Captain Motors Corporation produces two different models of a particular vehicle at each of two plants. The models are similar except for some minor styling differences (slightly different sheet metal designs, color combinations, and the availability of leather seats on the more expensive model). At each plant, CM can produce 1000 vehicles per day (split in any way between the two vehicle models).
Finished vehicles are shipped to each of five different regions of the country. Shipping costs to each region are the same for the two vehicle models, but differ by plant since the plants are located in different parts of the country. These shipping costs are as follows:
Production costs for the two models by plant are as follows:
These costs differ slightly because of differing suppliers. Also, many parts are supplied by the same supplier and most of the firm’s suppliers are closer to plant 1.
During 1 week in January with 5 production days for a total production capacity of 10,000 vehicles, the firm is planning to build the following types of cars for each of the five markets.
(a) Show that this problem can be structured as an out-of-kilter flow problem. Draw the OKF network. In a table give the lower bounds, upper bounds, and unit costs for all links. Describe in words what each class of links does.
(b) Use the MENU-OKF program to solve this problem. (Note you will need to divide all costs by 10 since unit costs cannot exceed 10,000 in the program.)
(c) By how much would the total cost go down if we increased capacity at plant 1 by one unit?
(d) By how much would the total cost go down if we increased capacity at plant 2 by one unit?
(e) For production planning and scheduling reasons and issues related to work flow balancing on the assembly line, the firm does not want the mix of vehicle models at either of the plants to exceed a 55 : 45 ratio in either direction. In other words, the percentage of production of either model cannot exceed 55% of the total production at either plant. (Note that this is actual production and not production capacity.) Again, use the MENU-OKF algorithm to find a new optimal solution in the face of this added constraint.
(f) What is the percentage increase in total cost as a result of adding the constraint outlined in part (e)?