FINAL ASSIGNMENT RESEARCH METHODS FOR MANAGERS ; Iseg ; Assignment ;
1. During the seminar we worked with the following cases:
a. Color chips
b. Computers S and L
c. Make or buy
d. Reallocating vehicles
e. Scheduling personnel
f. Assigning planes
g. Public health
Describe briefly the main lessons that you got from each one of these cases.
2. Explain with several examples why sensitivity analyses (objective function coefficients and RHS constraints) are so important.
3. Let's suppose that two constraints have the following shadow prices:
Constraint A = 345.55
Constraint B = 12.90
Is it obvious that duplicating the constraint A's RHS is more interesting that duplicating the constraint's B RHS?
4. With this final assignment you will find in Connect the slides that we used during the seminar (file named "RM slides - Group 1A"). Slides 12 to 14 were not used in class. In slide 13 you will find a network composed of nodes (circles in different colors) and arcs (links between nodes). White figures associated to each link represent the capacity of this link and red figures represent the cost of this link. Develop a LP model in order to answer the question at the bottom of the slide: which is the maximal quantity of flow that can reach the destination nodes (7 and 8) from the source nodes (1, 2 and 3)?
5. Slide 14 shows the same network in slide 13 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 (7 and 8) minimizing transportation costs?
[...] Duplicating the constraint A's RHS is more interesting that duplicating the constraint's B RHS? We suppose that two constraints have the following shadow prices: Constraint 345.55 and constraint 12.90 According to Wikipedia.com, in constraint optimization in economics, the “shadow price is the change in objective value of the optimal solution of an optimization problem obtained by relaxing the constraint by one unit.” But, in business application, a shadow price is “the maximum price that management is willing to pay for an extra unit of a given limited resource.” So, the shadow price is “the amount that the objective function value would change if the named constraint changed by one unit. [...]
[...] The available processing time of machine. We used the linear program in order to find the best and optimal solution. We noticed during this case that dealing with external suppliers that could be a great solution for a firm and it could be an economical way because the firm does not have to invest in new machines to produce more and the firm will also not have to do the maintenance. We notice thanks to the solver that the company will lose time if they produce itself the sub-assemblies. [...]
[...] Assigning planes It was a case of an airline company which needs to minimize its costs. We had to determine what the best solution is to save resources, to complete all planes and minimize the number of passengers who had to change plane. So, we had to find the best solution to minimize passengers moving and to full all the planes. It was practically the same case as the reallocating cars because we had to find what production process is the most profitable for the airplane company. [...]
[...] Each compartment has limits on both weight and space. We also have the weight of each compartment of the cargo which must be the same of compartment's weight capacity in order to maintain the balance of the plane. So, we have to determine how much of cargo we could have in the plane and how to distribute each compartmented in order to maximize the total profit of the flight. So, we have to formulate the linear program in order to maximize the total profit of the flight.the sensitivity analysis will satisfy entire constraints and the feasibility of the objective function. [...]
[...] So, it could be profitable for the firm to combine each possibility. Reallocating vehicles This case was dealing with car-renting company which needs to reduce its cost per car and also cost per cars between agencies. That was explain that each agencies need a minimum number of car each morning but we know that moving a car from an agency to another is an option but there are many solution to solve this problem and we have to find the best solution to minimize the relocating costs. [...]
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