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# Inventory and Master Production Schedule

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1. Economic order quantities calculations:

In this case study, I use POQ to calculate Optimal Quantities to Order because some the parts are made by company’s plastic-molding machines in an assembly operations and units can be assumed that are received incrementally during production. We also have the following assumptions:

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– Only one item is involved because each type of toy has its own assembly line, only one toy can be assembled at a time on this line. – Annual Demand is known
– Usage rate is constant
– Usage occurs continually but production occurs periodically – The production rate is constant ( i.

e. production rate of Toy Auto is 3500, Toy Truck, 1750; Toy Robot, 2333)
– There are no quantity discounts

Thus, we have to find out the Set up cost, Holding cost, Demand per year, Demand per week and production rate.

Therefore, we have
Ø Set up Cost:
According to the case study, we have the shop labor rate is the sum of \$6 per hour for wages, 33% fringe benefits and \$6 per hour charged for overhead.

Moreover, line 1 has 10 workers who engage in assembly. Thus, the setup cost is:

S = 1 hour * 10 workers *
( \$6 wages + 0.33*6 benefits+ \$6 overhead )= \$140

Ø Holding Cost:

There is some ambiguity here. The subcomponent costs in Exhibit 4 do not always add up to the Cost Each (e.g. the cost for Auto is \$3.9) which is level 0 item cost. So I assumed that Line 1 labor costs (at a fully burdened \$6 + 0.33*6 + \$6 = \$ 14 per hour) were not included.

Hence, Item Cost per unit is the sum o
f Cost Each Item and the labor cost per item. You can see the results of Item Cost in Excel worksheet. (The labor cost per item here is equal to labor cost per hour times the hour to make one toy.

For example:

It takes 0.1 hour to make one Auto and the labor cost per hour is \$14. Therefore, the labor cost per item is: C = 0.1 * 14 = \$1.4 )

As a result, we can have the Holding Cost which i
s 25% per year:
H = 0.25 * Item Cost per unit
( see results in Excel worksheet)

Ø Weekly Demand, Annualized Demand:

In Excel worksheet, I calculated the average demand in 6 weeks from Sept. 26 to Oct. 31. Because we only have the figures of these 6 weeks, so I assumed that this average demand is weekly demand which is constant. One year has 52 weeks, therefore, the annualized demand D equals to weekly demand d times 52 weeks:

d = sum (demand in week Sept. 26 to week Oct. 31)/ 6

D = d * 52

Ø Production rate:
– Toy Auto: 3500 units per week

– Toy Truck: 1750 units per week

– Toy Robot: 2333 units per week

After calculating these above data, we can compute the optimal quantity according to this formula:

Q* = © 2DS/ (H ( 1- d/p)
)

2. Master Production Schedule for the next six weeks:

First of all, we must calculate the run-out time of each toy at the beginning week which is the duration (in weeks) in which this company will can consume (use) all the beginning inventory. It is the ratio of beginning inventory to weekly demand. Therefore, we can know what the toy we must produce first is.

As you can see from the Excel worksheet, we have the run-out time for Auto, Truck and Robot approximately are 3, 5, 2 respectively. Thus, Toy Robot must be produced firstly, then is Auto and lastly is Truck.

The Master Production Schedule also satisfy full capacity to keep the workers busy as mentioned in the case study and the maximum hour per week is 350 for week Sept. 26 and 349 for week Oct. 3 onwards ( because it takes 1 hour to change the setup of the line).

Hence, if the entire week is used to make these toys but the optimal quantity has not reached yet, we must produce the rest in next week. For example: The run-out time for Robot is approximately 2 weeks and is the smallest one; Robot must be produced first in week Sept. 26. But we only have 350 hours per week which means we only can produce only 350 hours / 0.15 = 2333 units of Robot per week ( 0.15 is production rate of Robot). Thus, the remaining units is 2622 – 2333 = 289 units ( 2622 is optimal quantity). We have to produce these 289 units in the following week which is Oct. 3.

The Master Production Schedule must satisfy full capacity, then if 350 hours is not used entirely when the optimal quantity is reached already, we have to produce another type of toy to make it full capacity (in another words, to use the entire week which is 350 weeks for week Sept. 26 and 349 hours
for the following weeks) and so on. For example: In week Oct. 3, only 289* 0.15 = 43.35 hours is used, therefore, we still have 349 – 43.35 = 305.65 hours to produce 305.65 / 0.1 = 3056 units of Auto ( 0.1 is production rate of Auto. ). Keep continuing this method until week Oct. 31.

