The formulation of this problem has given below: Suppose a company has the option of advertising its
Question:
The formulation of this problem has given below:
Suppose a company has the option of advertising its product on certain months with a campaign cost of CH/month. If a campaign is on, we expect sales to go up by 15% on that month. But, in the next month we see a decrease of 8% in sales. Suppose we have forecasted demand of D(t) for next 6 months. A monthly capacity of CAP units per month is available for production. If inventory cost is h/unit/month and production cost (p(t)) is variable over the planning horizon due to inflation, formulate the problem to maximize profits, given a fixed sales price of P.
QUESTION1: Find a way to maximize NET PRESENT VALUE OF PROFITS in this formulation
QUESTION2: Also, add multiple products to this formulation and also add a monthly budget for multiple product campaigns.
The formulation of this problem:
Answer: Maximize sum(t, P*S(t)-CH*X(t)-p(t)*PROD(t)+h I(t))
s.t. S(t)= D(t)+0.15 *D(t) *X(t)-0.08* D(t)* X(t-1) for all t
I(t) = I(t-1)+PROD(t)-S(t) for all t
PROD(t) ≤ CAP for all t
Where X(t): binary variable indicating if there is campaign in month tPROD(t): production quantity in month tS(t): Sales quantity in month t
Mathematical Applications for the Management Life and Social Sciences
ISBN: 978-1305108042
11th edition
Authors: Ronald J. Harshbarger, James J. Reynolds