The Norwitch Company uses a continuous review (s, Q) system for inventory control.  Weekly demand for an item, Pressure Valve #5 (PV5), is distributed Normally with a mean and standard deviation of 20 and 10 respectively.  Norwitch uses an order quantity of 200 units for PV5 and its supplier takes 5 weeks to fill an order.  Each unit of PV5 costs $50 and carrying charges are $0.20/$/yr.  Norwitch uses a 99% fill rate as a target service measure.

(a) find out the reorder point, s, that would satisfy Norwitch's target fill rate.  What is the likelihood that Norwitch has stocked out of PV5 when a new shipment arrives from its supplier?

(b) Assume Norwitch has worked out a new contract, accepted by all its customers, of being allowed up to one week to satisfy every demand.  Norwitch still uses a 99% "fill rate" as a target service measure.  Though, stockouts satisfied within a week is considered as good as demand satisfied from on-hand inventory.

How will you modify logic of computing the re-order point, s, to take account of the one-week grace period?  Sketch the average behavior of the (s,Q) system to show your reasoning.

(c) find out the reorder point for the new contract.  What is the safety stock?  On an average, how much inventory Norwitch has on hand when new shipment of PV5 arrives?  

(d) find out approximately the annual cost savings due to one-week grace period.

(e) What would be the impact of one-week grace period on Norwitch's customers? Should Norwitch and its customers make the inventory status of PV5 known to each other?   What good would that do?

Bookstore buys a popular freshman physics book at $30 each and sells it to students at $50 each.  The same book is used for Fall and Winter terms.  Demand for books is distributed normally with a mean of 150 and 200 for Fall and Winter terms, respectively.  Standard deviation of demand is 50, for Fall as well as Winter terms.  The demand for each term can be supposed to be independent.

The publisher comes up with the new edition every year, making old edition of the book worthless.  Bookstore simply throws away any leftover books at the end of the academic year (Winter Term). You have been asked to help the Bookstore in its purchasing decision for Physics books.

(a)  Assume the Bookstore used a newsvendor model to order books for each term.  How many books must they order for Fall term and for the Winter term?

(b) Bill Nye, the new purchasing guy, at the Bookstore thinks one can just use the total demand for the year and make one purchasing decision for the whole year.  How much must he order using this reasoning?  Why this order quantity is different than the sum of order quantities computed separately for Fall and Winter in part (a)?

(c)  What will YOU recommend to the bookstore?  Propose an ordering policy (with numbers, if you can) and describe why this is a better alternative.  Is your policy the best one can do?  Why (not)?
Saki, a local bar, consumes Mehboob, the popular non-alcoholic drink, at a steady rate of 10 cases/week. Saki generally buys Mehboob at $6/case, delivered to its door. However, the supplier is presently offering a promotional price of $5/case.

(a) If the carrying cost for Mehboob is $0.25/$/year, how many cases must Saki buy to take advantage of this promotion? Suppose that present promotion might end any day and that next promotion is unlikely in foreseeable future. Indicate any other assumption(s) which you make for your analysis.

(b) How would your decision in part (a) modify in each of the following cases?

i. If you had reasons to believe that your supplier gives this promotion annually;

ii. If you had reasons to believe that your supplier might give this promotion again sometime between six months to a year from now, equally likely;

iii. To eliminate the ill-effects of forward buying, your supplier permits you to order any quantity you like, but delays the delivery until you actually need it.