We present formulation and heuristic solution of a container packing problem observed in a household equipment factory’s sales and logistics department. The main feature of the presented MIP model is combining several types of constraints following from the considered application field. The developed best-fit heuristic is tested on the basis of a computational experiment. The obtained results show that the heuristic is capable of constructing good solutions in a very short time. Moreover, the approach allows easy adjustment to additional loading constraints.
Containerisation of freight transport significantly facilitates the flow of traded goods between remote destinations. The most important container transport routes link Asia with North America and Europe. The seasonality and imbalance of trade are the main factors giving rise to problems related to empty container repositioning. The aim of this paper is to develop a concept of empty container supply chains and formulate prerequisites for its modelling in the search for the optimal solution with the help of linear programming and mixed integer programming methods. This paper indicates causes of the empty container relocation problem based on the literature analysis with a special focus on the Eurasian transportation route. Also, it provides a concept of empty container supply chain, prerequisites for its modelling and examples of container supply chains modelling presented in the literature. The main results of the paper include conceptualisation of an empty container supply chain and suggested modelling prerequisites. The paper contributes to research in the field of supply chain management and optimisation of transportation.
This paper is concerned with a competitive or voting location problem on networks under a proportional choice rule that has previously been introduced by Bauer et al. (1993). We refine a discretization result of the authors by proving convexity and concavity properties of related expected payoff functions. Furthermore, we answer the long time open question whether 1-suboptimal points are always vertices by providing a counterexample on a tree network.
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The paper is concerned with a new time and memory efficient representation of a disjunctive graph. The disjunctive graph is a popular model used for describing instances of the job shop scheduling problem. The proposed data structure has the form of a graph matrix and combines advantages of a few classical graph representations.
W pracy przedstawiono nową reprezentację maszynową grafu dysjunkcyjnego dla problemu szeregowania w ogólnym systemie obsługi - macierz grafu, charakteryzującą się korzystną złożonością pamięciową i wysoką efektywnością czasową procedur ją obsługujących. Łączy ona zalety trzech klasycznych reprezentacji struktur grafowych: macierzy sąsiedztwa, listy poprzedników i listy następników, umożliwiając łatwy dostęp do różnego rodzaju informacji opisujących operacje w ogólnym systemie obsługi.
EN
This paper is concerned with a new time and memory efficient representation of the disjunctive graph - the graph matrix, used for describing instances of the job shop scheduling problem. The proposed data structure combines advantages of the classical graph representations like a neighborhood matrix and predecessors' and successors' lists delivering combined information on a job shop and enabling easy manipulation of the problem data.
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