(i) For the next eight week period, a supplier will deliver orders of the same quantity every Monday morning. The customer's daily demand will be constant at 200 units over this period and there is no initial inventory. Plan what the order quantity should be such that the fill rate is 100% and the average inventory is minimized. For this and all the questions to follow, the weekly average inventory formula is
= MAX(0,IF(end.inv. = 0,(beg.inv.+end.inv.)/2,(beg.inv.)2/(2×(beg.inv.+end.inv.)) (ii) Same questions as in (i), but now the supplier delivers orders every Monday and Friday morning, and the order quantity is the same on both days for the entire period.
(iii) Orders are delivered by trucks with capacity of 1200 units. One truck delivery costs $800 irrespective of the load. Alternatively, units can be shipped by courier at a cost of $2 each. A combination of the two types of delivery is also acceptable. Average inventory comes at a cost of $3 per average unit held in storage for the entire period. The fill rate is kept at 100%. Should the customer receive deliveries on Monday, or on Monday and Friday? Should the $3 increase or decrease for the two options to become indifferent? Why?
(iv) The supplier starts the eight-week period again with an initial inventory of 200 units, and receives orders of 1350 units every Monday and Friday morning. The daily demand is still constant at 400 units. The holding and transportation costs are still identical. Units are sold to the customer's customers at $100 apiece. Compare the profits of the following two models. In the first, stockouts result in a lost sales. In the second, stockouts result in backlogs, each with a penalty cost for the customer of $10.
Can you also provide me with explanations as to how you arrive at the answers. Thank you!