TECHNISCHE

DRESDEN

Faculty of Transport and Traffic Sciences "Friedrich List" Institute of Transport and Economic

Chair of Transport Services and Logistics $-$ Operations Research & Logistics WS $2023/20244$th January $2024$

Partial Exam $3$

Bavarian Wood is a manufacturer of high$-$quality wooden furniture. The product portfolio includes all types of furniture, made from a wide variety of wood types. A typical quality and durable product.

The company faces the logistical challenge of organising the transport of wood as production raw material from various import warehouses on the North Sea coas Rotterdam $i=1,$ Wilhelmshaven $i=2,$ Bremerhaven $i=3,$ Hamburg $i=4)$ to the Prague $j=3).$ Since the Bavarian Wood does not use its own vehicles for the transport, it aims to organise the allocation of import warehouses to production sites in such a way that the

In the following table the stock of the import warehouses $a_i,$ the demand of the production sites $d_j$ as well as the transportation costs $c_{ij}$ between them are listed:

$($a$)$ Use the Matrix Minimum Method to calculate a feasible initial solution. Provide the complete solution.

$($b$)$ With the help of the Column Minima Method the following initial solution with total costs of $3635$ was determined.

$x_{13}=30,x_{21}=15,x_{31}=20,x_{41}=5,x_{42}=25,x_{43}=5$

Calculate $an$ optimal

of the Column Minima Method. Provide the complete optimal solution.

TECHNISCHE

DRESDEN

Chair of Transport Services and Lriences "Friedrich List" Institute of Transport and Econom

$4$th January $2024$

Because of increasing fuel costs Bavarian Wood seeks to reorganize its customer de$-$

livery from the production site in Salzburg. A new employee, who studied Transportacollected the following data:

Ten customers $(N=\{1,$dots,$10\},$ indices: $i,j)$ are to be supplied by the production $($CAP$)$ of $40$ units $(i=0)$; for this purpose five identical vehicles $(K)$ with a capacity The demands $a_i$ of the custom

TECHNISCHE

UNIVERSIT$$

Chair of Transport Services and Logistics $-$ Operatich List" Institute of Transport and Econo

$4$th January $2024$

$($c$)$ The transportation cost value $c_{14}(c_{41},$ respectively$)$ is missing. Use the Dijkstra's

algorithm to determine $c_{14}.$ Consider the following digraph:

$($d$)$ Determine the order in which the customers are served $(x_{\text{i}\text{j}\text{k}}),$ the vehicles used for supplying the customers $(y_{ik})$ as well as the total costs $F.$ Use the model $($c$)$ that $c_{14}=c_{11}=7.($c$),$ that $c_{14}=c_{41}=7$