30E00400 Simulation, Tomi T. Seppälä, fall 2015
Class exercise 1: Excel and probability basics
Dave’s Candies
Dave’s Candies is a small family-owned business that offers gourmet
chocolates and an ice cream fountain service. For special occasions, such as
Valentine’s Day, the store must place a special packaging order to its supplier
several weeks in advance. One product, Valentine’s Day Chocolate
Indulgence, is bought from the supplier for €7.50 a box and it is sold at a retail
price of €12.00. Any boxes that are not sold by February 14 th are discounted
by 50 percent and can always be sold easily. Historically, Dave’s Candies has
sold between 40 and 90 Valentine’s Day Chocolate Indulgence boxes each
year with no apparent trend (either increasing or decreasing). Dave’s dilemma
is deciding how many boxes to order for next Valentine’s Day. If demand
exceeds the order quantity, then Dave loses profit opportunity. On the other
hand, if he orders too many boxes, he will lose money by having to discount
them below cost.
Let Q=”number of boxes ordered” and D=”demand by February 14th”
Do not use simulation in this exercise but do it analytically using Excel.
1. Develop the profit function =(Q,D) as a function of Q and D.
2. Develop a spreadsheet model showing the profit assuming that Q=50
and that D has an equal probability of falling on any of the values 40,
50, 60, 70, 80, and 90 (discrete uniform distribution), i.e. show all the
corresponding profits in a table, including their probabilities. Make the
model such that it would be easy to change the numerical values of any
of the given parameters (selling price, purchase price and discount
price), as well as demand.
3. Present the probability distribution of the demand graphically.
4. Calculate the expected value of the profit.
5. Form the probability distribution of the profit and present it graphically.
6. How many boxes should Dave order to maximize expected profit?
Assume that the supplier only accepts orders in increments of 10 (i.e.
40, 50, 60, 70, 80, or 90 boxes).
7. What is the probability of stock-out at each order quantity?
Exercise 2: Excel basics
To be done at home; not to be returned for grading
Mantel Manufacturing
Mantel Manufacturing supplies various automotive components to major
automobile assembly divisions on a just-in-time basis. The company has
received a new contract for water pumps. Planned production capacity for
water pumps is 100 units per shift. Because of fluctuations in customers’
assembly operations, demand fluctuates and is historically between 80 and
130 units per day.
1. Develop a dynamic spreadsheet model to mimic the evolvement of the
inventory level for 10 days, assuming that the beginning inventory is 0.
Assume that the company allows back-orders, i.e. if inventory goes
below zero, the pumps will be delivered late. Calculate the back-orders
remaining at the end of each day and their average. Also calculate the
average ending inventory.
Note: You do not need to simulate the demand in this exercise, just
plug in numbers between 80 and 130 units per day to see that your
model works.
2. Modify the model so that no back-orders are allowed, i.e. if demand
exceeds the inventory level, then the sales are lost. Calculate the daily
and average lost sales.
3. To maintain a sufficient inventory to its just-in-time commitments,
Mantel’s management is considering a policy of running a second shift
if inventory falls to 50 or below. For the annual budget planning
process, managers need to obtain an estimate of how many additional
shifts will be needed. Modify the model accordingly.