International Journal of Industrial Engineering & Production Research

  In the classical versions of “Best Choice Problem”, the sequence of offers is a random sample from a single known distribution. We present an extension of this problem in which the sequential offers are random variables but from multiple independent distributions. Each distribution function represents a class of investment or offers. Offers appear without any specified order. The objective is to accept the best offer. After observing each offer, the decision maker has to accept or reject it. The rejected offers cannot be recalled again. In this paper, we consider both cases of known and unknown parameters of the distribution function of the class of next offer. Two optimality criteria are considered, maximizing the expected value of the accepted offer or the probability of obtaining the best offer. We develop stochastic dynamic programming models for several possible problems, depending on the assumptions. A monotone case optimal policy for both criteria is proved. We also show that the optimal policy of a mixed sequence is similar to the one in which offers are from a single density .

In any supply chain, distribution planning of products is of great importance to managers. With effective and flexible distribution planning, mangers can increase the efficiency of time, place, and delivery utility of whole supply chain. In this paper, inventory routing problem (IRP) is applied to distribution planning of perishable products in a supply chain. The studied supply chain is composed of two levels a supplier and customers. Customers’ locations are geographically around the supplier location and their demands are uncertain and follow an independent probability distribution functions. The product has pre-determined fixed life and is to be distributed among customers via a fleet of homogenous vehicles. The supplier uses direct routes for delivering products to customers. The objective is to determine when to deliver to each customer, how much to deliver to them, and how to assign them to vehicle and routes. The mentioned problem is formulated and solved using a stochastic dynamic programming approach. Also, a numerical example is given to illustrate the applicability of proposed approach.