Piecewise linearisation of the first order loss function for families of arbitrarily distributed random variables

We discuss the problem of computing optimal linearisation parameters for the first order loss function of a family of arbitrarily distributed random variable. We demonstrate that, in contrast to the problem in which parameters must be determined for the loss function of a single random variable, this problem is nonlinear and features several local optima and plateaus. We introduce a simple and yet effective heuristic for determining these parameters and we demonstrate its effectiveness via a numerical analysis carried out on a well known stochastic lot sizing problem

Locating a competitive facility in the plane with a robustness criterion

A new continuous location model is presented and embedded in the literature on robustness in facility location. The multimodality of the model is investigated, and a branch and bound method based on dc optimization is described. Numerical experience is reported, showing that the developed method allows one to solve in a few seconds problems with thousands of demand points.Ministerio de Ciencia e InnovaciónJunta de AndalucíaEuropean Regional Development Fun

Bi-criterion procedures to support logistics decision making: cost and uncertainty

In practical decision making, one often is interested in solutions that balance multiple objectives. In this study we focus on generating efficient solutions for optimization problems with two objectives and a large but finite number of feasible solutions. Two classical approaches exist, being the constraint method and the weighting method, for which a specific implementation is required for this problem class. This paper elaborates specific straightforward implementations and applies them to a practical allocation problem, in which transportation cost and risk of shortage in supplied livestock quality are balanced. The variability in delivered quality is modelled using a scenario-based model that exploits historical farmer quality delivery data. The behaviour of both implementations is illustrated on this specific case, providing insight in (i) the obtained solutions, (ii) their computational efficiency. Our results indicate how efficient trade-offs in bi-criterion problems can be found in practical problems

A simple heuristic for perishable inventory control under nonstationary stochastic demand

In this paper, we study the single-item single-stocking location non-stationary stochastic lot sizing problem for a perishable product. We consider fixed and proportional ordering cost, holding cost and penalty cost. The item features a limited shelf life, therefore we also take into account a variable cost of disposal. We derive exact analytical expressions to determine the expected value of the inventory of different ages. We also discuss a good approximation for the case in which the shelf-life is limited. To tackle this problem, we introduce two new heuristics that extend Silver’s heuristic and compare them to an optimal Stochastic Dynamic Programming policy in the context of a numerical study. Our results demonstrate the effectiveness of our approach

An Empirical Test of New Developments in Coalition Theory for the Design of International Environmental Agreements

We consider new developments in coalition theory for the design of international environmental agreements (IEAs). Applying an empirical model on climate change that comprises benefit and cost estimates from abatement for 12 world regions, we analyze how the design of an agreement affects the success of self-enforcing IEAs. We analyze single versus multiple coalitions, open versus exclusive membership with majority and unanimity voting, and no transfers versus transfers with four different transfer schemes

Pooling Problems with Polynomial-Time Algorithms

The computational challenge offered by many traditional network flow models is modest, and large-scale instances can be solved fast. When the composition of the flow is part of the model, the required computation time may increase substantially. This is in particular true for the pooling problem, where the relative content of certain flow components is restricted. Flow entering the network at the source nodes has a given composition, whereas the composition in other nodes is determined by the composition of entering flows. At the network terminals, the flow composition is subject to restrictions referred to as quality constraints. The pooling problem is known to be strongly NP-hard, even if the network has only one pool, but is solvable in polynomial time if also the number of terminals or the number of quality parameters (flow components) is bounded. The problem is also NP-hard if there are only two sources and terminals and only one quality parameter. Two related questions have been left open in the literature so far. For the single-pool version, it has not been known whether the problem is solvable in polynomial time if the number of sources is bounded. For the version with a single quality parameter and two sources and terminals, the question whether a pseudo-polynomial algorithm exists has been open. This paper gives positive answers to both questions

On Computational Procedures for Optimising an Omni-Channel Inventory Control Model

Dynamic programming (DP) and specifically Markov Decision Problems (MDP) are often seen in inventory control as a theoretical path towards optimal policies, which are (often) not tractable due to the curse of dimensionality. A careful bounding of decision and state space and use of resources may provide the optimal policy for realistic instances despite the dimensionality of the problem. We will illustrate this process for an omni-channel inventory control model where the first dimension problem is to keep track of the outstanding ordered quantities and the second dimension is to keep track of items sold online that can be returned

Coalition formation: the role of procedure and policy flexibility

Working paper GATE 2008-06In this paper, we analyze a spatial model of coalition formation with data from Dutch elections and with theoretical results. First, we study different procedures of coalition formation. The model shows that procedure plays an important role in reaching a coalition agreement and that political parties do not necessarily benefit from being a firstmover. Moreover, it is shown that a decrease in a party's flexibility can be beneficial in coalition negotiations. Furthermore, we find that certain power sharing tactics do not always lead to an agreement that is in a party's advantage. The main message put forward is that the process of coalition formation plays a more important role than is usually acknowledged in literature and practice