Supply Chain Batching Problem with Identical Orders and Lifespan

Abstract EN

In the real world, there are a large number of supply chains that involve the short lifespan products.

In this paper, we consider an integrated production and distribution batch scheduling problem on a single machine for the orders with a short lifespan, because it may be cheaper or faster to process and distribute orders in a batch than to process and distribute them individually.

Assume that the orders have the identical processing time and come from the same location, and the batch setup time is a constant.

The problem is to choose the number of batches and batch sizes to minimize the total delivery time without violating the order lifespan.

We first give a backward dynamic programming algorithm, but it is not an actually polynomial-time algorithm.

Then we propose a constant time partial dynamic programming algorithm by doing further research into the recursion formula in the algorithm.

Further, using the difference characteristics of the optimal value function, a specific calculating formula to solve the problem with the setup time being integer times of the processing time is obtained.