SUPPLY CHAIN MANAGEMENT

                         FIRST TEST

                      September 29, 2000

Attempt all questions. Duration of the Test is 80 minutes. Maximum
marks:15. The first question carries 3 points and the other questions
carry 4 points each.


1. Consider the following two stage factory-distribution network:

          ---------       --------
          |       |       |      |====>>
          |FACTORY|====>> | DIST |====>> CUSTOMERS 
          |       |       |      |====>>
          ---------       --------

   Assume the manufacturing lead time, X1, in the factory to be normally
   distributed with parameters (mu1, sigma1). The delivery time, X2, from
   the factory warehouse to the distributor is normally distributed
   with (mu2, sigma2). The delivery from the distributor to the 
   customers is instantaneous. The system works in a make-to-order
   mode. As a result, the order-to-delivery time, Y, is given by
   X1 + X2. Assume the following nominals and tolerances for the 
   processes:

                     Nominals (taui)       Tolerances (Ti)

             X1         20 days             3   days
             X2         5  days             1.5 days

   (a) If X1 and X2 are three sigma processes,  what are the lower 
       and upper limits for which the ODP is six sigma?
 
   (b) Assume the limits (20, 30) for the ODP. With respect to this,
       is it possible to substantiate the following statements:

       (i)   Y can be six sigma even if neither X1 nor X2 is six sigma
       (ii)  Y can be three sigma even if X1 and X2 are both six sigma
        

2. A make-to-order supply chain has customer orders arriving in Poisson
   fashion at the rate of 90 orders per day. Raw material and subassemblies
   are always on hand. The facility assembles these on receipt of an order
   and the customers receive them immediately. If the processing time
   is exponentially distributed with rate 96 orders per day (average 
   processing time = 15 minutes), compute the following:

       (a) Probability of at least 10 backorders
       (b) Probability of no backorders
       (c) Standard deviation of lead time for a typical order
       (d) Fraction of orders which have lead time greater than 1 day
       (e) Throughput rate of the system

   

3. In a make-to-stock, two stage supply chain, raw materials arrive at
   the factory in Poisson fashion at the rate of 10 lots per day.
   Each lot is processed in the factory, with an exponential factory
   lead time with rate 20 lots per day. Lots manufactured undergo
   inspection and usually about 10 percent of them return to the factory
   for reworking, with rework times identically distributed as the original
   factory lead times. About 5 percent of the jobs are rejected, while 
   about 85 percent of jobs go the second stage (assembly stage). The
   assembly lead time is exponentially distributed with rate 30 lots per
   day. However, after assembly, about 10 percent of the lots are rejected
   while about 10 percent of jobs come back for fresh reassembly. The
   remaining lots are instantaneously delivered to the customers.
   Create an open Jackson network model of this supply chain and compute

       (a) Average supply chain lead time
       (b) Throughput rate at which lots are delivered by the system
       (c) Average total inventory in the system


4. It is found that in a two week time horizon, the demand during the
   first week is d units whereas during the second week, the demand is
   D units. A setup cost of A is incurred for producing a lot of any size.
   There is an inventory holding cost of h per unit per week on individual
   items. Assume that production happens at the beginning of the week
   in an instantaneous way with a setup cost A. Compare the following three
   strategies of production scheduling:

    (a) Strategy 1: Produce d+D items in a single lot at the beginning 
        of the first week itself
    (b) Strategy 2: Produce d items in one lot at the beginning of the 
        first week and D items in one lot at the beginning of the second week.
    (c) Strategy 3: Produce d + D/2 items at the beginning of the first
        week and D/2 items at the beginning of the second week.

   Which one do you choose, assuming that the demand is deterministic and
   continuous during each week.