Darby Company, a producer of meters for measuring electric power consumption has expanded its business operations beyond their El Paso Plant in Texas towards the west coast and built a more cost efficient plant in San Bernardino (SanB), California. The firm also opened a third Distribution Centre (DC) Las Vegas to better serve customers in the larger markets zones of California. The current network presents several constraints to the firm to distribute meters at the lowest possible per unit cost as plants have differing production cost levels. In this case a fixed charge for production and transportation cost per unit has been imposed for each link between Plants and between DC’s and customer areas.
To improve the total transport cost of the current distribution system design the company aims at using its DC in Santa Fe, New Mexico as a transshipment hub serving all nine customer zones. The other two DC’s split the nine customer areas among them more effectively to serve all nine customer zones more effectively than one DC possibly could to increase service quality levels while reducing total transportation costs.
Thirdly a direct shipment scenario from both plants to 3 selected customer zones is supposed to further reduce total transportation cost. An optimization of the current network system design has been realized by utilizing MS -Excel linear programming technique with add - in solver function.
Linear programming is heavily used in microeconomics and company management, such as planning, production, transportation, technology etc. Although modern management problem are continuously changing, most companies would like to maximize profits or minimize costs with their limited resources. Therefore, many issues can boil down to linear programming problems, Bernd Gartner, Jiri Matousek (2006).
Linear programming consists of three main components; a decision variable, an objective function and limitation constraints, both of which are linear. The method is a mathematical statement of a problem written in a form that lends itself to solution using standard solution techniques.
Graph 1: Current Distribution System Design
What is the problem of the current distribution network design?
Currently the company does not perform direct shipments from plants to proximate customer zones or allow customers to pick up consignments under ex - works conditions to avoid incurring transportation costs at first instance.
Instead customer zones are being served by three DC’s which are in some cases further away from customer areas than the plant itself. Even so it is not mentioned in the case, it appears to be, that the company does not make extensive use of cross docking operations to reduce inventory holding cost. Whenever one of the three DC’s is restricted to serve customers in the same state which currently require meters; another customer area could be served by a DC nearer to the relevant customer area.
Due to limitations of the current Distribution Strategy in Graph 1 as in a one to one approach scenario from DC’s to customer zones the total production costs are the highest as the more expensive plant El Paso would have to run at a 100% production capacity which appears to be not viable in the long run. As a result excess capacity of the more efficient SB plant is build up.
Total distribution costs are $194,060.00.
Total Production + Distribution Costs El Paso $296,310.00
+ Total Production + Distribution Costs San Bernardino $130,400.00
= Total Production + Distribution Costs El Paso and San Bernardino $426,710.00
= Total Production + Distribution Costs are $620,770.00
Benefits and limitations of the current network system design
Linear programming technique helps us to make the best possible feasible solution of available productive resources (such as time, labor, machine...