**Overview**

As a general trend, firms are moving towards *mass customization* by allowing customers to configure products by selecting among *options* (features), e.g. automotive industry, consumer electronics, computers, furniture, and aircraft. Our research is motivated by the problems faced by a global auto manufacturer that offers 100-500 options for a car. These options can be combined in different ways resulting in 10^25-10^40 different *configurations* (end-products). Since it is impossible to forecast the demand for configurations, firms forecast options’ demand.

We study three major problems. First, the current forecasting approach ignores the relationships between options and, as a result, the forecasts are frequently incorrect, which results in excess inventories, shortages, and customer dissatisfaction. The second problem is to determine how many units of each part is required over the planning horizon, known as *parts’ capacity planning* problem. The firm signs contracts with parts’ suppliers based on the predicted parts’ capacities. These contracts mandate the firm to utilize the reserved capacity in suppliers over the planning horizon. Consequently, at the end of the planning horizon, some of the parts’ capacities are depleted while there are some other left-over capacities. Therefore, the third problem, which arises at the end of a planning horizon, is to determine which configurations to produce and in what quantities to effectively (in the most profitable manner) utilize the existing parts’ capacities.

**Background**

Large auto manufacturers (LAMs) allow customers to configure their cars on the Internet. Automobiles consist of a number of modules such as engines, interiors, and suspensions and each module has a number of different variants or *options*. A customer configures his or her product by choosing options that are compatible. The number of valid configurations can be extremely large (10^25-10^40). Manufacturers need demand forecasts at the level of configurations for production planning, supplier contracts, and pricing decisions. Unfortunately, the number of potential configurations and the difficulty in enumerating feasible (producible) configurations make it impossible to forecast configuration demand.

Most firms forecast their demand at the option level. The forecast demand of options is then used to plan inventories and contracts with suppliers. Errors in demand forecast can be extremely costly since it can result in excess inventories, shortages, and customer dissatisfaction. A major challenge of LAMs is that their current forecasting approach fails to ensure the consistency of forecast with the *rules* (the restrictions that prevent selecting incompatible options together). As a consequence, forecasts are frequently infeasible (inaccurate). Thus, LAMs need an effective method for determining the feasibility of the forecast and modifying it in the case of infeasibility.

The second challenge of LAMs is to determine the number of units of each part (the components that are assembled together and build cars) that will be used over the planning horizon, which is referred to as parts’ capacities. Close to 60% of the parts required to produce a car depend on the combination of options used. For example, the combination of engine type and transmission type generates a substantial number of additional parts (in addition to the parts that are solely based on the engine type as well as the parts that are defined based on the transmission type). The dependency of parts’ requirements to combination of options makes it challenging to determine parts’ capacities. In our partner global auto manufacturer, parts are procured from over 20,000 suppliers and account for approximately two-third of the total cost (roughly $90 billion). It is therefore crucial to correctly determine parts’ capacities.

Once LAMs determine parts’ capacities, they sign contracts with their suppliers according to which they guarantee to utilize pre-specified capacities of parts over the planning horizon. If LAMs violate the reserved capacities (use less or more than what is specified in the contract), they have to pay penalties. Due to the uncertainty of demand, some of the parts’ capacities are depleted at the end of the planning horizon while there are unused capacities for some other parts. Hence, the third challenge arises at the end of the planning horizon which is to determine which configurations to produce and in what quantities to effectively (in the most profitable manner) utilize the unused capacities of parts.

**Findings**

First, the problem of determining the feasibility of the forecast demand of options and finding the best feasible forecast in the case of infeasibility is NP-hard. We have presented a novel mathematical formulation for this problem and proposed an effective approach (algorithm) for solving it. We have mathematically proved that our approach is correct and it can solve large industrial instances.

- Fattahi, A., Dasu, S., Ahmadi, R. (2018) Mass Customization and “Forecasting Options’ Penetration Rates Problem.”
Accepted. Download (Selected as a*Operations Research*.*finalist*in POMS College of Supply Chain Management 2018 Best Student Paper Competition.)

Second, we have studied a generalization of our mathematical model and methodology and showed that it can be applied in several important disciplines. In particular, our approach has applications in manufacturing, machine learning, clustering, pattern recognition, and statistics.

- Fattahi, A., Dasu, S., Ahmadi, R. (2018) The Weighted Non-Negative Least-Squares Problem with Implicitly Characterized Points.
Accepted. Download.*Operations Research*.

Third, we have modeled, analyzed, and solved the problem of determining parts’ capacities. Additionally, we have provided estimates for the variability of parts’ capacities, interdependency between the different parts, and joint capacities for multiple parts.

- Fattahi, A., Dasu, S., Ahmadi, R. (2018) Mass Customization and Parts’ Capacity Planning Problem. 1st Major revision submitted to
*Operations Research*.

**Direction for Future Research**

We are planning to study and address LAMs’ third major challenge which is determining, at the end of the planning horizon, which configurations to produce and in what quantities to maximize the profit. We call this “the end-of-horizon portfolio optimization problem.”