Knowledge that Transforms

We consider the cutting of rectangular order pieces into stock pieces of specified width and length. The cutting process involves three stages of orthogonal guillotine cutting: Stock pieces are cut into sections that are cut into slits that are cut into order pieces. Restrictions imposed on the cutting process make the combinatorial structure of the problem more complex, but limit the scope of solution space. The objective of the problem is mainly to minimize waste, but our model also accounts for other issues such as aging stock pieces, urgent or optional orders, and fixed setup costs. Our solution approach involves a nested decomposition of the problem and the recursive use of the column-generation technique: We use a column-generation formulation of the problem (Gilmore and Gomory 1965) and the cutting-pattern—generation subproblem is itself solved using a column-generation algorithm. LP-based lower bounds on the minimum cost are computed and, by rounding the LP solution, a feasible solution and associated upper bound is obtained. This approach could in principle be used in a branch-and-bound search to solve the problem to optimality. We report computational results for industrial instances. The algorithm is being used in industry as a production-planning tool.

This paper proposes a quantitative modification of standard utility elicitation procedures, such as the probability and certainty equivalence methods, to correct for commonly observed violations of expected utility. Traditionally, decision analysis assumes expected utility not only for the prescriptive purpose of calculating optimal decisions but also for the descriptive purpose of eliciting utilities. However, descriptive violations of expected utility bias utility elicitations. That such biases are effective became clear when systematic discrepancies were found between different utility elicitation methods that, under expected utility, should have yielded identical utilities. As it is not clear how to correct for these biases without further knowledge of their size or nature, most utility elicitations still calculate utilities by means of the expected utility formula. This paper speculates on the biases and their sizes by using the quantitative assessments of probability transformation and loss aversion suggested by prospect theory. It presents quantitative corrections for the probability and certainty equivalence methods. If interactive sessions to correct for biases are not possible, then the authors propose to use the corrected utilities rather than the uncorrected ones in prescriptions of optimal decisions. In an experiment, the discrepancies between the probability and certainty equivalence methods are removed by the authors' proposal.

In models of decision making under uncertainty we often are faced with the problem of representing the uncertainties in a form suitable for quantitative models. If the uncertainties are expressed in terms of multivariate continuous distributions, or a discrete distribution with far too many outcomes, we normally face two possibilities: either creating a decision model with internal sampling, or trying to find a simple discrete approximation of the given distribution that serves as input to the model. This paper presents a method based on nonlinear programming that can be used to generate a limited number of discrete outcomes that satisfy specified statistical properties. Users are free to specify any statistical properties they find relevant, and the method can handle inconsistencies in the specifications. The basic idea is to minimize some measure of distance between the statistical properties of the generated outcomes and the specified properties. We illustrate the method by single- and multiple-period problems. The results are encouraging in that a limited number of generated outcomes indeed have statistical properties that are close to or equal to the specifications. We discuss how to verify that the relevant statistical properties are captured in these specifications, and argue that what are the relevant properties, will be problem dependent.

Motivated by applications in the manufacturing and service industries, we consider two models for coordinating scheduling with lead-time quotation: a basic model with a single customer type, and an enhanced model where an additional second customer type expects immediate service or production. In both models, revenues obtained from the customers are sensitive to the lead time, there is a threshold of lead time above which the customer does not place an order, and the quoted lead times are 100% reliable. These models are related to well-known scheduling problems, which have been studied in both offline and online settings. We introduce the immediate quotation case and study it with the (traditional) online version. We provide complexity results for the offline case, and perform competitive analysis for the online cases. A natural question of bridging the gap between the online and quotation models leads us to the delayed quotation model, which we study briefly. The analysis of these models provides useful qualitative insights as well.

The emergence of carriers that deliver items to geographically dispersed destinations quickly and at a reasonable cost, combined with the low cost of sharing information through networked databases, has opened up new opportunities to better manage inventory. We investigate these benefits in the context of a supply chain in which a manufacturer supplies expensive, low-demand items to vertically integrated or autonomous retailers via one central depot. The manufacturer's lead time is assumed to be due to the geographical distance from the market or a combination of low volumes, high variety, and inflexible production processes. We formulate and solve an appropriate mathematical model based on one-for-one inventory policies in which a replenishment order is placed as soon as the customer withdraws an item. We find that sharing and transshipment of items often, but not always, reduces the overall costs of holding, shipping, and waiting for inventory. Unexpectedly, these cost reductions are sometimes achieved through increasing overall inventory levels in the supply chain. Finally, while sharing of inventory typically benefits all the participants in decentralized supply chains, this is not necessarily the case—sharing can hurt the distributor or individual retailers, regardless of their relative power in the supply chain.

