Suppose you are overseeing the purchasing of a certain commodity for the following year. The demand for this item is estimated to be 20,000 units/year, and steady throughout. Every time you process and receive a shipment of this commodity, you incur a cost of $800. Finally, the cost to keep one item in inventory is $3.00 annually.

Ordinarily, cost per unit is $18. However, if you purchase 10,000 or more in a delivered lot, the cost drops to $17.50 each.

(a.) Determine the optimal quantity of this commodity to be purchased in each lot. (Write down the relevant figures that enable you (and POM-QM) to choose.)

(b.) Consider the lot of 10,000 items (regardless of whether you chose this policy). By how much does the inventory cost of this policy differ from that of the other candidate policy? (Specify the relevant costs.)

(c.) Suppose you could lease, for free, superior forklift equipment that would drop the ordering cost to $100 for each delivered lot. Would this reduction cause you to change your optimal policy? Why or why not (write down the results)? How much money will this save you annually?

(d.) These days, third party logistics (3PL) are all the rage. With 3PL, other firms are subcontracted to carry out some or all of the inventory function. Suppose the supplier offers such a service to you. Their idea is to hold inventory for you; this will reduce both your ordering costs and your holding costs.

Specifically, you still pay for the goods when a lot is purchased but you do not actually stock the items in large quantities. Suppose this convenience reduces the holding cost to $1.50 per item per year (instead of $3). Additionally, your warehouse space, equipment and operators are not tied up because only small quantities are released to you. Suppose, then, that because of this the ordering cost for the small size "releases" is just $5 (instead of $800).

There is a catch to all of the above savings. To provide this service, your supplier will charge you the increased price of $18.50 per item. No quantity discounts apply. (Your demand is still 20,000/year.)

FIND: In this new regime, figure out what the optimal policy is and its associated cost (write them down!). Is this a better deal for your company than the policy in part (a.)?

(e.) Thus far, we have assumed that the demand of 20,000 units/year is steady over time. Now suppose that the demand varies. Specifically, suppose that the lead time (LT) to receive this product is 5 working days (assume 250 working days to the year). This implies that the demand during LT averages 400 units. Additionally, suppose that the standard deviation of demand during LT is 100 units.

FIND: How much safety stock will you need to meet a 99% service level? What will the annual cost of providing this additional stock? [NOTE: please work with the original problem description, NOT the modifications in (c.) and (d.).]