# Information Sciences Letters

## Abstract

In this paper, we introduce the multi-period single sourcing problem as an assignment problem. The multi- period single-sourcing problem in this research is seen as a problem of finding assignments, from time to time to obtain the minimum possible total transportation and inventory costs for distributing goods to customers. The case considered in this problem is the case of placing inventory items that are distributed to customers online, so this case is seen as a non-polynomial or NP hard problem that requires a solution algorithm, and the algorithm we offer is a direct search algorithm to solve the problem. multi period single sourcing. The direct search algorithm offered is the Branch and Price algorithm which was developed for Generalized Assignment Problems (GAP) to a much more complete class of problems, called CAP (Convex Assignment Problems). We offer this algorithm because the results it will obtain are more optimal, the computing time is superior, and it shows greater stability, that is, fewer outliers are observed. Specifically, we generalize the strategy of separating nonbasic variables from their constraints, combined with using active constraint methods to solve the Generalized Assignment Problem (GAP) into a Convex Assignment problem. Then, identification of important subclasses of the problem is carried out, which contains many variations of multi- period single sourcing problems, as well as GAP variants. The final result we found is an active depth-based single source multi-period model that can minimize the damage to the optimal integer solution for solving the MPSSP convex problem.

## Recommended Citation

S. Situmorang, A.; Mawengkang, H.; Tulus, T.; and S. Sitompul, O.
(2023)
"Single-Source Multi-Period Problem Model with Active Constraints-Based Approach Algorithm,"
*Information Sciences Letters*: Vol. 12
:
Iss.
10
, PP -.

Available at:
https://digitalcommons.aaru.edu.jo/isl/vol12/iss10/20