Decision-Making Models - Math Problem Example

The researcher states that the amount of inventory that Company A needs to order can be determined with the use of economic order quantity (EOQ) model. According to Williamson EOQ models are used for identifying the optimal order quantity. In order to do this the model minimizes the sum of certain costs that vary with order size and the frequency of orders. Williamson (2012) describes three order size models – the basic economic order quantity (EOQ) model; the economic production quantity (EPQ) model; and the quantity discount model.

The basic EOQ model is used to find the order size that would minimize company A’s total annual cost. The formula and the calculations follow. Q0 = √(2DS/H) Where, Q0 is the order quantity in units D is the annual demand in units S is the order cost for each order made H is the holding or carrying the cost for each unit of inventory per year Company A’s information is as follows: - Annual demand (D) is 18,000 units per annum - Ordering cost (S) is $38 per order - Holding cost (H) is 26% of the cost of the inventory which is $12 per unit Q0 =  √[(2 x 18,000 x $38)/(0.26 x $12)]      = √(1,368,000/3.12)      = √438461.

54 = 662 units      = 662 units The results indicate that the economic order quantity that will minimize total annual cost is 662 units per order. Company A produces the goods that it sells and so the economic production lot size model is the most appropriate model for use in this scenario (Williamson 2012). The formula for performing the calculations that provide the results is as follows: Qp = √(2DS/H) √[p/(p-u)] Where, Qp is the economic run quantity p is the production or delivery rate u is the usage rate Qp = √[(2 x 15,000 x $84)/(0.28 x $19)] √[60,000/(60,000-15,000)]  Qp = √(2,520,000/5.32) √1.

33 Qp = 699.25 x 1.15 Qp = 791 The results indicate that the economic production lot size that will minimize total annual cost id 791 units per production run.