This paper focuses on the connection between product complexity and vertical integration using original empirical evidence from the auto industry. A rich literature has addressed the choice between internal production and external sourcing of components in the auto industry. More recent literature has developed the concept of product architecture as another choice variable that may be one of the important contributors to product complexity. In this paper, we connect these two important decisions and study them jointly. We use the property rights approach to argue that complexity in product design and vertical integration of production are complements: that in-house production is more attractive when product complexity is high, as firms seek to capture the benefits of their investment in the skills needed to coordinate development of complex designs. We test this hypothesis with a simultaneous equations model applied to data from the luxury-performance segment of the auto industry. We find a significant and positive relationship between product complexity and vertical integration. This has implications for optimal incentive structures within firms, as well as for interpreting firm performance.

This article analyzes the costs and benefits of job rotation as a mechanism with which the firm can learn about the employees' productivities and the profitability of different jobs or activities. I compare job rotation to an assignment policy where employees specialize in one job along their career. The gains from adopting a job rotation policy are larger when there is more prior uncertainty about employees and activities. I argue that this firm learning theory fits the existing evidence on rotation better than alternative explanations based on employee motivation and employee learning.

Not many authors have attempted to classify projects according to any specific scheme, and those who have tried rarely offered extensive empirical evidence. From a theoretical perspective, a traditional distinction between radical and incremental innovation has often been used in the literature of innovation, and has created the basis for many classical contingency studies. Similar concepts, however, did not become standard in the literature of projects, and it seems that theory development in project management is still in its early years. As a result, most project management literature still assumes that all projects are fundamentally similar and that “one size fits all.” The purpose of this exploratory research is to show how different types of projects are managed in different ways, and to explore the domain of traditional contingency theory in the more modern world of projects. This two-step research is using a combination of qualitative and quantitative methods and two data sets to suggest a conceptual, two-dimensional construct model for the classification of technical projects and for the investigation of project contingencies. Within this framework, projects are classified into four levels of technological uncertainty, and into three levels of system complexity, according to a hierarchy of systems and subsystems. The study provides two types of implications. For project leadership it shows why and how management should adapt a more project-specific style. For theory development, it offers a collection of insights that seem relevant to the world of projects as temporary organizations, but are, at times, different from classical structural contingency theory paradigms in enduring organizations. While still exploratory in nature, this study attempts to suggest new inroads to the future study of modern project domains.

The fundamental question encountered in acquiring capacity to meet nonstationary demand over a multiperiod horizon is how to balance the trade-off between having insufficient capacity in some periods and excess capacity in others. In the former situation, part of the demand is subcontracted while, in the latter, capacity that has been paid for is rendered idle. Capacity and subcontracting decisions arise in many economic activities ranging from production capacity planning in semiconductor fabs to leasing communication networks, from transportation contracts to staffing of call centers. In this paper, we investigate the trade-offs between acquiring capacity, subcontracting, production, and holding inventory to satisfy nonstationary demand over a finite horizon. We present capacity acquisition models with holding and without holding inventory and identify forecast-robust properties of the models that restrict the dependence of optimal capacity decisions on the demand forecasts. We develop algorithms for numerous practical cost structures involving variable and fixed charges and prove that they all have polynomial time complexity. For models with inventory, we solve a sequence of constant capacity lot-sizing and subcontracting subproblems, which is also of independent interest.

Managing highly skilled employees is extremely complex because of the need to balance the costs and time lags associated with their training against the need to meet demand as quickly as possible. Unlike previous approaches to this problem in the staffing literature, this paper develops an optimal staffing policy at the strategic level to cope with nonstationary stochastic demand for a staff characterized by unproductive apprentice employees and fully productive experienced employees. The paper then explores the implications of this policy in different industries, using empirical data. Aside from the optimal policy, this paper's primary results include: (1) demand volatility reduces average productivity, most especially under conditions of low (or slightly negative) growth and—nonintuitively—low employee turnover or knowledge obsolescence rates; (2) there is a trade-off between meeting demand and high productivity; (3) firms with longer business cycles should smooth their hiring and firing policies; and (4) firms in industries with longer training times should smooth their hiring and firing policies. The paper also explores the possible rewards from reducing training times and turnover rates. Finally, it discusses managerial implications and possible future directions in research.