The fixed charge (fixed cost) may present the cost of renting a vehicle, landing fees in an airport, setup cost for machines in a manufacturing environment, etc. In this paper, we discuss fixed charge capacitated in a non-linear transportation problem. Thereby, we establish local optimum condition of this problem. Next we establish an algorithm for solving this transportation problem. Also, we ...

• Mathematics Subject Classification: 60E15, 90C40, 49N15 •

In this paper, we study the stochastic transportation-inventory network design problem involving one supplier and multiple retailers. Each retailer faces some uncertain demand. Due to this uncertainty, some amount of safety stock must be maintained to achieve suitable service levels. However, risk-pooling benefits may be achieved by allowing some retailers to serve as distribution centers (and ...

In this note, we propose a case study of freeway traffic flow modeled as a hybrid system. We describe two general classes of networks that model flow along a freeway with merging onramps. The admission rate of traffic flow from each onramp is metered via a control input. Both classes of networks are easily scaled to accommodate arbitrary state dimension. The model is discrete-time and possesses...

Sudoku is a popular combinatorial puzzle. A new method of solving Sudoku is presented, which involves formulating a puzzle as a special type of transportation problem. This model allows one to solve puzzles with more than one solution, keeping the constraints of the problem fixed, and simply changing a cost matrix between solutions.

Let R,B ⊂ R, for constant d, be two point sets with |R| + |B| = n, and let λ : R ∪ B → N such that ∑ r∈R λ(r) = ∑ b∈B λ(b) be demand functions over R and B. Let d(·, ·) be a suitable distance function such as the Lp distance. The transportation problem asks to find a map τ : R × B → N such that ∑ b∈B τ(r, b) = λ(r), ∑ r∈R τ(r, b) = λ(b), and ∑ r∈R,b∈B τ(r, b)d(r, b) is minimized. We present thr...

We consider the so-called Transportation Problem with Exclusionary Side Constraints (TPESC), which is a generalization of the ordinary transportation problem. We confirm that the TPESC is NP -hard, and we analyze the complexity of different special cases. For instance, we show that in case of a bounded number of suppliers, a pseudo-polynomial time algorithm exists, whereas the case of two deman...

The dairy transportation problem (DTP) consists of determining the best routes to be performed for collecting milk from farms and delivering it to processing plants. We study the particular case of the province of Quebec, where the Fédération des producteurs de lait du Québec is responsible for negotiating the transportation costs on behalf of producers. Several issues are highlighted in the ac...

Providing safe transportation for Hazardous Materials (Hazmat) is a concern that attracts a wide range of resaerchers. Different types of problems have been defined in the literature in order to cope as much as possible with real situations. Most of existing studies consider the transportation between two points, while few of them considered resolving the Vehicle Routing Problem (VRP) in the co...