Question

Summer-Fun, Inc., produces a various commodities related to recreation and leisure. The production manager has developed an aggregate forecast: Apr May Aug Sep Total Mar June July Demand 50 1 44 | 55 | 59 | 50 | 41 51 350 Use the following information to develop aggregate plans. Regular production cost $ 80 per unit Overtime(OT) production cost $ 120 per unit Subcontracting(SC) cost $ 140 per unit Regular capacity 40 units per month Overtime capacity 8 units per month Subcontracting capacity 20 units per month Regular/Overtime Subcontracting capacity in June 078/11 units Holding cost $10 per unit per month Beginning Inventory O units Develop an aggregate plan using a level strategy. (1) Please show me the aggregate planning under the condition of "No shortage allowed" (2) Please show me the aggregate planning under the condition of "No shortage allowed" and "O inventory at the end of planning horizon". (3) Compare the total costs of (1) and (2).

Answer 1

Assignment 4

We need to compare the total inventory cost of the order quantities at the various discount levels with that of the economic order quantity.

Since the holding cost is partially determined on the basis of purchase price, we need to re-calculate the EOQ by applying a discount price.

EOQ       =           √2 x (Order Cost per order) x (Annual Demand)

                                                            Carrying Cost per unit

EOQ at unit price $10

=           √2 x (10) x (200*50)

                        .20*10

=    316 units

EOQ at unit price $8

=           √2 x (10) x (200*50)

                        .20*8

=    353 units

Order Quantity	316 units	353 units
Number of orders (Annual demand ÷ Order Quantity)	10000 ÷ 316 = 31.64	10000 ÷ 353 = 28.33
Ordering Cost (number of orders × $100)	32*10 = $320	29*10 = $290
Carrying Cost (20% × Purchase Price × Average Inventory)	0.20×(10)×(316/2) = $320	0.20×(8)×(353/2) = $290
Cost of Purchase (Purchase Price × Annual Demand	10×10000 = $100000	8*10000 = $80000
Total Inventory Cost	$100640	$80580

Based on the above analysis, the optimum order quantity is 353 units.