Suppose you buy a certain product from the producer and sell it to your customer

Question

Suppose you buy a certain product from the producer and sell it to your customers. You must decide how much to stock in anticipation of demand, before knowing exactly what the demand will be. The purchasing and storage cost of each unit of product is $10, and selling price is $15 / unit. From prior sales, you know that demand follows Normal Distribution with mean 60 and st. dev. 12. If all of the units cannot be sold due to low demand, an excess inventory occurs. Conversely, if due to high demand, all of the demand cannot be satisfied, a shortage occurs. Assume there are no additional costs associated with excess and shortage but they must be incorporated in the formulation.

a) Formulate this problem using stochastic programming.

b) Solve it with a solver, by sampling demand 10 times from the Normal distribution (10 demand scenarios). Explain your findings.

Explanation / Answer

a) Problem Formulation

Let d be demand. from given, d~N(60,12)

Let s be stock in anticipation of demand to be figured out

such that maximizes

profit due to sale($5) - foregone profit due to shortage($5) - loss due to excess inventory($10)

Hence our objective equation is

Maximize : 5*d - 5 * (d-s) - 10 * (s-d)

constraints : d~N(60,12)

b) solving with solver

By Generating 10 random demand scenarios from N(60,12) and using solver to attain stock in anticpation of demand while maximizing the above equation we find

when using solver multiple times, the stock is in the range of 60-12(48) and 60+12(72) generates maximum average profits for all scenarios

60 is Mean and 12 is standard deviation of demand

Mean (+ or -) 1 standard deviation is the stock that is feasible given the uncertainity of demand

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.