Arrow Manufacturing Ltd$.$ distributes golf clubs. Its annual demand for next year is forecasted at $14,000$ sets at an average cost of $$425$ per set. In reviewing its historical ordering costs for the past $3$ years it noted that costs were $$12,900,$ $$16,400$ and $$20,100$ at order volumes of $20,50$ and $80$ respectively. Arrow is forecasting an increase of $10\%$ in its fixed ordering costs and a $15\%$ increase in its variable ordering costs. The fixed ordering costs relate to allocations of supervisory time, computer time, and warehouse space. In addition to the order processing, the company must receive and inspect the units. Receiving and inspecting activities require $5$ hours per order at a direct labour rate of $$12$ per hour. Variable overhead related to receiving and inspecting activities is applied at a rate of $40\%$ of direct labour dollars.

In reviewing its other activities, Arrow came up with the following estimates for next year:

Annual storage costs

Estimated annual damage$/$loss

Annual inventory

insurance costs

Annual building

$$12\mathrm{.}50$ per set

$$0\mathrm{.}80$ per set

$$1\mathrm{.}50$ per set

Annual building insurance costs

Opportunity cost

$$1\mathrm{.}20$ per set $($allocated based on square metres$)$

$12\%$

The company is closed for two weeks in the summer and again for $2$ weeks over Christmas. This results in $48$ work weeks in the year and the company operates $5$ days per week.

Required:

Determine the Economic Order Quantity $($EQ$)$ for Arrow for next year. What are

a$.$ the total annual inventory costs at the EOQ?

b$.$ Determine the reorder point in units assuming that the lead time is $7$ days.

c$.$ Now assume the company has found a new supplier that is willing to supply on a just$-$in$-$time basis. Inspection and receiving time would be lowered to $1\mathrm{.}5$ hours per order and the annual estimated damage would be cut by $75\%.$ Storage and inventory insurance would drop to $$4\mathrm{.}50$ and $$0\mathrm{.}60$ respectively. The variable ordering cost would drop to $$65$ due to integrated ordering systems. However, the annual cost to purchase the golf sets will increase to $$428.$ Determine the new EOQ. Should the company go with the new supplier or maintain its current arrangements?