INTRODUCTION PROBLEM 1 Relevant definitions: $$minimize\quad ^{6} ^{6} ^{6} ^{6} c_{ij}x_{ij}^{kl} \qquad \left ( i\neq j , k\neq l\right )$$ $$ b_{i}^{kl} = \left\{ b^{kl} & i = k \\ b^{kl} & i = l\\ 0 & otherwise \right. $$ $$^{6} \left ( ^{6} x_{ij}^{kl} - ^{6} x_{ji}^{kl} = b_{i}^{kl} \right ) \qquad \left ( i\neq j , k\neq l\right )$$ $$^{6} ^{6} x_{ij}^{kl} \le u_{i,j} \qquad \forall i,j \left ( i\neq j , k\neq l\right )$$ $$ x_{i,j} \ge 0 $$ $$ u_{i,j} &= 30 + 2(-1)^i + 3(-1)^j \\ c_{i,j} &= 50 + 10(-1)^{j+i} & i \ne j\\ b_{i,j} &= 10 + 2(-1)^{i+j} & i \ne j $$ PROBLEM 3 Relevant definitions: - Let xs, t be the amount of drugs bought from supplier s on month t - Let $y_{s,t} = \left\{ 1 & \\ 0 & \right. $ &: min ^{6}( c_{1,t}*x_{1,t} + c_{2,t}*x_{2,t}+ c_{3,t}*x_{3,t}- 7*E_t)\\ &\\ &y_{1,t} + y_{2,t} + y_{3,t} = 1 & t\in \{1, \dots ,6\}\\ &y_{s,t}*d_s \leq x_{s,t} & t\in \{1, \dots ,6\}, s \in \{1,2,3\}\\ &y_{s,t} \leq 1 & t\in \{1, \dots ,6\}, s \in \{1,2,3\}\\ &I_{t} \leq 40 & t\in \{1, \dots ,6\}\\ &I_{t-1} + x_{1,t} + x_{2,t} + x_{3,t} = d_t+I_t + E_t & t\in \{1, \dots ,6\}\\ Month t amp; c1, t amp; c2, t amp; c3, t amp; dt --------- ------------ ------------ ------------ ---------- 1 amp; 15 amp; 11 amp; 11 amp; 99 2 amp; 14 amp; 12 amp; 15 amp; 113 3 amp; 13 amp; 13 amp; 11 amp; 107 4 amp; 12 amp; 14 amp; 15 amp; 121 5 amp; 11 amp; 15 amp; 11 amp; 115 6 amp; 10 amp; 16 amp; 15 amp; 129 : Problem 3. Coefficients d₁ = 129; d₂ = 131, d₃ = 129 Month t amp; ys, t amp; xs, t amp; It amp; Et --------- ---------------- ------------------ -------------- -------------- 1 amp; y3, 1 = 1 amp; x3, 1 = 129 amp; I₁ = 0 amp; E₁ = 30 2 amp; y2, 2 = 1 amp; x2, 2 = 131 amp; I₂ = 0 amp; E₂ = 18 3 amp; y3, 3 = 1 amp; x3, 3 = 129 amp; I₃ = 16 amp; E₃ = 6 4 amp; y1, 4 = 1 amp; x1, 4 = 131 amp; I₄ = 26 amp; E₄ = 0 5 amp; y3, 5 = 1 amp; x3, 5 = 129 amp; I₅ = 40 amp; E₅ = 0 6 amp; y1, 6 = 1 amp; x1, 6 = 131 amp; I₆ = 0 amp; E₆ = 42 : Problem 3. Solution (All the other xs, t and ys, t not mentioned in the table are 0. )