Facility Layout 2 Basic Data and Layout Evaluation

The objective is to design a block layout. 2 3 1 5 4 4 b Block Layout Show the general placement, dimensions and relative position of departments

Next, how do we evaluate the block layout. • Flow Patterns – qualitatively • Qualitatively generated reward matrix – REL chart – Maximize A-based measure 2 1 100 • Quantitatively generated reward matrix – Flow x Distance x Cost – Minimize this D-based objective 100 3 4 100 200

Flow patterns – qualitative measure

An example ABC Widgets Inc. is trying to create a layout for a new facility. The lot of terrain available is a square, 300 ft. by 300 ft. The company is organized in four departments, with the following dimensions: Dept 1: Dept 2: Dept 3: Dept 4: 100’ x 300’ 100’ x 200’ First, try to build a couple of feasible layouts in the next page

Let’s play with layouts 300 x 300 2 4 1 300 x 300 1 4 2 3 3

Now, let’s explore the relationships between the departments Rating It is absolutely necessary that depts. 1 and 2 are close, and it is especially important that 1 and 4 are close. It is also important that 3 and 4 are somehow close and it’s OK if departments 2 and 4 are close to each other. Other than that, all other relationships are unimportant. Definition A Absolutely Necessary E Especially Important I Important O Ordinary Closeness OK U Unimportant X Undesirable REL 1 2 3 4 1 - A U E 2 - - U O 3 - - - I 4 - -

In this example, we will calculate an Adjacency Based and a Distance Based Score for two layouts 2 100 1 1 3 100 Layout 1 4 100 REL 1 2 3 4 1 - A U E 2 - - U O 3 - - - I 4 - - 2 100 4 100 3 100 200 Layout 2

Step 1: Convert REL data to a Reward Matrix A E I O U (X = = = 8 4 2 1 0 -8) Scores are usually powers of a base number fij REL 1 2 3 4 1 - A U E 1 - 8 0 4 2 - - U O 2 - - 0 1 3 - - - I 3 - - - 2 4 - - - -

Step 2: Find the Adjacency-Based score xij = 1 if the departments are adjacent = 0 if the departments are not adjacent • Adjacency means that they share a border, not corners • Layouts with same adjacency score may have different travel distances

Here is the data we need 2 ABS 1 = 11 100 fij 1 100 3 4 100 200 Layout 1 2 1 100 4 100 3 100 200 Layout 2 REL 1 2 3 4 1 - 8 0 4 2 - - 0 1 3 - - - 2 4 - - ABS 2 = 15

Step 3: Find the Relative Efficiency for both layouts Rel. Efficiency 1 = Rel. Efficiency 2 = ABS 1 ABS 2 = 73% = 100%

Back to the company Now we will obtain some data related to the production processes that take place on ABC Widgets fij Size of the unit load 50 1 1 3 25 200 2 100 4 200 units a day Flow 1 2 3 4 1 - 8 0 4 2 - - 0 1 3 - - - 2 4 - -

Step 1: Find the flow data In this example, we will use the number of daily trips between departments fij f flow between dept i and j c cost of moving the load (independent of MHE) d distance from dept i to j (Centroid-to-Centroid and Rectilinear) Flow 1 2 3 4 1 - 8 0 4 2 - - 0 1 3 - - - 2 4 - -

How do we calculate Rectilinear Distances? Rectilinear Distance means that we move horizontally and vertically, not diagonally Does this make sense? When or where? Rect. Dist. = dx + dy y 2 dx y 1 x 1 dy Rect. Dist. = |x 1 -x 2| + |y 1 -y 2| x 2

Step 2: Let’s find the distances between departments Rectilinear Centroids 2 100 1 1 3 100 4 3 100 2 3 4 x 50 200 150 250 y 150 250 100 d 1 2 3 4 1 - 250 150 2 - - 200 3 - - - 100 4 - - d 1 2 3 4 100 2 1 Distances 200 100 1 2 3 4 1 - 250 150 x 50 200 200 2 - - 200 100 y 150 250 50 150 3 - - - 100 4 - -

Step 3: Find the Distance Based score d 1 2 3 4 1 - 250 150 2 - - 200 3 - - - 100 4 - - d 1 2 3 4 1 - 250 150 2 - - 200 100 3 - - - 100 4 - - DBS 1 = 3400 fij Flow 1 2 3 4 1 - 8 0 4 2 - - 0 1 3 - - - 2 4 - - DBS 2 = 2900

Next few classes will we discuss FLP algorithms. • Methods to generate layouts from scratch or just generating improvements to layouts. 2 1 • Once we have a layout, we use our D-based and Abased measures to compare the layouts and select the best alternative. 4 3 5 4 b