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Warranty policies for certain products, such as automobiles, often involve consideration of two attributes, for example, time and usage. Since consumers are not necessarily homogeneous in their use of the product, such policies provide protection to users of various categories. In this chapter, product usage at a certain time is linked to the product age through a variable defined as usage rate. This variable, usage rate, is assumed to be a random variable with a specified probability distribution, which permits modeling of a variety of customer categories. Another feature of the chapter is to model the propensity to execute the warranty, in the event of a failure within specified parameter values (say time or usage). In a competitive market, alternative product/warranty offerings may reduce the chances of exercising the warranty. This chapter investigates the impact of warranty policy parameters with the goal of maximizing market share, subject to certain constraints associated with expected warranty costs per unit not exceeding a desirable level.

Some consumer durables, such as automobiles, involve warranties involving two attributes. These are time elapsed since the sale of the product and the usage of the product at a given point in time. Warranty may be invoked by the customer if both time and usage are within the specified warranty parameters and product failure occurs. In this chapter, we assume that usage and product age are related through a random variable, the usage rate, which may have a certain probabilistic distribution as influenced by consumer behavior pattern. Further, product failure rate is influenced by the usage rate and product age. Of importance to the organization is to contain expected warranty costs and select appropriate values of the warranty parameters accordingly. An avenue to impact warranty costs is through research on product development. This has the potential to reduce the failure rate of the product. The objective then becomes to determine warranty parameters, while constraining the sum of the expected unit warranty costs and research and development (R&D) costs per unit sales, under a limited R&D budget.

Vintage capital growth models have been at the heart of growth theory in the 1960s. This research line collapsed in the late 1960s with the so-called embodiment controversy and the technical sophisitication of the vintage models. This chapter analyzes the astonishing revival of this literature in the 1990s. In particular, it outlines three methodological breakthroughs explaining this resurgence: a growth accounting revolution, taking advantage of the availability of new time series; an optimal control revolution, allowing to safely study vintage capital optimal growth models; and a vintage human capital revolution, along with the rise of economic demography, accounting for the vintage structure of human capital similarly to physical capital age structuring. The related literature is surveyed.

This chapter considers warranty policies involving two attributes, such as the time elapsed since sale of the product and product usage at a given point in time. Examples of such policies are found for automobiles, where warranty may be invoked by the consumer if both time and usage are within specified warranty parameters when a product failure occurs. Here, we assume that usage and product age are related through a random variable, the usage rate, which may have a certain probabilistic distribution as influenced by consumer behavior patterns. Furthermore, product failure rate is influenced by the usage rate and product age as well as research and development expenditures per unit. It is assumed that, in production, there is a learning effect with time. The attained market share of a product will be influenced by the warranty policy parameters of warranty time and usage limit and also by the product price and product quality. An integrated model is developed to address multiobjective goals such as attainment of a specified level of market share and net profit per unit when manufacturing and warranty costs are taken into account. The impact of the goal priorities are investigated on the attained warranty policy parameters.

Two-attribute warranty policies are considered that incorporate, for example, the time elapsed since sale of the product and product usage at a given point in time. Such policies occur in consumer products, such as automobiles, where warranty may be exercised if both time and usage are within specified warranty parameters when a product failure occurs. In this chapter, it is assumed that usage and product age are related through a random variable, the usage rate, which may have a certain probabilistic distribution as influenced by consumer behavior patterns. Product quality is modeled through the product failure rate, which is influenced by unit research and development expenditures as well as the usage rate and product age. The attained market share of the product is modeled as a function of the warranty policy parameters of price, warranty time, and usage limit, with product quality also having an influence. Attainment of single and multiple objectives are explored. Such objectives encompass expected total unit costs as a proportion of unit product price and market share.

Various types of warranty programs are offered for consumer products. The two most common are a linear pro-rata warranty or a lump-sum warranty, if product failure occurs prior to the specified warranty time. In this chapter we consider additional types of warranty programs that allow the consumer to purchase a one-time extended warranty in the event of no failure within the initial warranty period. For the extended period, warranty may be linearly pro-rated, starting at an amount that is lower than the initial purchase price. Alternatively, for the extended period, warranty may be a lump-sum amount, that is less than the initial warranty amount. Expressions for the expected costs under each of the programs are derived. Guidelines are provided for determining the parameters of each warranty program under relevant constraints. Sensitivity analysis is also conducted to determine the effect of the problem parameters on the expected warranty costs.

Two-dimensional warranty policies exist for certain consumer products, such as automobiles. Here, warranty is specified in terms of the time since the sale of the product as well as mileage incurred during that period. Thus, at the time of purchasing the product, the manufacturer may offer a warranty of three years or 30,000 miles, whichever occurs first. Failures in the product within this specified period of time or mileage will be covered by the manufacturer.

In this chapter, we consider the scenario of enterprise warranty programs, where customers are given the option of extending the original warranty. Thus, the buyer could be given an option to purchase a five year—50,000 mile warranty, whichever occurs first. Of course, the buyer will be expected to pay a premium to purchase this extended warranty. Such enterprise warranty programs are also found in other consumer durables, such as refrigerators, washers, dryers, and cooking ranges.

This chapter explores determination of the decision variables, such as product price, warranty time, and usage limit under the original conditions and further, for the enterprise warranty, that is, the extended warranty time and extended usage limit, as well as the premium to be charged to the buyer who selects the extended warranty. Mathematical models are developed based on maximizing the expected unit profit by selecting an enterprise warranty program. Additionally, some other objectives are also considered based on the proportional increase in the expected unit profit due to the increased market share attained through the offering of an enterprise warranty program. Some results are obtained through consideration of various goal values of the chosen objectives.

For certain consumer durables, such as automobiles, warranty policies involve two attributes. These could be the time elapsed since sale of the product and usage of the product at a given point in time. Warranty may be invoked by the consumer if both time and usage are within specified warranty parameters when a product failure occurs. In this chapter, we assume that usage and product age are related through a random variable, the usage rate, which may have a certain probabilistic distribution as influenced by consumer behavior patterns. Additionally, product failure rate is influenced by the usage rate and product age. The integrated model includes expected unit warranty costs, expected unit research and development costs, and expected unit production costs. It is assumed that in production, there is a learning effect with time. A multiobjective model is incorporated with the objectives being market share and proportion of expected warranty costs relative to total manufacturing expenditures per unit. The goals could be conflicting in nature. The problem then is to determine the warranty policy parameters while attaining certain desirable values of the two objectives.