Fundamentals of Supply Chain Theory, 2nd Edition

Appendix A Multiple‐Chapter Problems

PROBLEMS

1. A.1 (Worst‐Case Bound for Deterministic Newsvendor Approximation) As noted in Section 5.3.2, the papers by Zheng (1992) and Axsäter (1996) suggest bounds on the error that results from approximating a stochastic inventory model (the model of Section 5.1, for which an policy is optimal) by a deterministic one. Suppose we do the same thing for the newsvendor model, setting S equal to the optimal solution to the deterministic problem, i.e., . Assume the demand is distributed .
   1. Prove that
      

      where is the expected newsvendor cost if S is the order‐up‐to level and .

   2. Is it possible to identify a fixed worst‐case bound that holds for any values of the parameters , and ? Explain your answer.
2. A.2 (Optimizing Compost Inventory)