A bagel shop buys each bagel for .08 and sells each bagel for .35. Leftover bagels at the end of they day are purchased by a local soup kitchen for .03 per bagel. The shop owner has observed daily demand (Q), the following probabilities (F(Q)

Q=0, F(Q)= .05

Q=5, F(Q)= .1

Q= 10 F(Q)= .1

Q= 15, F(Q)= .2

Q= 20, F(Q)= .25

Q= 25, F(Q)= .15

Q= 30, F(Q)= .1

Q= 35, F(Q)= .05

1. What is the optimal daily order, in multiples of 5?

2. If the daily demand is normally distributed (the meanand variancecan be obtained from the table above), then what is the optimal daily order?

Answer

The given problem is a problem from stochastic inventory models, popularly known as ‘News Paper Boy problem’.

General description

In this model we consider items which are produced at the beginning of a period are of either no use or to be sold at loss after the period. The problem is to find out optimum order quantity which maximizes the expected profit for a single period. The following notations are used.

a – production cost or purchase price

b – unit selling price during the period ( b > a)

c – selling price after the …

In this solution, a stochastic inventory model, popularly known as “News Paper Boy Problem” is solved. The problem is solved as two cases, first assuming demand distribution as the given discrete distribution and then assuming as normal distribution. The general theory is discussed first and then the numerical example is worked out.