Final answer:
The Toyota dealer should use an order quantity of 44 units and a reorder point of 17 units for the shock absorbers, based on the application of economic order quantity and reorder point formulas.
Step-by-step explanation:
To determine the optimal order quantity (Q) and the reorder point (R) for the Toyota dealer using a continuous review system (also known as Q system), we need to apply inventory management formulas.
Based on the given information, we have a demand of four units per month, a standard deviation of demand of four units per month, and a replenishment lead time of two months.
Given a carrying charge of 30 percent per year (0.30) and a cost per unit of $25, the annual holding cost per unit (H) is $25 × 0.30 = $7.50. The ordering cost (S) is $15 per order.
To calculate the economic order quantity (EOQ), we use the formula:
EOQ = √((2DS)/H)
where D is the annual demand. Since our monthly demand is 4 units, the annual demand D = 4 units/month * 12 months/year = 48 units/year. Plugging in the values:
EOQ = √((2×48×15)/7.5) = √(1920) ≈ 43.84
Since we cannot order a fraction of a unit, we'll round the EOQ to 44 units.
For the reorder point (R), which is the inventory level at which an order should be placed, we use the formula:
R = dL + Zσ√L
where d is the average demand rate per period, L is the lead time, Z is the Z-score corresponding to the desired service level, and σ is the standard deviation of demand. Given our service level of 95%, the Z-score for a normally distributed variable is approximately 1.645. The monthly standard deviation is given as 4, so the standard deviation of demand during the lead time is σ√L = 4× √2 = 5.66. Plugging in the values:
R = 4×2 + 1.645×5.66 ≈ 8 + 9.31 = 17.31
Again, rounding to the nearest whole number, we get an R of 17 units.
Therefore, the Toyota dealer should use an order quantity of 44 units and a reorder point of 17 units if a continuous review system is employed.