Contrary to serial replacement, parallel replacement problems require a decision maker to evaluate a portfolio of replacement decisions in each time period because of economic interdependencies among assets. In this paper, we describe a parallel replacement problem in which the economic interdependence among assets is caused by capital rationing. The research was motivated by the experience gained from a vehicle fleet replacement study where solutions to serial replacement problems could not be implemented since they violated management's budget plan. When firms use budgets to control their expenditures, competition for the limited funds creates interdependent problems. In this paper, we formulate the problem as a zero-one integer program and develop a branch-and-bound algorithm based on Lagrangian relaxation methodology. A multiplier adjustment method is developed to solve one Lagrangian dual.equipment replacement, capital rationing, integer programming, Lagrangian relaxation, multiplier adjustment method

In 1995, Volkswagen of America began a review of its vehicle-distribution system looking for opportunities to improve customer responsiveness and simultaneously reduce system costs. An analytical tool was required to evaluate alternative designs in terms of cost and customer service level, both of which are functions of probabilistic and dynamic elements. These elements include inventory policies, demand seasonality and volume, customer-choice patterns, and transportation delays. By using an innovative combination of simulation and discrete optimization models, we addressed the problem of analyzing a large number of alternatives efficiently. Our analysis indicated opportunities for significant savings in estimated annual transportation costs, and it provided insights on how to implement the proposed system.

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1For modeling investment decision situations, we present a mathematical basis that views the cash flow sequences as growth processes. We first emphasize the pedagogical value of the basic model by showing that all traditionally established measures of worth (profitability) as well as the compound interest formulas of financial mathematics can actually be derived from it by simple algebraic manipulations. Then, we argue that the traditional measures fail to recognize the particularities of certain decision situations and point out the need for developing tailor made measures for each specific problem. We demonstrate, using real life examples, our approach for developing new measures and, by incorporating decision variables, practical optimization models from this mathematical basis.