What I tried: - Variables
Let [; x_{ijk} = 1 ;] if, in month [; k ;], product [; i ;] should be made in production line [; j ;], where [;i=1-3, j=1-2, \ \text{and} \ $k=1-6;]. Let [; d_{ik} ;] represent how much of product [; i ;] should be made in month [; k ;]. Let [; c_{ij} ;] represent unit production cost of producing product [; i ;] in production line [; j ;]. Let [; p_{ij} ;] represent production rate of producing product [; i ;] in production line [; j ;]. Let [; s_{ij} ;] represent cost of switching... - Objective Function
Min $$z = 0.5\sum_{k=1}^{6} x_{1,j,k} + 0.35\sum_{k=1}^{6} x_{2,j,k} + 0.45\sum_{k=1}^{6} x_{3,j,k} + \sum_i \sum_j \sum_k c_{ij} p_{ij} x_{ijk}$$ $$- \sum_i \sum_j \sum_k s_{ijk} y_{ijk} x_{ijk}$$ where [; y_{ijk} = 1 ;] if, in month k, production line [; j ;] switches (to or from?) product [; i ;] and [; 0 ;] otherwise. Or is that the other way around? - Constraints:
For all [; k ;], all [; j ;] and all [; i ;], $$\text{Constraints} \ 1-36: \sum_{m=1}^{k} p_{ij}x_{ijm} - d_{i,0} \ge \sum_{m=1}^{k} d_{im}$$ $$\text{Constraints} \ 37-72: x_{ijk} \le My_{ijk}$$ where [; d_{i,0} ;] represents how much of product i is in the initial inventory. Is that right? To what is [; s_{ijk} ;] supposed to refer? Cost of switching Does it matter? Is my [; y_{ijk} ;] wrong? From Chapter 3 here.
asked
BCLC |