Question

Juicy & Fresh U&F) produces and bottles fruit juices in different flavors and container sizes.J&F is implementing a new Advanced Planning System APS) to manage its production planning. The new system provides flexibility in the selection of the lot-sizing method to be used in the MRP calculations. The APS offers a set of different standard lot-sizing methods and the possibility to use a customized method. The company's manager is not sure about which lot-sizing method would benefit most to J&F. In this sense, she asked Joseph Miller, the production planner, to assess the different options available Joseph took a representative SKU to run multiple tests. The SKU selected, a 1/2-liter orange juice in PET bottle, incurs a production setup cost of $300. The estimated inventory holding cost is $2 per 24-bottle pack per week. Joseph assumes no bottles are available in inventory at the beginning of the planning horizon. The estimated weekly demand (in 24-bottle packs) is shown below: Week 2 4 220 Demand 521 270 40 120 10 30 70 Joseph started analyzing two simple methods to define production lot sizes: one time run (1TR) and lot for lot (L4L). Based on his analysis, which of the following statements are true? Select all correct answers. L4L's total cost (setup and holding costs) is higher than the total cost using the 1TR approach. L4L's total setup cost is higher compared to 1TR's total setup cost 0 J&F won't incur in inventory holding costs using the L4L approach. J&F won't incur in inventory holding costs using the 1TR approach. | None of the above.

Answer 1

Using L4L ( Lot for lot) method, planned production is in quantities equal to the estimated demand in each week. Hence, there is no extra on hand inventory.

On the other hand, using one time run (1TR) method for lot sizing there is one time production and inventory moves from one week to another week.

Hence, looking at the last two statements given. The third option "J&K won't incur in inventory holding cost using the L4L approach" is a TRUE statement. On the other hand fourth option "J&K won't incur in inventory holding cost using the 1TR approach" is a FALSE statement.

In terms of setup cost, for L4L method there will multiple setup required in each period hence the total setup will be higher ($300 * 8 weeks = $2,400) as compared to 1TR method where production setup is done only once i.e. $300.

Hence, second statement "L4L's total setup cost is higher compared to 1TR's total setup cost" is TRUE.

Now, we will calculate total cost (setup and holding cost) for both lot size option to assess first statement.

For L4L, setup cost is $300 * 8 weeks = $2,400 and with on-hand inventory the holding cost is $0. So, the total cost is $2,400.

For 1TR, setup cost for one time run is $300 and on hand inventory for each period is calculated below.

* First week production run produces to address the demand for all 8 weeks i.e. sum of demand for all 8 weeks (780)

Week	1	2	3	4	5	6	7	8
Demand	120	10	30	20	70	270	220	40
Production	780
On hand inventory	660	650	620	600	530	260	40	0
Holding cost ($2per week)	$1320	$1300	$1240	$1200	$1060	$520	$80

Hence, the total inventory holding cost is $6,720.

So, total cost for 1TR method is $300 + $6720 = $7,020

Overall the total cost for 1TR method is higher as compared to L4L method. Hence, the first statement "L4L's total cost is higher than the total cost using the 1TR approach" is FALSE.

Second and third Statements are only TRUE.

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