Team #2 Mingang Fu Lin Ben Kuowei Chen

Traditional Manufacturing Processes Product Layout Functional Layout GMLD Lathe department Milling department Drilling department Grinding department (a) Product layout (b)Functional layout Introduction

(c) Group layout Group Technology Introduction

A part family may consist of groups of parts requiring similar and sometimes identical operation processes, materials, and tools. A manufacturing cell is formed by the machines which are required to produce a part family. Goal: form a manufacturing system that consists of cells to maximize the moves of parts processed within the cells, at the same time, to minimize the parts flow between cells Problem Description

Example: Problem Description

Notations: i and j are machine indexes (i, j = 1, 2,…, N m ). k is a part index (k = 1, 2, 3,…, N p ) c is a cell index (c = 1, 2, 3,…,N c ) is the production volume of part k is available transfer units per trip for part k using a transfer device is the upper limit of cell size is the number of trips made by part k between machines i and j: Where indicates the smallest integer value greater than or equal to w. Variables: Formulation 1

Objective function: Constraints: Formulation 1

X 11 =1, X 21 =1 X 32 =1, X 42 =1, X 52 =1 X 63 =1, X 73 =1 Formulation 1 - Example N m = 7, N p = 7, N c = 3 Objective function value = 2

Formulation 1 - Example X 21 =1, X 51 =1 X 32 =1, X 42 =1, X 62 =1 X 13 =1, X 73 =1 Objective function value = 10

m machines and n parts with k cells and there are a total of k(m+n) variables and (m+n) constrains. Formulation 2

With the size of problem increases, the model becomes too large to handle. To overcome this problem, we can change the integer programming model with following declaration: Then we define “group efficiency” as following and maximize it.

Cell 1, Family 1 X 11 =1, X 21 =1, X 31 =0, …X 71 =0 X 12 =0, X 22 =0, X 32 =1, X 42 =1, X 52 =1, X 62 =0, X 72 =0 X 13 =0, …X 53 =0, X 63 =1, X 73 =1 Y11=1, Y21=1, Y31=0, …Y71=0 Y12=0, Y22=0, Y32=1, Y42=1, Y52=1, Y62=0, Y72=0 Y13=0, …Y53=0, Y63=1, Y73=1 Cell 2, Family 2 Cell 3, Family 3 X1=1, X2=1, X3=2, X4=2, X5=2, X6=3, X7=3; Y1=1, Y2=1, Y3=2, Y4=2, Y5=2, Y6=3, Y7=3 e=17, ev=10, eo=10, Gamma=7/27 Formulation 2 - Example

X1=3, X2=1, X3=2, X4=2, X5=1, X6=2, X7=3; Y1=1, Y2=3, Y3=2, Y4=2, Y5=3, Y6=2, Y7=1 e=17, ev=0, eo=0, Gamma=17/17=1, best Formulation 2 - Example

Thank you !