Operations Research

Download e-book for kindle: An Introduction to Fuzzy Linear Programming Problems: by Jagdeep Kaur, Amit Kumar

By Jagdeep Kaur, Amit Kumar

ISBN-10: 3319312731

ISBN-13: 9783319312736

ISBN-10: 331931274X

ISBN-13: 9783319312743

The e-book provides a photograph of the cutting-edge within the box of absolutely fuzzy linear programming. the focus is on displaying present tools for locating the bushy optimum answer of absolutely fuzzy linear programming difficulties during which all of the parameters and choice variables are represented via non-negative fuzzy numbers. It provides new equipment constructed by means of the authors, in addition to present equipment constructed by means of others, and their program to real-world difficulties, together with fuzzy transportation difficulties. in addition, it compares the results of the various tools and discusses their advantages/disadvantages. because the first paintings to gather at one position crucial tools for fixing fuzzy linear programming difficulties, the ebook represents an invaluable reference consultant for college students and researchers, supplying them with the mandatory theoretical and sensible wisdom to accommodate linear programming difficulties less than uncertainty.

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Extra info for An Introduction to Fuzzy Linear Programming Problems: Theory, Methods and Applications

Example text

3): n [pj + (qj − pj )λ, rj − (rj − qj )λ][xj + (yj − xj )λ, zj − (zj − yj )λ] Maximize j=1 subject to n [aij + (bij − aij )λ, cij − (cij − bij )λ][xj + (yj − xj )λ, zj − (zj − yj )λ] j=1 = [bi + (gi − bi )λ, hi − (hi − gi )λ] ∀ i = 1, 2, . . , m xj ≥ 0, yj − xj ≥ 0, zj − yj ≥ 0 ∀ j = 1, 2, . . 2 Existing Method for Solving Fully Fuzzy Linear … 19 Step 3 Using the arithmetic operations of intervals, defined in Sect. 4) n [aij xj + λ(aij yj + bij xj − 2aij xj ) + λ (bij − aij )(yj − xj ), cij zj − λ(2cij zj − cij yj 2 j=1 − bij zj ) + λ2 (cij − bij )(zj − yj )] = [bi + λ(gi − bi ), hi − λ(hi − gi )] ∀ i = 1, 2, .

1 Description of the Problem Dali Company is the leading producer of soft drinks and low-temperature foods in Taiwan. Currently, Dali plans to develop the South-East Asian market and broaden the visibility of Dali products in the Chinese market. Notably, following the entry of Taiwan to the World Trade Organization, Dali plans to seek strategic alliance with prominent international companies and introduced international bread to lighten the embedded future impact. In the domestic soft drinks market, Dali produces tea beverages to meet demand from four distribution centers in Taichung, Chiayi, Kaohsiung and Taipei, with production being based at three plants in Changhua, Touliu and Hsinchu.

M j=1 y j − x j ≥ 0, z j − y j ≥ 0, w j − z j ≥ 0 ∀ j = 1, 2, . . 6) can be written as: n Maximize/Minimize ( (min{ p j , p j }, min{q j , q j }, max{r j , r j }, max{s j , s j })) j=1 subject to n min{ai j , ai j } = bi ∀ i = 1, 2, . . , m j=1 n min{bi j , bi j } = gi ∀ i = 1, 2, . . 7) j=1 n max{ci j , ci j } = h i ∀ i = 1, 2, . . , m j=1 n max{di j , di j } = ki ∀ i = 1, 2, . . , m j=1 y j − x j ≥ 0, z j − y j ≥ 0, w j − z j ≥ 0 ∀ j = 1, 2, . . 8): n Maximize/Minimize ( (min{ p j , p j }, min{q j , q j }, max{r j , r j }, max{s j , s j })) j=1 subject to n min{ai j , ai j } = bi ∀ i = 1, 2, .

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An Introduction to Fuzzy Linear Programming Problems: Theory, Methods and Applications by Jagdeep Kaur, Amit Kumar


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