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A customer would like to buy a given set of products in a given set of Internet shops. For each Internet shop, standard prices for the products are known as well as a concave increasing discounting function of total standard and delivery price. The problem is to buy all the required products at the minimum total discounted price. Computational complexity of various special cases is established. Properties...
In the last decades, many problems involving equilibria, arising from engineering, physics and economics, have been formulated as variational mathematical models. In turn, these models can be reformulated as optimization problems through merit functions. This paper aims at reviewing the literature about merit functions for variational inequalities, quasi-variational inequalities and abstract equilibrium...
Bicriteria scheduling problems are of significance in both theoretical and applied aspects. It is known that the single machine bicriteria scheduling problem of minimizing total weighted completion time and maximum cost simultaneously is strongly NP-hard. In this paper we consider a special case where the jobs have equal length and present an $$O(n^{3}\log n)$$ O ( n 3 log n ) algorithm...
One recently proposed criterion to separate two data sets in Classification is to use a hyperplane that minimizes the sum of distances to it from all the misclassified data points, where misclassification means lying on the wrong side of the hyperplane, or rather in the wrong halfspace. In this paper we study an extension of this problem: we seek the hyperplane minimizing the sum of concave nondecreasing...
This paper deals with a continuous-time Markov decision process in Borel state and action spaces and with unbounded transition rates. Under history-dependent policies, the controlled process may not be Markov. The main contribution is that for such non-Markov processes we establish the Dynkin formula, which plays important roles in establishing optimality results for continuous-time Markov decision...
This paper considers a multi-class batch service problem that involves a class-dependent waiting cost and a service cost in determining customer batch sizes. Unlike a fixed service cost used widely in standard models, the service cost considered in this work is incurred only if the total service time is over the capacity. We formulate this problem as an infinite horizon Markov decision process, and...
In this paper, a supply chain management problem from a real case study is modeled and solved. A company in Pakistan wanted to outsource part of its warehousing activity to a third party logistics (3PL) provider. Consequently, the company had to decide on where to rent space in the 3PL warehouses. Knowing that such a strategic decision is affected by tactical and operational decisions, the problem...
The quay crane scheduling problem (QCSP) is at the basis of a major logistic process in maritime container terminals: the process of discharging/loading containers from/on berthed vessels. Several groups of containers, laying in one or more stowage portions of a containership, have to be assigned to multiple cranes and discharge/loading operations have to be optimally sequenced, under some complicating...
In this paper, we give an overview of the main results obtained on the complexity of scheduling under the non-idling constraint, i.e, when the jobs assigned to each machine must be processed with no intermediate delay. That constraint is met in practice when the cost of intermediate idle time is too high due to the idle time itself and/or the machine restarting. The non idling constraint is a strong...
The problem we address in this paper, is the minimization of the energy consumption of an electrical vehicle achievable on a given driving cycle. This can be formulated as an optimal control problem with a discrete switch control. In this paper, we present a new formulation of this problem by taking into account the electrical and mechanical parts of the vehicle. By using prototype optimal control...
This article tackles the multi-trip vehicle routing problem with time windows and limited duration. A trip is a timed route such that a succession of trips can be assigned to one vehicle. We provide an exact two-phase algorithm to solve it. The first phase enumerates possible ordered lists of clients which match the maximum trip duration criterion. The second phase uses a Branch and Price scheme to...
The best formulations for some combinatorial optimization problems are integer linear programming models with an exponential number of rows and/or columns, which are solved incrementally by generating missing rows and columns only when needed. As an alternative to row generation, some exponential formulations can be rewritten in a compact extended form, which have only a polynomial number of constraints...
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