- During the seminar we worked with the following cases: Describe briefly the main lessons that you got from each one of these cases
- Explain with several practical examples why sensitivity analyses (objective function coefficients and RHS constraints) are so important
- Let's suppose that two constraints have the following shadow prices
- In this slide 16 will find a network composed of nodes and arcs. White figures associated to each link represent the capacity of this link and red figures represent the cost of this link
The core problem in this case was related with a production planning again. How many S and how many P can I produce in order to maximize my profit with production’s constraints like limited raw materials (USB ports), limited assembly hours and limited quality control hours. The main lesson of this case is graphical application and interpretation of linear programming method in order to search the optimal solution.
Make or buy:
In this case, things are more complicated because we had to determine how much to produce of each product and how much to buy of each same product (with a total units pre-defined) in order to minimize total cost (production’ cost + purchase’s cost). There were two types of constraints: productions’ constraints and purchase’s constraints. The mean shrewdness of this case is to name A, B, C, D, E production’ units and A’, B’, C’, D’, E’ purchasing’ units in order to differentiate sources of units and constraints related in the same time.
This case was a problem of re-distribution. The decision variable was how many bikes we need to move from X to Y (with a total of 8 different bike’ stations). The objective was to minimize transportations cost. The number of bike had to correspond with a number of place pre-determined. It was constraints.
In this exercise, we have seen it exists two ways to solve the problem with two different answers. The manner to write the problem can influence your solution. It is essential to analyze your model after the resolution.
[...] Indeed, nurses can be or 3 but they can’t be 1,32 or Finally, constraints are personnel cost. That is to say the weekly salary. f. Assigning planes Through this example, we have discovered combinations are not possible. In fact, before doing any model to compute and find the optimal solution, we have to take a critical look. Work too rapidly with a computer is not a good manner to process. In order to avoid strange solution, we have to eliminate by hand all the impossible combinations. [...]
[...] So thanks to this method, the result I found amounts to Slide 17 shows the same network in slide 16 but now the destination nodes have a given demand associated to these nodes (82 for node and 75 for node 8). Develop a LP model in order to answer the question at the bottom of the slide: which is the optimal distribution of flow (from source nodes via transshipment nodes to destination nodes) to satisfy demand in destination nodes and minimizing transportation costs? [...]
[...] The explanation is simple. Here, the new profit of C is not included in the original range of possibilities (remember between 2,5 and 80). It is why the optimal solution changed. d. Analysis of changes with Right Hand Side (RHS) constraints Table V Optimal solution obtain by solver changing RHS constraints (Flavour) B C Used Availabl e Here we have changed the quantity of F (flavour) available (original) 2500 (actual) The result is that I have to produce the same quantity of bread and croissant dough than in the original model. [...]
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