Multi-criteria decision analysis (MCDA), or multi-criteria decision making (MCDM) encompasses a wide set of mathematical methods to compare alternatives whilst considering multiple criteria and the relative importance (weight) of each criterion or the allowable trade-off between criteria. MCDA/MCDM may be implemented in a decision support system to aid decision makers compare multiple alternatives. A key consideration in any MCDA is the sensitivity of the results obtained to alterations of the criteria weights used. Prior methods to determine the weight stability interval ( , the range of values for individual weights for which the ranking of alternatives will not change) include the manual alteration of criteria weights, the use of different sets of criteria weights in a form of scenario analysis, or the process of iteratively searching for the maximum and minimum allowable alterations to individual criteria weights to determine the weight stability interval. The first contribution of this paper is the development of a novel method for determining precise weight stability intervals which does not rely on enumeration or simulation for use with the weighted sum model (WSM, based on the Minkowski norm), one of the most widely used aggregation methods within MCDA. The second contribution of this work is the use of these s to identify the most sensitive weight(s) based on a Pareto dominance approach whilst considering both the allowable increase and decrease in criteria weights. The above points are demonstrated and applied in an analysis of several alternatives for renewable energy (biogas) production.

We present an extended mixed-integer programming formulation of the stochastic lot-sizing problem for the static-dynamic uncertainty strategy. The proposed formulation is significantly more time efficient as compared to existing formulations in the literature and it can handle variants of the stochastic lot-sizing problem characterized by penalty costs and service level constraints, as well as backorders and lost sales. Also, besides being capable of working with a predefined piecewise linear approximation of the cost function—as is the case in earlier formulations—it has the functionality of finding an optimal cost solution with an arbitrary level of precision by means of a novel dynamic cut generation approach. The online appendix is available at https://doi.org/10.1287/ijoc.2017.0792 .

We introduce statistical constraints, a declarative modelling tool that links statistics and constraint programming. We discuss two statistical constraints and some associated filtering algorithms. Finally, we illustrate applications to standard problems encountered in statistics and to a novel inspection scheduling problem in which the aim is to find inspection plans with desirable statistical properties.

In this paper, we address the general multiperiod production/inventory problem with nonstationary stochastic demand and supplier lead time under service-level constraints. A replenishment cycle policy is modeled. We propose two hybrid algorithms that blend constraint programming and local search for computing near-optimal policy parameters. Both algorithms rely on a coordinate descent local search strategy; what differs is the way this strategy interacts with the constraint programming solver. These two heuristics are first, compared for small instances against an existing optimal solution method. Second, they are tested and compared with each other in terms of solution quality and run time on a set of larger instances that are intractable for the exact approach. Our numerical experiments show the effectiveness of our methods.