Myopic policies

Myopic policies. Consider a dynamic program of the type presented, e.g., in Proposition 8, and define the following myopic policy At the beginning of period t, given a state space value qu Xt), solve the problem... 

The solution to this problem will be the order quantity for that period. In other words, in a myopic policy, we ignore the future consequences (beyond a lead time) of the actions we take today. Recall that in the elementary i.i.d. demand case this is indeed optimal to do. But, as expected, myopic policies may perform poorly if demand patterns fluctuate significantly from one period to another. To illustrate this, suppose that during a peak period the demand... 

In fact, in many papers, the policy (10.14) is specifically confined to myopic order-up-to policies in which the safety-stock parameter 7 is set in a way that minimizes the expected cost at the end of a lead-time. However, this should not necessarily be the correct thing to do. Recall that a myopic order-up-to policy may fail to be optimal if the order-up-to level cannot be reached in almost every period. In such cases, myopic policies may perform poorly, and it would be reasonable to assume that their performance vis-a-vis optimal policies would worsen as Px d — -h Dt- < 0 grows. Thus, it may be beneficial to set the safety stock 7 to a level that is different than that suggested by a myopic policy, while still maintaining the base stock structure (10.14). We start with an illustration of this point, using the following special case ... 

Lovejoy, W.S. 1990. Myopic policies for some inventory models with uncertain demand distributions. Management Set 36 (6) 724-738. 

We note that, at its simplest, the optimization will be on an epoch by epoch basis (the so-called greedy or myopic approach). In this case, the mode is chosen just to optimize for the next epoch and defer consideration of future behavior. A more sophisticated system would look several epochs ahead in applying the measure of effectiveness, though it would also update the scheduling policy on an epoch by epoch basis. Such an approach is, a priori, very computer intensive, and much work is needed to develop shortcuts to calculation of the optimal policy. Sometimes it may be appropriate to choose to measure the effectiveness of a policy only at the last epoch of application of that policy. 

If this U.S. policy seems extreme, so are its philosophical underpinnings, as laid out in Earth in the Balance. The apocalyptic central thesis of Mr. Gore s book is that we need to take bold and unequivocal action. .. [to] make the rescue of the environment the central organizing principle for civilization. The events of September 11,2001, and the ensuing efforts against international terrorism illustrate how unspeakably myopic and self-absorbed was this view of the civilization s appropriate priorities. 

A slightly different approach to the justification of myopic order-up-to policies was taken by Lee et al. (2000) and most recently by Dong and Lee (2001) Consider a base-stock policy and let + 7 be the myopic target level... 

When a myopic base-stock policy is applied to this case, the target level... 

The second possible reason for why a myopic order-up-to policy may not work well is because of potential supply delays beyond the nominal lead-time L, that may occur due to shortages at the supplier. In order to design our inventory policies to cope with potential supply delays, we propose an upward... 

Johnson, G., H. Thompson. 1975. Optimality of myopic inventory policies for certain dependent demand processes. Management Sci. 21 1303-1307. 

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