The Bee Hive

All manufacturers and distributors are dependent on transportation to get their goods and services to markets and customers. Therefore, reliable transportation at an economical cost is critical to realizing business profitability goals. To respond to these challenges, transportation and logistics providers need to be lean. They also should use scientific techniques to provide competitively priced, value-added services to their customers.

An efficient, effective and economical transportation network becomes even more important in an industry such as paper. A paper distributor usually receives paper from mills in rolls at one or more central distribution centers (CDCs), cuts them to customer specifications at these facilities, and dispatches them to customers through satellite distribution centers located close to the market or customer.One of the key activities that sustain such a business is on-time receipt and delivery of finished paper. The location of CDCs, proximity of the satellite facilities to the CDCs, and availability of a reliable and economical transportation provider thus become critical to the success of a paper distribution business.

Successful paper distributors aim to ship product from one or more CDCs to affiliated satellite distribution centers on a daily basis, at an economical cost, with reliable on-time delivery schedules, using as few trucks as possible. This challenge can be met by directly addressing two critical components – optimal location of facilities and optimal routing of trucks within facilities. Optimization methods can help with this challenge.

Optimizing your business Optimization is a mathematical procedure for allocating resources where they are needed in the most effectual way possible, keeping cots to a minimum and improving sales, profits, or outputs. Optimization techniques can be used for transportation and logistics modeling to achieve considerable dollar savings while establishing better-operating transportation networks along the way. One useful technique to consider is optimization modeling.

“Travelling salesman optimization” is a classic optimization model that is of considerable practical importance and has found diverse applications. In its basic version, this model involves a traveling salesman who has to journey from an origin city to several destination cities exactly once and return to the origin city, minimizing the round-trip cost of travel. In the basic model, all the possible destinations and associated costs are known in advance. More complex variations of this model involve dynamic destination picking, where the traveling salesman knows his next destination and associated costs only after reaching an initial destination.

One well known application of the travelling salesman optimization model is in printed circuit board manufacturing, where the challenge is to drill holes on a circuit board in a preselected order to minimize the cost and time of drilling.

Consider paper distribution using the travelling salesman optimization model in facilities planning and transportation logistics. A paper distributor has three CDCs: CDC A, CDC B, and CDC C. Orgnaization decision makers wishes to pair nine satellite distribution facilities with the three CDCs to reduce the distance travelled and associated costs. As an additional goal, the organziation leaders wishes to determine the best routes to be taken by trucks servicing the satellites, enabling annual transportation costs to be minimized. Table 1 provides the actual distances in kilometers between the CDCs and the satellites.

The first step in the optimization process is to pair the satellites to the CDCs, shortening the total distance travelled among them. From Table 1, it is evident that satellites 1,2, and 3 are nearer to CDC A than they are to CDCs B or C. Thus it makes logical sense to pair satellites 1,2, and 3 with CDC A. With this arrangement, the total distance travelled by a truck moving from CDC A to satellites 1,2, and 3 would be 560 kilometers. Extending the same logic to other satellites, it can be concluded that optimal pairing for satellites 4,5, and 6 will be to CDC B and for satellites 7.8 and 9 to CDC C.

Although the pairing processes may appear simple from this example, it can be time-consuming when there are 10 or more CDCs and satellites, But the time spent on this first step is worthwhile because it ensures minimization of overall transportation costs. In complex scenarios involving hundreds of CDCs and satellites, it may be advisable to use operations research software to accomplish the pairing.

Refining your techniques

The next step in the optimization process is to determine the best truck route for reducing the overall transportation costs. Consider a truck starting from CDC A that must service satellites 1,2, and 3. A common trend is to have the truck service satellites 1,2, and 3 in that order. In the example described, because satellite 2 is nearest to CDC A, it may not make sense for the truck to go to satellite 1 first.

Although such intuitive deductions can be made easily in the case of the example, the answers may not come so easily in cases involving large networks. Again, using the travelling salesman optimization model, the best truck route from CDC A to satellites 1,2, and 3 needs to be determined with minimization of cost and distance travelled. A matehmatical solution to this truck routing problem uses a strategy called the "nearest neighbor method." To use the nearest neighbor method, the data are first arranged as shown in Table 2.

In Table 2, actual distances between the locations are shown except for the distance from a location to itself. Because it would be absurd to ship products from a location to itself., such a transaction is listed as N/A. Doing this will ensure that the optimal solution does not include illogical truck routes.

Assuming a transportation cost per kilometer of $2 per run, the distances shown in Table 2 may be converted to a cost-per-run basis, as shown in Table 3.

Solving the transportation problem in our example results in the optimal, low-cost solution, which follows.

• Start at CDC A

• Travel to Satellite 2, at cost of $180

• Travel to Satellite 1, at a cost of $200

• Travel to Satellite 3, at a cost of $800

By implementing the optimal solution, the total transportation cost per run between CDC A and its affiliated satellite will be $1,180 per run. In contrast, the total cost would have been $1,410 per run had the truck travelled from CDC A to satellites 1,2, and 3 in that order. Thus, the savings obtained by using the optimized truck route is $230 per run. Assuming there is a run every business day between CDC A and its affiliated satellites, the annual savings in this scenario would be $60,000. Likewise, the additional savings can be computed for runs among the other CDCs and their affiliated satellites.

In complex networks involving hundreds of CDCs and satellites located all over the country, it is conceivable that the total annual savings obtained using the optimized truck routes will exceed $1 million!

Optimization methods may be used to locate facilities, such as CDCs and satellites, in the best possible way and the establish optimal truck routes to minimize transportation costs. For individuals who do not wish to do the computations manually, several off-the-shelf operations research software packages are available at reasonable prices. The other alternative is to program the required calculations into a spreadsheet and enable software to perform the calculations.

Because location, time, and cost have been considered for an optimal solution, the overall quality of the solution obtained has not been compromised. the information generated from this exercise will enable an organization to solicit quotes from transportation providers based on optimally located facilities and truck routes. the organization can choose a low quote from the most reliable provider to get the best deal on transportation costs withouot fear of compromising the quality of service.

Real world use of optimization models for facilities planning and transportation logistics can result in substantial savings - sometimes millions of dollars. These savings can be invested in other value-added activities to enable company decision makers to innovate and grow their businesses. after all, maintaining a competitive edge is the only way companies can survive in this intensely competitive global economy.