OR/MS Today - June 2002|
Product Mix Analysis
How to Conduct Product Mix Analysis
By Thomas Hsiang
When I first began studying operations research/management science techniques in the mid-1970s, a simple product mix optimization problem was the first example used in Hillier and Lieberman's best selling text "Operations Research" to illustrate the power of linear programming. The concept of product mix analysis is simple to illustrate and the result is easy to comprehend. It is therefore not surprising that numerous textbooks also use a product mix problem to introduce the concept of optimization and linear programming.
The principle of product mix analysis, as described in all these texts is, in fact, correct and essential. The appeal of product mix analysis results from its simple yet powerful application, providing a platform to base the search for higher profitability and production throughputs. After years of practicing OR and quantitative methods in industry, however, I have come to the realization that an effective application of product mix analysis is not nearly as simple as illustrated in these texts. I will therefore outline the necessary steps, challenges and possible pitfalls of a practical application of product mix analysis to improve the profitability of an operation or business.
Product mix analysis is not as simple as it looks. In a typical textbook illustration of a product mix problem, a company produces several products, each requiring a certain amount of labor and materials. Constraints, such as total amount of resources and the maximum number of units that each product can sell, as well as the unit profit for each product, are given. The analysis focuses on how many products to produce in order to maximize the overall profit, correctly illustrating the essence of the product mix problem. However, the case does not even begin to reveal the complexities of a real and practical product mix study commonly used in industry.
First, the data needed for product mix study does not come in a handy form that is ready to import by an OR/MS practitioner into a spreadsheet for quick analysis. Obtaining and formatting the necessary information for analysis requires at least a few days and up to several months, depending upon the scope, complexity and purpose of the analysis.
After the first hurdle in data requirements is crossed and initial analysis of the product mix is conducted, a practitioner will usually be faced with the next issue: Is the current "optimized" product mix truly the best? In practical applications, the product mix study is rarely a one-shot deal, taking time and effort. Analysis is iterative, each iteration representing one of numerous different business and/or production scenarios.
The third difficulty of product mix analysis is its implementation. Even after an "optimal" product mix is found, the realization of the product mix within the operation is a challenge. An optimized product mix usually represents an idealized and somewhat macro view of the production profile, delivering a profit obtained in the analysis. In many cases, however, operational constraints in production and in the supply chain that were not or cannot be specifically formulated into the product mix optimization such as availability of raw materials, seasonality of customer demand and bottlenecks of equipment and resources may deem your product mix results infeasible.
I therefore suggest the following roadmap to improve the success rate of a product mix study.
Step 1: Define the product mix problem. The purpose of a product mix study for a profit making entity is usually to maximize the profit. Assuming this general principle, one needs first to define and understand the project. The following questions clearly identify the problem/opportunity and provide focus to the project.
Step 2: Collect data for base-line product mix evaluation. The most important decision of this step is to define the product categories to use as the basic unit to collect needed information. A typical company sells hundreds or even thousands of products representing various product lines, product classes, product sub-classes, packing codes, etc. It is extremely cumbersome and difficult to conduct product mix analysis at the lowest product classification level with thousands of categories. Aggregation is always needed. The question is therefore how to aggregate product sub-classes such that the analysis will still yield insightful outputs. My motto for this step is to aggregate as much as possible while retaining enough identity for useful interpretation. This is not an exact science, perhaps even requiring some piloting to ensure that the data collection is neither overly detailed nor too general.
This is a very time-consuming period of the project. In the case of an entity with a good database containing accurate financial and operation information, effort is usually spent on the aggregation of information to arrive at the desired product category level. To alleviate any ambiguity during the data collection and aggregation process, design a spreadsheet, clearly listing product categories and information to be collected first. With a clear list of information needs, the goal of the data collection is simply to complete the spreadsheet that was specifically designed for data collection.
Typical information to be collected for product mix analysis will include items such as product price, product costs fixed, variable and overheads and estimated demand for the product at the planned horizon. I frequently ask the sales and marketing group to provide me with two numbers for the estimated demand: one number for the expected demand and the other for a higher estimated demand if the product is pushed given a price reduction. Processing information for each product such as equipment usage requirements for key equipment and resources must also be collected. Detailed processing information for all equipment is not really necessary. Identify the key constraints in the production process first, and then collect equipment usage requirements for the potentially constrained equipment only.
