Lot sizing
The University of Hong Kong
Department of Industrial and Manufacturing Systems Engineering
IELM6028 – Enterprise Logistics and Facilities Design
Part 2- Modelling and analysis – Tutorial problems on plant layout
Question 1
Three existing manufacturing facilities A, B and C are located in sites 1, 2 and 3 respectively as shown in Fig Q1 (a). Increase of production volume calls for three more new facilities K, L and M to be set up, which will occupy the sites adjacent to the present ones. Sites 1, 2 and 3 are depicted as the grey areas in the figure.
The expected quantities of material flow between the existing and the new facilities, and that amongst the new facilities, have been estimated and given in the flow-between charts in Fig Q1 (b). Consideration must be given to the material flow when planning for the layout of new facilities, given that the site arrangements for A, B and C remain the same.
Fig Q1 (a) Site arrangement (all the sites are 1 unit square in area)
A B C K L M K 7 9 4 K - 4 3 L 10 6 8 L - 6 M 5 6 9 M -
Fig Q1 (b) Flow-between charts showing the material flow between the facilities
a) Assuming all the material flow are rectilinear movements between centroids, construct a model representing the total quantity-distance product for this set-up.
b) Establish a systematic approach to obtain the global optimum assignment of facilities K, L and M to sites 4, 5 and 6. The calculations must be shown clearly at all stages.
Suggested solution
The model representing the total quantity-distance product: TC: is the total cost, or quantity-distance product. a: the assignment vector of the new departments. c(i,k) : a cost incurred if department i is located at site k (due to transportation of dept i with the existing departments.)
Material flow matrix Distance matrix (from Fig Q1(b)) (Calculated from Fig Q1(a)) A B C 4 5 6 K 7 9 4 1 2 2 3 L 10 6 8 2 1 3 2 M 5 6 9 3 1 1
Department of Industrial and Manufacturing Systems Engineering
IELM6028 – Enterprise Logistics and Facilities Design
Part 2- Modelling and analysis – Tutorial problems on plant layout
Question 1
Three existing manufacturing facilities A, B and C are located in sites 1, 2 and 3 respectively as shown in Fig Q1 (a). Increase of production volume calls for three more new facilities K, L and M to be set up, which will occupy the sites adjacent to the present ones. Sites 1, 2 and 3 are depicted as the grey areas in the figure.
The expected quantities of material flow between the existing and the new facilities, and that amongst the new facilities, have been estimated and given in the flow-between charts in Fig Q1 (b). Consideration must be given to the material flow when planning for the layout of new facilities, given that the site arrangements for A, B and C remain the same.
Fig Q1 (a) Site arrangement (all the sites are 1 unit square in area)
A B C K L M K 7 9 4 K - 4 3 L 10 6 8 L - 6 M 5 6 9 M -
Fig Q1 (b) Flow-between charts showing the material flow between the facilities
a) Assuming all the material flow are rectilinear movements between centroids, construct a model representing the total quantity-distance product for this set-up.
b) Establish a systematic approach to obtain the global optimum assignment of facilities K, L and M to sites 4, 5 and 6. The calculations must be shown clearly at all stages.
Suggested solution
The model representing the total quantity-distance product: TC: is the total cost, or quantity-distance product. a: the assignment vector of the new departments. c(i,k) : a cost incurred if department i is located at site k (due to transportation of dept i with the existing departments.)
Material flow matrix Distance matrix (from Fig Q1(b)) (Calculated from Fig Q1(a)) A B C 4 5 6 K 7 9 4 1 2 2 3 L 10 6 8 2 1 3 2 M 5 6 9 3 1 1