1.
Learning Curve Based Production Planning

Open the file Learning.xlsx.

Many labor-intensive production operations experience a learning curve
effect. The learning curve specifies that the cost to produce a unit is a
function of cumulative production, that is, as production volume increases, the
cost to produce each unit drops. One form of the learning curve is as follows:
Ci = p*(i)q where Ci is the cost of producing
the ith unit. The parameter p
is called the first unit cost and q
is the learning slope parameter. The total cost of producing a batch of size x can then be approximated by

(p x1+q)/(1+q).

We now consider a specific production setting where there is learning.
Demands for our single product over the next five periods are 100, 150, 300,
200, and 400. Holding cost per unit per period is $.30.

a. In the worksheet Learning.xlsx,
use Solver to find the best fitting learning curve (that is, find the values of
p and q) so as to minimize the sum of squared error where the predicted
value of unit i is p*(i)q. Report your results below.

Value of p: __________________

Value of q: __________________

Sum of Squared Errors: __________________

b. Based on your results from part a), use the approximation (px1+q)/(1+q)
as the cost (in dollars) of producing a batch of size x. Assume that the learning from one time period to another is
lost (so there is no transfer of learning between time periods) and the amount
we produce in a given period is one batch. Solve the production planning
problem of minimizing the sum of production and inventory costs, while
satisfying demand. Assume we must have an ending inventory in period 5 of at
least 50. Report your results below.

Total Cost: __________________

c. Solve the same production planning problem ignoring the learning
curve, that is, assume that every unit costs p dollars (where the parameter p
was estimated in part a) above). Report your results below.

Total Cost: __________________

d. Compare the optimal production plans you obtained in b) and c). Explain
any differences.

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