Research Methods for Managers - publié le 08/05/2012

Résumé du document

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.

Reallocating vehicles:
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.

Extraits

[...] Public health This last case is about investment planning. There are 5 decision variables: X1 = Amount of $ assigned to county 1 X2 = Amount of $ assigned to county 2 X3 = Amount of $ assigned to county 3 X4 = Amount of $ assigned to county 4 X5 = Amount of $ assigned to county 5 Objective function: MAX X1 + X2 + X3 + X4 + X5 = $ Subject to numerous constraints: X1 + X2 + X3 $ X3 + X4 $ X1 + X2 + X3 + X4 + X5 $ X1; X2; X3; X4; X5 $ Women (X1 / 1000)*1,5 + (X2/1000)*1,5 /1000)*0,5 + (X5 /1000)*1,5 1500 Infants (X1 / 1000) + (X2/1000)*2 /1000)*1,5 + (X4 /1000) 1800 Children (X1 / 1000) /1000) + (X4 /1000)*2 + (X5 /1000) 800 The most important in this case is understand all the constraints and to use the solver correctly in order to find rapidly the good solution. [...]

[...] I have to produce 464,52 bread dough and 70,97 croissant dough. Table II- Original report of sensibility analysis Thanks to this sensibility analysis report, we can see allowable increase and allowable decrease for each product and each ingredient. c. Analysis of changes with Objective Functions coefficient Table III Optimal solution obtain by solver changing OF Coefficient (cell I have to produce the same quantity of bread and croissant dough than in the original model even if the maximum profit increase. [...]

[...] Shadow prices definition To begin our explanation we can give a definition of shadow price. It represents the amount of the objective function value will change just with an extra value of the RHS of the constraint. The shadow price is the same as long as we have the same range of feasibility. b. Solution Here we don't know the range of feasibility of the both constraints and the quantity of each component we need to use to produce one product. [...]

[...] Sensibility analysis is important to know aZŒ Œ Œ $Œ %Œ HŒ IŒ iŒ jŒ ŠŒ ªŒ µŒ àŒ áŒ âŒ ýŒ ? ? Ž ÒŽ Æ' È' Ê' Î' Ð' l ýäÏäÏäÏäÏäÏäÏäÏäÏ'¡Â¡Â¡'“ƒ“ƒ“ƒ“ƒ“ƒ“¡llowable range and shadow price for each data in order to adjust a lot of parameters and to answer: How much I will earn add profit if I increase B or C ? How much I have to produce if How much I will loss if . This graph represents the feasible solution area in white bounded by three lines. [...]

[...] 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. e. Scheduling personnel Scheduling personnel is a perfect case to illustrate a personal planning issue. The mean aim is to know how many nurses should participate in each schedule in order to respect the minimal daily requirement pre- determined. The objective is to minimize the cost of personnel. [...]