Independence axioms similar to those proposed for multiattribute von Neumann–Morgenstern linear utility theory are examined in the context of new nonlinear utility theories developed by Chew and MacCrimmon, and Fishburn. These new theories weaken the independence axiom of von Neumann and Morgenstern, and Fishburn's theory does not require preferences to be transitive. The paper shows that axioms for independence between attributes lead to decompositions of utility for the nonlinear theories that are related to standard decompositions for linear utility.

This paper seeks to get behind specific contextual referents of risky situations to consider characteristics of risk that apply to many situations. It is guided by previous theoretical and empirical research in perceived risk, and focuses on the joint effects on risk of loss probability and the distribution of losses. The approach taken follows modern axiomatic theory by proposing conditions on a relation “is at least as risky as” between pairs of probability distributions over an outcome variable. Several sets of axioms for risk that characterize different forms for risk measurement are presented.

This paper is concerned with the development of an optimal budget holdback policy for a multi-item procurement process. An annual budget is made available for the purchase and resupply of n items. The issue is to determine how much of the budget to commit initially and how much to hold back for spot purchases later in the year. An analytic solution to the problem is developed for the single item case and compared to the unconstrained “newsboy” solution. In the multi-item case we develop stochastic linear programming with resource models under two views of the organization's procurement process. The first view is that the overall budget is allocated to the individual item managers and spot purchase monies earmarked for one item cannot be used for another. The computational and data requirements for solution of this model are reasonable. The second view is that spot buy monies are pooled and allocated to individual items on an “as needed” basis. The linear programming model of this procurement process is much more complex and not computationally feasible for more than a few items. However, the budget allocation model of the first view is shown to be a good heuristic for determining the percent of funds to hold back for the pooled process. A numerical example and sensitivity analysis are included.

In multivariate decisions under risk, assessing the complete utility function can be a major obstacle. Decision rules are investigated which characterize uniformly better alternatives with respect to a whole class of utility functions. In this paper independence assumptions are imposed on the preference structure while the levels of attributes may be stochastically dependent in an arbitrary way. The utilities considered are additive, multiplicative, or multilinear. Necessary and sufficient conditions are developed for uniform decisions over utilities with common substitutional structure and where the univariate conditional utilities show qualitative properties such as risk aversion. The rules are direct extensions of known univariate rules and easy to evaluate.

We consider the problem of smoothing production in a job shop in which all production is to customer order and the demand process is a stationary stochastic process. We present an approach to production smoothing based on the concept of a planning window. A planning window is the difference between the promised delivery time and the planned production time for a product. It represents the degree of flexibility available for planning the production of committed orders. We characterize the production smoothing benefits for a range of planning windows by means of an approximate analytic model and a simulation study. These analyses show that substantial smoothing benefits result from small changes in the length of the planning window. We discuss the implementation of the production smoothing approach and illustrate this implementation with an industrial case study that was the motivation for this work.

Previous work dealt with the problems of nervousness in Material Requirements Planning (MRP) Systems when production schedules were modified to include setups which previously had not been scheduled. In this work we further examine nervousness and its cost. By modifying the setup costs used in the Wagner-Whitin algorithm, we develop a generalized solution methodology for dealing with situations in which new setups are added to the production schedule and existing setups are cancelled.

In many practical applications or multi-item inventory systems significant economies of scale can be exploited when coordinating replenishment orders for groups of items. This paper considers a continuous review multi-item inventory system with compound Poisson demand processes; excess demands are backlogged and each replenishment requires a lead time. There is a major setup cost associated with any replenishment of the family of items, and a minor (item dependent) setup cost when including a particular item in this replenishment. Moreover there are holding and penalty costs. We present an algorithm which searches for a simple coordinated control rule minimizing the long-run average cost per unit time subject to a service level constraint per item on the fraction of demand satisfied directly from on-hand inventory. This algorithm is based on a heuristic decomposition procedure and a specialized policy-iteration method to solve the single-item subproblems generated by the decomposition procedure. The model applies to multi-location inventory systems with similar cost structures for coordinated deliveries.