How do I figure this out? The president of Hill Enterprises, Terri Hill, project

Question

How do I figure this out?

The president of Hill Enterprises, Terri Hill, projects the firm's aggregate demand requirements over the next 8 months as follows January February March April 1,400 1,700 1,800 1,700 May June July August 2,200 2,200 1,900 1,300 Her operations manager is considering a new plan, which begins in January with 200 units of inventory on hand. Stockout cost of lost sales is $65 per unit. Inventory holding cost is $20 per unit per month. Ignore any idle-time costs. Evaluate the following plan This exercise contains only Plan D Plan D: Keep the current workforce stable at producing 1,600 units per month. In addition to the regular production, another 20% of the normal production units can be produced in overtime at an additional cost of $55 per unit. A warehouse now constrains the maximum allowable inventory on hand to 600 units or less Note: Do not produce in overtime if production or inventory are adequate to cover demand

Explanation / Answer

Plan D :

Contraints is to satisy demand , ensure there is no stockout and 600 units of inventory can be ending inventory of any month .

Now the table below is given

We need to find the right number of OT units , ending inventory and stock out in any month if any.

We do not have to use the OT production unless it is required to satisfy the demand. But the problem is if demand increases drastically the OT units produced during a particular month will not be sufficent to satisy the demand. Because OT production can only be 20% of total production during the month.

As per the given data there are 1600 units can be produced in a particluar month. So if maximum 20% of it will 320 units can be produced as OT.  

The total demand for 8 months is = 14200

the carry over from Dec to january = 200

so the production in january = 1600. So the total available inventory in january = 1600+200 = 1800

The demand in January is 1400. As inventory available is more than that of demand. The overtime is not required. The ending inventory is 1800 - 1400 = 400. Stocko out will be 0 in january.

Similarly the demand in feb is 1700. The production in Feb is 1600. the avialable inventory in february = production + carry over from previous month= 1600 + 400 = 2000. the ending inventory = 2000-1700 = 300

Similarly the OT , ending inventory and stock outs calculated and shown in below table

In above table conside the April month. The demand is 1700 and avialable inventory is 1700 . So the ending inventory will be 0 .

In may month the demand is 2200. The production is 1600. OT is 320 .So the total inventory avialable is 1920. But still avialable inventory is less than that of demand. So the sock out quantities = 2200 - 1920 =280 units.

The ending inventory will definately be 0.

Month Demand Production Units OT Production units Ending inventory stockouts December 200 January 1400 1600 February 1700 1600 March 1800 1600 April 1700 1600 May 2200 1600 June 2200 1600 July 1900 1600 August 1300 1600

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