GILI TEST Sept 4th, 2014

Bakery Case: Inventory Aggregation and Saving Matrix

(Re-adapted from Nahmias, Production and Operations Analysis, 2013, pp 334)

 INTRODUCTION TO  THE TEST  OF September 4th, 2014

In the following the solution of the test is provided. The subject concern the Inventory Aggregation, Saving Matrix Methods. 

Please refer to Silver, Pyke, Peterson, Inventory Management and Production Planning and Scheduling, 1998 for any further information or to Nahmias, Production and Operations Analysis, 2013


Grain Mill is a small bakery that supply 5 major customers with bread each morning. Daily Demand in each customer follows a normal distribution and it is independent one customer to the others. Considering the Location Bakery in (0,0) and the following data for the customers:


Customer Coordinates

Average Daily Demand


Daily Standard Deviations


1 (15,30) 85 25
2 (5,30) 162 35
3 (-10,20) 26 13
4 (-5,5) 140 90
5 (-20,10) 110 25


a)      What are the quantities to be supplied to each customer to guarantee a P1, the cycle service level of 80%? And 99%?

b)      By the Saving Matrix Method, considering trucks of capacity of 300 units, determine the number of trucks and the routes for the distribution of the bread in the 3 cases:

b1.   Quantities equal to the average daily value

b2.   Quantities that guarantee P1=80%

b3.   Quantities that guarantee P1=99% 

Now consider a new scenario when bread is made and stocked in the Bakery each morning. At beginning of the day clients book the bread and then bread is distributed between customers in the exact quantities booked.

c)       What is the reduction of the Total inventory that we can reach, keeping the same P1=80% and P1=99%?

d)      What is the probability than surely more than 3 trucks are necessary for the distribution in the case c)?

     e)      What are the Fill Rates in cases a and c considering a complete lost sales scenario?



a)Explain the Wagner Within method. 

b)Show the rule for determine the k coefficient of safety stocks in the case a model cost B1 is considered.

c)What is it the Availability?