Question

please be sure to do part E its the hardest part

3) A toy manufacturer makes its own wind-up motors, which are then put into its toys. While the toy manufacturing process is continuous, the motors are intermittent flow. Data on the manufacture of the motors appears below.
Annual demand (D) = 50,000 units Daily subassembly production rate = 1,000

Setup cost (S) = $85 per batch Daily subassembly usage rate = 200 Carrying cost = $.20 per unit per year

a. To minimize cost, how large should each batch of subassemblies be? b. Approximately how many days are required to produce a batch?
c. How long is a complete cycle?
d. What is the average inventory for this problem?

e. What is the total inventory cost (rounded to nearest dollar) of the optimal behavior in this problem?

Answer 1

a) Minimizing cost is one of the most crucial aspect of any production. On the other hand thinks of increasing production. Now lets see how increasing subassemblies can reduce cost?

Subassemblies in simple words refers to small batches or quantities of work done. For example : Assembling of a large machinery is done in bits, here the whole work is divided into small batches which is referred to as subassemblies.

When the work assigned in each subassemblies are increaed the workers work at a rapid pace and thus become more efficient as they can find time for other works also . In this way, a work of 20 days can be reduced to 10-15 days which saves a lot of cost. Now , moving on to above problem where in daily production = 1,000 units and one assembly is of 200 it can be increased to 300-350 which can make huge difference and at the end lead us to cost reduction.

b) Batch processing time or cycle time refers to the complete days or time required to process each batch.Calculating batch processing time is one of the toughest thing. For this , we can either use EOQ formula or say VBA coded excel formula.

The time or days for processing can be expressed in units/ hour . For example : ABC is a manufacturing company and it produces xyz products, per hour it produces 200 units, then the time can be expressed as 200 unitsper hour.

c) The time duration as mentioned above can vary depending upon the sub assemblies and how fast each batch is processed. it can be short or long depending upon the quantity.

d) Average inventory :- Average inventory can be defined as a mean value or average of inventory at a certain point of time. Average is calculated by dividing the value by 2. Example :- The total inventory of ABC industry is 60,000 and when taking average = 60,000/2 =30,000.

Now moving to the above problem,

Average Inventory = Inventory at the beginning + Inventory at the end /2

Now, here it is not specifically mentioned, assuming the annual demand to be total inventory ie ; 50,000 units

Average Inventory = 50,000/2 =25,000.

e) Total inventory cost is the total cost incurred while production which includes purchasing costs, ordering costs and holding costs.

Therefore , Total inventory cost = Purchasing cost+Ordering cost+ Holding cost

Now here we see ordering cost and purchasing cost is not specified.

So, we will calculate using another formula

TC = DC+(Q/2)*H+(D/Q)S

here TC = Total cost of inventoryper unit

DC = Annual Demand

Q/2= Average Cost

H= Holding cost per unit

S = Cost to place a single order

Now substituting the value

TC = 50,000+25,000*27.397+(50,000/25,000)*85

=50,000+25,000*27.397+(2)*85

= 50,000+684931.506+170

= 735101.506