WINTER 2007 MGTSC 352 LEC B1 > DOCUMENTS > LABS > LAB 6 AGGREGATE PLANNING (WESTPLAST)
Lab 6 - Aggregate Planning (Westplast)
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Lab6_Westplast (59 Kb)
Lab 6 - Aggregate Planning (Westplast)
March 2, 2007
Agenda:
1. Setting up the model
2. Solver
3. SolverTable
4. Additional poblems
5. Solutions
Setting up the model
The first thing that you may notice about this case is that there are two object
We would like to maximize the Plant Capability Index (PCI) but at the same
would like maximize our revenue. Since Solver does not allow you to have m
objectives, we will have to use alternative methods in order to provide a pra
solution to this model.
Calculating the Indexes and Revenue for the current plan:
1. Multiply the current production plan by the associated PCI in order to get a
value for our index:
2. Calculate a similar value for revenue:
3. Create a column that will calculate the same values under our plan:
4. Calculate how much of our capacity we are using under each plan.
Solver
Now that we have created our model we need to try and find a better solution
the first plan. One option is to run Solver and make sure that the Total Inde
amount does not decrease from the current plan, while trying to maximize r
The solver settings for this option are as follows:
Constraints were added to ensure:
i) Our plan's total index is greater than or equal to the current plan's total in
ii) Production does not exceed 350,000 tons
iii) Production is not more demand for each product
iv) Production is sufficient to meet the contractual amounts required for eac
product
Additional Questions for the Problem
Each question should be considered to be individual. Reset your settings to the
original solution for each subsequent problem.
a) What is the impact of the contractual obligations on the decision? Could the
company come up with a better product mix if the contractual obligations we
treated as simple demand (without an obligation to fill them)?
b) How would expectations of changes in currency exchange rates influence th
product mix? Specifically, suppose that the executives expect a 5% increase
value of the US dollar during the year. Would that change the product mix?
that the price paid by customers in the US, as measured in US dollars, does
change.
c) The company chose to produce pellet D since they wanted to keep Smithere
(the only buyer) a satisfied customer. This is perceived as desirable, in case
future downturn in the economy. What is the economic cost of this choice to
company?
d) Washington Plastics, Inc. in Seattle may undersell WestPlast in the US mark
the executives of WestPlast notice an attempt in this direction, what is their
counter-strategy?
e) Criticize the company’s production plan considering the marketing strategy
company “fewer products, greater tons”. Suppose it is possible to increase t
production capacity of the mill by 5% by dropping one product from the pro
mix. Is it possible to improve upon the product mix by dropping one product
percent-increase in the capacity is necessary to justify the dropping of one p
Solver Table Time!
Solver Table is an effective tool for sensitivity analysis. To download SolverTab
here.
Instead of maxmizing revenue with a minimum limit on the PCI index, why no
combine the two objectives using weighting?
We want to vary the weight for the PCI index and capture the index and reven
outcomes to generate the efficient frontier of solutions. Before setting up the
SolverTable we need to solve the problem with Solver. We no longer have the
minimum limit on the PCI index, so this constraint is removed. We also want t
change the objective cell to the weighted objective.
Now that Solver is set up we can use SolverTable to compute the various weig
combinations. SolverTable is similar to a data table. Basically it takes new valu
runs Solver each time in the 'background', and returns the outputs for each ru
Go to Data -> SolverTable.
We want to create a oneway table since we are only varying one parameter (th
weight).
We want to vary the PCI weight. The minimum value is 0 and the maximum va
1. The variation will be in increments of 0.1. The output cells are the solution v
we want to track. Select all the of the decision cells as well as the Total Index
Total Revenue. The location of the table can be anywhere on your worksheet.
that it will overwrite anything in it's way so choose your location carefully.
After changing the headings, here is what the outputs should look like.
Solutions
a) To complete this question we must remove the constraint that production m
sufficient to meet the contractual obligations and run Solver again. Compare
the original solution.
We could increase our revenue by 42 if we did not need to meet contractual
obligations.
b) There are two export products. A 5% increase in the value of the US$ will in
our cash flows by 5% on these two products. You cannot use the sensitivity
to answer this question since we are changing more than one number in the
problem. You need to increase the revenues of the export products by 5% a
resolve.
Rewrite the Total Revenue formula so that you are multiplying by the new reve
Rerun Solver. When you do this, you will notice that the solution (product mix)
not change. Of course, the revenue goes up.
c) To evaluate this cost, change the Pellet D contract figure from 0 to 35 and r
solver again. You will find a revenue reduction of 0.68%.
d) The allowable decrease figures for the two exports in the “sensitivity report”
tell you how much room you have to reduce your unit revenues without cha
the optimal mix--there is some room to counter a price reduction by the
competitor. However, if you want to find the impact of reducing both export
revenues simultaneously, then you have to run the solver again with new re
figures.
e) To complete this problem we will have to add a new set of variables. These
allow us to determine the amount of products to produce
For the first question:


Introduce a new column titled Yes/No. The 0-1 variables in this colu
determine whether or not to produce a product. Sum up this colum
track the number of products we're producing.
Introduce another new column, titled “Conditional Demand”, which
product of the demand with the Yes/No variable for each product. N
cannot multiply changing cells by changing cells, as this would mak
problem non-linear. This is the reason we do not simply multiply ou
Yes/No variable by the variables listed under "Our Plan"

Compute the % increase in capacity as the difference between the numb
products produced in the original plan and the new plan multiplied by 5%
 Change the capacity to =335*(1+% increase)
 Add the Yes/No variables to the changing cells.
 Add a constraint that says the Yes/No variables are “binary”.



Add a new constraint: Production < Conditional Demand and remov
Production < Demand constraint.
Add another new constraint that sets the sum of the Yes/No variab
the total number produced in the original plan.
Change integer options tolerance to be 0.0005 (instead of default o
In Premium solver, you select the integer options button then insid
tolerance input box you change this. At home when you go into the
options menu you change the tolerance to be 0.05% - this will chan
integer tolerance.

Run the solver to maximize revenue and compare the result to the
solution
For the second question:
The idea behind this question is that by dropping one less product you gain
production capcity. If you were to not increase capcity and just drop one
product, you will not be able to achieve the needed revenue and index ne
improve the solutions. You can't do it becuase there is no product mix th
allow you to stay within the capacity constraints while still achieving the C
index and revenue that you would get with 9 products. In order to have a
the same values for index and revenue while also dropping one product
(changing the max number of products allowed to be 8 instead of 9) ther
be an increase in capacity. This question is trying to determine what the
minimum percentage that is needed to achieve at least the same index a
revenue values while only having 8 products. Because we are mimimizing
percentage increase we know that the number of products that will be pr
is 8 and this is because of what was discussed in the previously. For each
product that you drop, if you still want to achieve the same revenues and
production needs to increase and to see the minimum production increas
will produce the maximum number of products. You'll notice when you dr
the problem is infeasible. Why? Just some things to think about on your o
How to solve this problem:
Keep all the changes from above
Target: minimize percentage increase in production
Decisions: add your target cell as a decision sell, since we want Solver to
how much this should be
 Create two new constraint: that Revenue > the revenue from the p
found original solution, and Number of products produced < the nu
found in part 1 of this question.
The capacity should now be calculated as follows:




The optimal increase in production is 0.27%. If you have an answer of 0.731
you have not re-adjusted your tolerance level for the binary integer cons
See the constraints from the first part of this problem above for an explin
on how to do this.