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Solving optimization problems with specialized software

Business planning often requires identifying the best option among many. Optimization software can be a big help.

There are business problems in which a company wants to identify the best option. Solving these optimization problems requires modeling the business situation, describing the constraints (limitations) in certain areas, creating an objective function that describes the optimal mathematical outcome to be achieved, and then running the model to maximize the objective function, which often is net profits.

Here is an example. A handbag company manufactures in 10 locations and ships to five of its own retail stores. Each factory has constraints on what it can manufacture, and each factory can ship to any store at a given cost. The company must anticipate the likely demand for handbags in each store for the next quarter. The question is how to minimize costs and maximize revenue.

Many optimization problems involve answering key questions about suppliers, the manufacturing process, the transportation needed to move goods to the customer, and the variability of customer demand.

To better understand these optimization issues, let's look at another business case in detail, using River Logic's Enterprise Optimizer (EO) software. River Logic is a capable vendor in this space.

Analyzing an optimization business case

Our company mines iron ore and delivers it via rail to shipping ports, then to its final destinations to be sold. In the mining process, the company produces lump ore and fine ore, and each product is distinguished by the percentage of iron ore it contains -- generally 55-64%. Figure 1 is a representation of the business model in EO.

River Logic Enterprise Optimizer (EO) model of mining company operations.
Figure 1. River Logic Enterprise Optimizer (EO) model of a mining company's operations.

The graphic flow in EO is quite simple to understand and shows three mines that are preparing ore to be shipped to rail line 1 or 2, and then to ports for final shipment. Rail line 3 is not considered in the initial run of the model.

Table 1 provides details about each of the business symbols in the figure 1 diagram. Each mine has a minimum and maximum amount of lump and fine ore it can produce, which are the constraints. We also know the cost of producing a unit of lump or fine ore for each mine.

Table showing constraints on each mine shown in River Logic EO model.
Table 1. Constraints on each mine's capacity to produce two kinds of ore.

There are further constraints in the blending and loading processes, both at the mine and at the port. There are also additional costs for rail shipping. The cost of ocean shipping is absorbed by customers.

At this point, we have a base model and have identified costs and constraints. All that remains before running the model is to select the mathematical function to be optimized. This will be derived from the corporate profit and loss (P&L) statement. The objective is to maximize profits.

The mine planning demo model (see figure 2) is essentially that P&L statement.

Mine planning demo model drawn from profit and loss (P&L) statement.
Figure 2. Mine planning demo model drawn from profit and loss (P&L) statement.

Running the River Logic EO model

Now we're in a position to run the model and examine its outputs. The output of the model shows what to make at each mine and how to ship it, as well as the bottlenecks, costs, revenues and profits.

EO provides considerable analytic capabilities to assist in the analysis. The graphs in figure 3 show how fully each mine is being used. Mines 2 and 3 are running at 100% capacity, but mine 1 is underutilized. Clearly, some bottleneck is holding it back. Perhaps there is a way around it.

River Logic EO graphs of mine capacity utilization.
Figure 3. Graphs showing capacity utilization of each mine.

Now, return for a moment to figure 1. All of the areas that are fully utilized -- the bottlenecks -- are highlighted in yellow.

Once we have these intermediate results, how can we improve profitability? EO provides a list of the top 10 opportunities, ranked in order, starting with the best one (see table 2).

River Logic EO table showing profit opportunies of objects in optimization model.
Table 2. Top 10 profit opportunities for objects shown in model in figure 1.

Ship loading at port 1 presents the greatest opportunity, and we know we have excess capacity at mine 1. If only we could find another way to get its excess capacity to market. Rail 3 (referring back to figure 1) is the answer.

We rerun the model, making rail 3 available. The results, as expected, are more production at mine 1 and more ship loading at port 2, complements of rail 3.

Finally, note the improvement in the P&L shown in table 3. Net income appears in line 6.

P&L statement in River Logic EO showing improvement in net income after rerunning mining-company model.
Table 3. P&L statement showing higher net income from rerunning EO model with rail line 3 activated to take advantage of unused capacity in mine 1.

River Logic EO: One user's experience

I spoke with a customer of River Logic whose company has a large presence in the consumer packaged goods area. He described the scope of the company's optimization problem and how EO helps solve it.

There are 5,000 distributors who place orders on a regular basis. For each stock-keeping unit there is a question of what to make and where to make it. The EO model recognizes differences in manufacturing and shipping costs and can take purchasing and inventory data into account. The model solves the optimization problem in 90 seconds versus eight hours the old way, and it's possible to run multiple scenarios or change the probability assumptions. The model integrates financial statements and does a good job of managing time periods, according to the user.

The model can help answer the following types of questions:

  • What integrated plan of manufacture, transfer and delivery maximizes net income over the next 52 weeks?
  • What pallet and column configurations of finished goods will maximize trailer volume utilization?
  • Given drastic changes in either demand or supply, what manufacture, transfer and delivery plan maximizes net income in a given week?
  • What distribution center assignment for each customer maximizes net income subject to expected demand, manufacturing capabilities and cost, as well as transfer and delivery costs?

There is a great deal of power in the model, and model building in EO is quite intuitive, this user said. The only issue is on the reporting side. If EO's canned reports don't suffice, creating custom ones is less intuitive than the model building itself.

Optimizing the optimizers

Finding the optimal solution is often better than running simulations to find solutions that are merely good. While some business problems can only be optimized with products like River Logic EO, the products can be more complex than the problems they are meant to solve.

At least two analysts will have to be thoroughly trained on the software, and care must be taken to produce both detailed operational reports and summarized reports for top management.

About the author:
Barry Wilderman has more than 30 years of experience as an industry analyst, researcher and consultant at such companies as Meta Group, Lawson Software, SalesOps Analytics and McKinsey and Co. He is currently president of Wilderman Associates. Contact him at [email protected] and on Twitter @BarryWilderman.

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