With all the needed information collected in a spreadsheet, formulating the product mix question is relatively easy using the spreadsheet solver. In my experience, I have yet to encounter a product mix problem that can't be solved by a standard spreadsheet solver that is included in a spreadsheet program. If there is too much information for a standard solver, you are probably unnecessarily complicating your product mix analysis with too many product categories.
The output of the product mix profile is best presented in a graphical format. Some people use a pie chart to present the results. I personally prefer to show the results in a combined bar and dot chart. (See figure 1 for an example.) In this sample chart, the bars represent the production profile and the dots represent the percentage contribution to overall revenue. There are many different potential combinations using this bar and dot chart. For example, actual revenue or profit could replace the percentage revenue contribution. Multiple charts may be necessary to present all desired output information. Outputs of this step will usually include at least two parts: 1. the existing product mix, and 2. the "optimized" product mix, both of which are derived from the currently available equipment/resources and existing processes.
Figure 1: Optimal production profile and revenue percentage.
Step 3: Develop new scenarios for additional product mix analyses. The so-called "optimized" product mix output from Step 2 is the current best under a limited scope no changes are made to the currently available equipment and resources. The real challenge of a product mix analysis is to create new business and production scenarios that frequently require major "structural" changes. The structural changes might involve the bold "re-engineering" of the business; for example, shutting down some portion of the operation thereby eliminating some product lines, or adding some product lines by realigning existing equipment/resources among several production sites or acquiring new equipment/resources etc. The principle concept behind the scenario development is to come up with a viable and feasible business plan and structure that will improve the bottom line. The scenario development is by far the most challenging part of a product mix study because it involves business strategy, breaking the existing product mix paradigm and invoking "outside-the-box" thinking to brainstorm good scenarios for the business to pursue.
For each scenario, appropriate data will of course need to be added and incorporated into the existing data structure discussed in Step 2. Product mix analysis will need to be conducted for each scenario. Results will need to be evaluated for assessing the viability of the scenario. Frequently, the result of one analysis will direct the development of a new scenario for further analysis. In fact, product mix analysis is likely to be iterative in practical applications.
If structural changes suggest acquisition, the same product mix analysis must be conducted assuming the acquisition has taken place. The merit of this possible acquisition can be assessed from the analyses by comparing product mix results with and without acquisition.
Step 4: Select an optimal product mix profile. Since the product mix analysis involves entertaining multiple scenarios and the process of searching for the best scenario, the process is usually iterative. So in actual practice, Step 3 and Step 4 are closely linked. In this step, the following questions help the selection process:
Step 5: Map out the actual production sequence to verify the feasibility of the optimal production profile. The optimal product mix profile obtained in Step 4 may not necessarily be feasible to execute on the production floor. The reason is simple. The product mix analysis is usually conducted at a macro level where only major constraints are considered in the optimization formulation. Additionally, some of the constraints on the production floor cannot easily or even possibly be handled by a mathematical programming formulation. As a result, the "optimal" product mix profile obtained in Step 4 is in fact an upper bound. Actual profit figures may be lower due to additional practical constraints that fail to be included in product mix optimization formulation.
To overcome this possible gap, it is necessary to map out the production runs using the optimal product mix profile and to verify production feasibility. There are, of course, many ways to accomplish this task. Some people use simulation while other people prefer traditional paper and pencil to test the actual production schedule. It is best to have an optimal scheduling system and a specialized equipment utilization chart to schedule production sequences and to map out the detailed production run hour-by-hour equipment utilization for the total duration of a production sequence. A typical output of this type of equipment utilization chart is shown in Figure 2. The scheduling and equipment utilization chart outputs provide us the necessary verification that the optimal product mix profile as obtained in Step 3 and Step 4 is feasible.
Figure 2: A Sample printout of equipment utilization of a production campaign.
Additional Thoughts and Conclusions
I have used the above five-step process with successful results. Additional comments on the application of product mix analysis are:
Thomas Hsiang (firstname.lastname@example.org), Ph.D., is Director of Management Science at Sensient Technologies Corporation in Milwaukee. He also teaches at the School of Business Administration, University of Wisconsin at Milwaukee, in the Production and Operations Management Program.
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