enter image description here


enter image description here


What I tried:

  1. 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...to product [; i ;] ? or from ?

  1. 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?

  1. 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 to product i? from?

Does it matter?

Is my [; y_{ijk} ;] wrong?


From Chapter 3 here.

asked 20 Mar '16, 08:44

BCLC's gravatar image

BCLC
8312
accept rate: 0%

edited 08 Apr '16, 06:12

Be the first one to answer this question!
toggle preview

Follow this question

By Email:

Once you sign in you will be able to subscribe for any updates here

By RSS:

Answers

Answers and Comments

Markdown Basics

  • *italic* or _italic_
  • **bold** or __bold__
  • link:[text](http://url.com/ "Title")
  • image?![alt text](/path/img.jpg "Title")
  • numbered list: 1. Foo 2. Bar
  • to add a line break simply add two spaces to where you would like the new line to be.
  • basic HTML tags are also supported

Tags:

×231
×101
×37
×25
×4

Asked: 20 Mar '16, 08:44

Seen: 1,016 times

Last updated: 08 Apr '16, 06:12

OR-Exchange! Your site for questions, answers, and announcements about operations research.