로 산출되었기 때문에 설계한 최적 식품섭취패턴의 실현성을 높이기 위해서는 나트륨의 목표섭취량을 실제섭취량이 고려된 보다 현실적인 기준으로 재설정할 필요가 있다. Purpose: The aim of this study was to design optimized food intake patterns that meet the nutritional recommendations with minimal changes from the current food intake patterns among Korean adults using linear programming. Methods: Data of a one day 24-hour dietary recall from the 2010 ~ 2014 Korea National Health and Nutrition Survey were used to quantify the food items that Korean adults usually consumed. These food items were categorized into seven groups and 24 subgroups. The mean intakes and intake distributions of the food groups and the food subgroups were calculated for eight age (19 ~ 29, 30 ~ 49, 50 ~ 64, and over 65 years old) and gender (male and female) groups. A linear programming model was constructed to minimize the difference between the optimized and mean intakes of the food subgroups while meeting the Dietary Reference Intakes for Koreans (KDRIs) for energy and 13 nutrients, and not exceeding the typical quantities of each food subgroup consumed by the respective age and gender groups. Results: The optimized food intake patterns, which were a set of quantities of 24 food subgroups, were obtained mathematically for eight age and gender groups. Overall, major modifications of current diet were required to increase the intake of vegetables and milk/dairy products and decrease the Kimchi intake. The optimized intake of seasonings, including salt, was calculated to be 0 g for all the age and gender groups. Conclusion: The optimized food intake patterns designed using linear programming in this study lack feasibility because they suggest a seasoning consumption of 0 g. Modification of intake goal for sodium is needed to obtain optimized food intake patterns with improved feasibility.

Interactive Fuzzy Linear Programming Approach to Distribution Network Problem

Jonghwan Lee(이종환) 한국지능시스템학회 2009 한국지능시스템학회 학술발표 논문집 Vol.19 No.1

In this research, a distribution network problem is approached by an interactive fuzzy linear programming. A produced products in the factory are distributed to a distribution centers and warehouses. This problem is modeled as a distribution network problem. The network problem has a global optimal solution; however, decision maker may want to see the various kinds of solutions, according to the resource's upper bound and lower bound. Decision maker can make a better decision using fuzzy set theory rather than just having an optimal solution. User dependent and problem oriented concept is used to obtain a flexible linear programming solution. Decision maker plays an important role in this problem. Because the decision can be different depend on each fuzzy situations. But, we will provide an abundant numerical output to make a robust decision; however, decision maker have to make a final decision.

선형 제약 만족 최적화 문제를 위한 정수계획법 기반 지역 탐색 기법

황준하(Jun-Ha Hwang),김성영(Sung-Young Kim) 한국컴퓨터정보학회 2010 韓國컴퓨터情報學會論文誌 Vol.15 No.9

선형 제약 만족 최적화 문제는 선형식으로 표현 가능한 목적함수 및 복잡한 제약조건을 포함하는 조합 최적화 문제를 의미한다. 정수계획법은 이와 같은 문제를 해결하는 데 매우 효과적인 기법으로 알려져 있지만 문제의 규모가 커질 경우 준최적해를 도출하기까지 매우 많은 시간과 메모리를 요구한다. 본 논문에서는 지역 탐색과 정수계획법을 결합하여 탐색 성능을 향상할 수 있는 방안을 제시한다. 기본적으로 대상 문제의 해결을 위해 지역 탐색의 가장 단순한 형태인 단순 언덕오르기 탐색을 사용하되 이웃해 생성 시 정수계획법을 적용한다. 또한 부가적으로 초기해 생성을 위해 제약 프로그래밍을 활용한다. N-Queens 최대화 문제를 대상으로 한 실험 결과, 본 논문에서 제시한 기법을 통해 다른 탐색 기법들보다 훨씬 더 좋은 해를 도출할 수 있음을 확인할 수 있었다. Linear constraint satisfaction optimization problem is a kind of combinatorial optimization problem involving linearly expressed objective function and complex constraints. Integer programming is known as a very effective technique for such problem but require very much time and memory until finding a suboptimal solution. In this paper, we propose a method to improve the search performance by integrating local search and integer programming. Basically, simple hill-climbing search, which is the simplest form of local search, is used to solve the given problem and integer programming is applied to generate a neighbor solution. In addition, constraint programming is used to generate an initial solution. Through the experimental results using N-Queens maximization problems, we confirmed that the proposed method can produce far better solutions than any other search methods.

FUZZY NUMBER LINEAR PROGRAMMING: A PROBABILISTIC APPROACH (3)

Maleki, H.R.,Mashinchi, M. 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.15 No.1

In the real world there are many linear programming problems where all decision parameters are fuzzy numbers. Several approaches exist which use different ranking functions for solving these problems. Unfortunately when there exist alternative optimal solutions, usually with different fuzzy value of the objective function for these solutions, these methods can not specify a clear approach for choosing a solution. In this paper we propose a method to remove the above shortcoming in solving fuzzy number linear programming problems using the concept of expectation and variance as ranking functions

Mixed Integer Linear Programming을 이용한 온칩 크로스바 네트워크 토폴로지 합성

전민제(Minje Jun),정의영(Eui-Young Chung) 대한전자공학회 2013 전자공학회논문지 Vol.50 No.1

Development of Organic Material Recommendation System for Organic Rice Using Linear Programming

Cho-Rong Lee,Sang-Min Lee,Hyun Young Hwang,Jae-Hoon Shin,Jung-Hun Ok,Hong-Shik Nam,Jung-Lai Cho,Kwang-Su Kim,Nan-Hee An 한국토양비료학회 2021 한국토양비료학회지 Vol.54 No.4

Fertilizer recommendation system (FRS) is a useful method for environmentally friendly agriculture. However, the conventional FRS does not deal with organic materials such as green manure and oilcake, which used for domestic organic farming. In this study, we developed an organic material recommendation system (OMRS) using linear programming. This procedure calculates the amount of organic material that maximizes the fertilizer effect under constraints such as N input range and C/N ratio. A combination of two organic materials, including green manure etc., is considered. The procedure was tested in the R statistic program using lp_solve, a library for the mixed integer linear programming solver. Application of this model increased rice yield index than standard rate of fertilizer. This program was also implemented to Korea Soil Information System. This system will be useful for farmers to make decisions that meet their specific needs, such as organic resources, crop nutrient requirements, and environmental regulatory policies.

다선택 다차원 배낭 문제를 위한 정수 계획법 기반 지역 탐색

황준하(Junha Hwang) 한국컴퓨터정보학회 2018 韓國컴퓨터情報學會論文誌 Vol.23 No.12

The multiple-choice multidimensional knapsack problem (MMKP) is a variant of the well known 0-1 knapsack problem, which is known as an NP-hard problem. This paper proposes a method for solving the MMKP using the integer programming-based local search (IPbLS). IPbLS is a kind of a local search and uses integer programming to generate a neighbor solution. The most important thing in IPbLS is the way to select items participating in the next integer programming step. In this paper, three ways to select items are introduced and compared on 37 well-known benchmark data instances. Experimental results shows that the method using linear programming is the best for the MMKP. It also shows that the proposed method can find the equal or better solutions than the best known solutions in 23 data instances, and the new better solutions in 13 instances.