These above steps are done in Excel worksheet and you can see the Master Production Schedule for the next six weeks.

From the Master Production Schedule and the Master
Schedule Forecast Input, we can calculate Projected Inventory On Hand (POH) which equals to the Available Inventory plus the number of units produced minus the forecast demand in week. For example:

POH of Auto in week Sept. 26 = Available Inventory + number of units produced – forecast demand= 4000 + 0 – 1100 = 2900 (units)

3. MRP Plan:
One week of safety stock is weekly demand d for each toy and is weekly demand d times number of components required per unit for components of each toy. It is calculated in the Excel Worksheet.

Ø MRP Plan for Toy Auto, Toy Truck and Toy Robot:

– The Gross Requirements of each toy is its Planned Production in each week. For example, the Gross Requirements of Auto is 3056, 1693, 1390 and 3305 in week Oct. 3, Oct. 10, Oct. 24 and Oct. 31 respectively.

– No Scheduled Receipts for these toys.
– Available Inventory: + If the amount of the previous available inventory minus Gross Requirement in a specific week is more than safety stock of each toy, it is the current available inventory in this week. + If this amount is less than safety stock of each toy, the current available inventory is safety stock. And therefore, the Net Requirement equals to safety stock (current available inventory) plus Gross Requirement minus previous available inventory.

– Planned Order Receipts equals Net Requirements because we use lot-for-lot sizing.

– Planned Order Releases is Planned Order Receipts offset by lead time of each toy which is 1 week.

Ø MRP Plan for Components of each toy:
– The Gross Requirements of each component is Planned Order Releases of each toy times number required per unit.

– There are 3 Scheduled Receipts which are 100 in week Oct. 3 for Car Body, 800 in week Oct. 3 for Cab and 1200 in week Oct. 10 for Trailer according to Exhibit 4.

– Available Inventory:
+ If the amount of the previous available inventory plus Scheduled Receipts minus Gross Requirement in a specific week is more than safety stock of each toy, it is the current available inventory in this week.

+ If this amount is less than safety stock of each toy, the current available inventory is safety stock. And therefore, the Net Requirement equals to safety stock ( current inventory) plus Gross Requirement minus previous available inventory minus Scheduled Receipts.

– Planned Order Receipts equals Net Requirements because we use lot-for-lot sizing.

– Planned Order Releases is Planned Order Receipts offset by lead time of each component.

Ø According to the MRP plan, parts should be ordered:

Sept. 26
Oct. 3
Oct. 10
Oct. 17

Car Body
1390
3305

Wheel
1965

Side windows
2190

2780
6610

Windshield

1390
3305

Body
1400

Arms
806
2800

Legs
286
2800

3
1400

What should Andre Meline do to meet the inventory and service goals stated by management?

Toys Plus Inc. is encountering the overstocking of items. It can tie up funds that might be more productive elsewhere. And the inventory management also has two main concerns which is level of customer service and costs of ordering and carrying inventories. In another words, it have to meet customers’ satisfaction while keeping inventory costs with reasonable bounds. Therefore, Andre Meline has to achieve a balance in stocking. She must make two fundamental decisions: the timing and the size of orders. (i.e. when to order and how much to order).

One measure she can use to judge an effectiveness of inventory management is Inventory turnover which is the ratio of average cost of goods sold to average inventory investment. It indicates how many times in a year the inventory is sold. The higher inventory turnover is, the more efficient use of inventories.

She also has the following:

– A system to keep track of the inventory on hand and on order.

– A reliable forecast of demand that includes an indication of possible forecast error

– Reasonable estimates of inventory holding costs, ordering costs and shortage costs.

– A classification system for inventory items

She must assure that inventory costs be kept accurate and up t o date. Estimates of holding costs, ordering costs, setup costs and lead times
should be reviewed periodically and updated as necessary.

5. How Andre should deal with the organization issues presented in this case:

These issues are improving service levels and reduce inventories. Therefore, Andre Meline has to achieve a balance in stocking. She must make two fundamental decisions: the timing and the size of orders. (i.e. when to order and how much to order). She can reduce the economic order quantity by working harder to reduce the ordering cost S. Another possibility is to examine holding cost H. She also can reduce the amount of safety stock to reduce inventory. Important factors in safety stock are lead time and lead time variability, reductions of which will results in lower safety stock. She can judge the timing of orders to set a reasonable lead time.

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