Production Systems and Inventory Control

King Fahd University of Petroleum and Minerals Department of Systems Engineering

ISE 422: Production Systems and Inventory Control, Term: 161

Instruction: Submit the HW in class before the due date (October 23, 2016). Submit a hard

copy in class.

Question 1 [50 marks]: Consider the following data (Table 1) from a small workshop located at

Al-Khobar:

Product Route Demand/period

1 4-1-6-2 150

2 4-5-8-6-1 100

3 7-3-6-1-2 200

4 6-1-2-4 50

Data Preprocessing (this will be a typical step before a layout analysis):

1) Construct the flow matrix for the above data. 2) Calculate the flow dominance measure. What can you infer from the measure?

Figure 1: Spline Layout

Evaluation (let us see how good the above layout is w.r.t to the flow criterion):

3) Calculate the flow path of all the products, if the machines are arranged as in Figure 1.

4) Let 𝐹𝑃𝑝 be the flow path of product 𝑝 for the above spline layout (take from Part (3)). Let

𝑣𝑝 be the demand per period for product 𝑝 (given in Table 1). Calculate the total flow

distance 𝑇𝐹𝐷1, defined as :

𝑇𝐹𝐷1 = ∑ 𝐹𝑃𝑝 ∗ 𝑣𝑝 𝑝∈𝑃

5

1 2 3 4

6 7 8

1 m

1 m

1 m

The distances between every intersection on spline is 1 meter.

King Fahd University of Petroleum and Minerals Department of Systems Engineering

ISE 422: Production Systems and Inventory Control, Term: 161

5) Let 𝑤𝑖𝑗 be the 𝑖 𝑡ℎ row 𝑗𝑡ℎ column element of the flow matrix (take from Part (1)). Let

𝑑𝑖𝑗 be the distance between machine 𝑖 and machine 𝑗 for the line layout given in Figure 1.

Calculate the total flow distance 𝑇𝐹𝐷2, defined as :

𝑇𝐹𝐷2 = ∑ ∑ 𝑤𝑖𝑗 ∗ 𝑑𝑖𝑗

8

𝑗=1

8

𝑖=1

Loop layout 1 (what if we make a loop layout?):

Assume that a single LUL is added to the given system, i.e., the give data is changed by

adding one LUL station before and after every route.

6) Update the flow matrix from Part (1) to incorporate the change (i.e, add a new row and column for the LUL station).

7) Calculate the total flow distance for the following machine position assignment:

𝛼(𝑖) = 𝑖, ∀ 𝑖 = 0,1,2 … ,8.

Cellular layout 2 (what if we make a cellular layout?):

Additional data preprocessing: To answer following questions, you will have to construct

the machine-product index matrix from Table 1.

8) Create a cellular layout for the data given in Table 1 using the DCA algorithm. If there are any bottlenecks, then duplicate minimum number of machines to resolve the

bottlenecks.

9) Calculate the total flow distance assuming that the distance between any two pair of machines is 3 meters.

Space calculations:

Question 2[25]: Consider the data related to number of machines within the department:

Machines Quantity Foot prints

(L x W)

Personal

Space

Material

Space

Max travel

(L)

Max travel

(W)

1 4 5 x 15 sqft 5 x 5 sqft 40 sqft 4 ft 2 ft

2 7 4 x 12 sqft 5 x 5 sqft 30 sqft 2 ft 7 ft

3 5 5 x 5 sqft 5 x 5 sqft 60 sqft 3 ft 3 ft

Calculate the minimum space in sqft required for a department containing all the above

machines. Use an aisle allowance of 18% of the total area while calculating the space.

King Fahd University of Petroleum and Minerals Department of Systems Engineering

ISE 422: Production Systems and Inventory Control, Term: 161

Between Department Analysis:

Question 3[25]: Calculate the TFD for the following block layout using the information from

the following flow matrix. Assume each small box in the layout is of size 2m x 2m. The thick

lines indicates the boundary of the departments.

-- 28 39 18 29

41 -- 21 33 26

F = 28 38 -- 48 29

19 27 36 -- 37

32 22 22 45 --