Open question 1: Inventory management + ILP
A bakery buys flour in large bags. The bakery uses 1,404 of these bags a year. For every order they
place,
... [Show More] they pay €9. The annual carrying costs are €78 per bag.
a. Determine the optimal number of bags to order every time to minimize the annual ordering and
carrying costs. How much are these annual costs? Show your computations. (4 points)
b. The demand seems to follow a normal distribution and the bakery estimates the standard
deviation of the annual number of bags to be 20 bags. It takes 2 days for an order to arrive and the
bakery wants to ensure that they have enough flour in stock at least 99% of the time. Give the bakery
some advice on when they need to order new bags to ensure this service level. Show your
computations. (5 points)
However, the reality for the bakery is a bit more complicated. The owner facesthe following issues:
• The bakery is open from Monday to Saturday. On Monday to Thursday the demand is
constant at 4 bags a day. The demand peaks at 6 bags on Friday and decreases to 5 bags on
Saturday. The demand on Sunday is 0.
• Due to the Corona situation, deliveries can only take place on Monday and Thursday morning
before the owner starts baking. Deliveries on other days are not possible.
c. Explain why this means the bakery cannot simply apply the EOQ framework. Use 30 to 50 words. (2
points)
The bakery decides to optimize their inventory management using integer linear programming. They
want to have the same order pattern every week. They already have a start of the setup of the
program to determine the weekly ordering process as follows.
• Sets: The days of the week are numbered by j = 1, 2, 3, 4, 5, 6, 7.
• Parameters: The bakery denotes the demand on day j by dj, the ordering costs per order (€9)
by S and the holding costs per day (78 / 365 = €0.21) by H.
• Decision variables: The bakery introducesthe following decision variables:
o x1 and x4 denote the number of bags to receive on Monday and Thursday
respectively;
o y1 and y4 denote whether the bakery receives a delivery (1) or not (0), on Monday
and Thursday; and
o I1 up to I7 denote the number of bags in the inventory at the end of that day that are
carried to the next day.
• The objective of the bakery is to minimize the weekly costs, which is the sum of the ordering
and carrying costs.
• Unfortunately, the bakery was not able to formulate ideas for the constraints yet.
d. Write down the ILP (consisting of the objective function and the constraints) for the bakery to
minimize their weekly costs. You are encouraged, but not required, to use the parameters that [Show Less]