# GILI TEST July 15th, 2014

# EOQ and Savings Matrix

# INTRODUCTION TO THE TEST OF JULY 15th, 2014

In the following the solution of the test is provided. The subject concern the Economic Order Quantity, the reorder point s and Savings Matrix Methos.

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

# EXERCISE:

A Distribution Center supplies products (in packages) to a set of 20 clients.

Package weekly demand is normal distributed for each client with average and standard deviations shown in the following table. Weekly days in a week are 5 days/week. The price **v** of each package is 20 €. **A**, the order setup cost is 10 €/order. Order lead time is 1 day. **r**, the carrying cost interest rate on daily basis is 10% €/€-day.

The total amount of money allocated for the safety stocks is 230 €.

Determine:

A. **EOQ** for each client (approximate EOQ to the nearest integer)

B.The reorder point **s** of each client, by imposing the same Client service Level P1 (approximate s to the nearest integer)

At the end of each day all the clients with inventories below or equal to the reorder point orders and EOQ to the Central Depot.

C. By considering the Present values of inventory in the table, find the clients that need to launch and order to the Distribution Center. (hint: the total of the packages to be order is less than 50).

D. Determine the routing by using the saving matrix methods, considering that the Distribution Center can use 2 trucks of 25 packages of capacity each one. In the following table the matrix of distances between the 20 clients and the Distribution Center is shown.

# QUESTIONS:

a)Write a Linear programming model for the optimization of the Aggregate Planning, taking into account workers, people hiring, layout, material costs, inventory carrying costs, stock out costs (considering a backorder model), overtime costs, production level, outsourcing costs.

b)Show the rule for determine the k coefficient of safety stocks in the case a model cost B2 is considered.

c)What is it the Mix Production capacity?

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