GILI TEST Jun 19th, 2014

STOVIGLIE (DISHES) Inventories Exercise


In the following the solution of the test is provided. The subject concern the Time Supply, simple minded approach, Economic Order Quantity, the reorder point s, The Periodic Review R, order up to level S inventory policy. 

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


Rinchi Casalinghi is a Point of Sale of Dishes. Dishes come from a supplier in the North of Italy. Rinchi Casalinghi, the owner, wants to avoid any stockouts.  For this reason he decides to keep a minimum Inventory  level of 3 months of supply time. 

When inventory level goes below the level of 3 months of supply, he launches an order of other 3 months of supply. He follows this simple rule since ten years ago and he never had any Inventory trouble.

The value v of each single dish is 10 €/item. The cost for the ordering and the receiving of new items is equal to 130 €/order and it requires 5 weeks of time. 

Monthly is distributed approximately normally with an average value of D=200 items/months and a standard deviation of σl=80 items/months. The rate of interest for the holding costs is r=20% €/€-y

a) What is the value of Q and s that Rinchi is using for Dishes inventory Control? 

        b) What is the Fill Rate you can reach with this policy?

        c) What are the optimal value of  Q and s for a Fill Rate service = 99%?

        d)Determine the difference in terms of holding and setup averaged annual costs between solution a and c.

        e)Rinchi is considering a change in inventory policy. He is considering to make an order each third months. What are the change in terms of holding and setup costs, by keeping the same service level?


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