A DSS based on optimizer tools and MTS meta-heuristic for the Warehousing Problem with Conflicts

Highlights

• Supporting conflicts in the warehousing problem.

• Modeling the warehousing problem as a bin packing problem.

• Solving the warehousing problem using a multi-start tabu-search metaheuristic.

• Comparing the proposed heuristic to the stade-of-the-art ones.

Abstract

In this paper, we propose a new global warehousing problem supporting advance conflicts: the Warehousing Problem with Conflict (WPC). A predefined number of items, with different weights, are to be loaded into a set of identical warehouses with fixed capacity. The main goal of the WPC is to minimize the overall used number of warehouses under the incompatibility constraint of some pairs of items. We model this optimization problem as a Bin Packing Problem with Conflict (BPPC). As the complexity of the BPPC is NP-Hard, a Multi-start Tabu Search (MTS) is proposed as a solution approach. We also propose a Decision Support System (DSS) based on multi-start the MTS algorithm that performs advanced features in order to well approximate optimal solutions. A comparison to a state-of-the-art approaches is performed and results, with wide variety of instances, showed that the MTS produces considerably better results than the various existing approaches to the detriment of the gap values.

Introduction

The BPP is one of the basic problems in combinatorial optimization that can be classified in the category of $\mathcal{NP}$-hard problems ( David et al., 1974 [1]). The hardness of the BPP is derived from its objective of assigning a set of items into a minimum number of available bins [2]. Such problems are extensively studied in various contexts as the industrial and logistic areas [3].

The basic version of the BPP can be defined as follows: given a set of items and a set of identical bins with fixed capacities, each item is characterized by its weight. The main objective of the BPP is to minimize the number of operated bins for the storage of the whole set of items.

As discussed in Krichen and Ben Jouida (2015) [4], many variations of the BPP can be pointed out as the variable size bin packing problem where items must be packed within a set of heterogeneous bins characterized by possibly different volumes and fixed costs. Also, the bin packing problem with conflict (BPPC) [5], [6] is considered as a challenging extension of the BPP that assumes the possibility of conflicts that might occur between pairs of items [7]. Such conflicts arise in many real-world applications, such as examination scheduling [8], parallel computing and database storage [9], product delivery [10] and resource clustering in highly distributed parallel computing [11].

As it is the case, the BPPC, has a potential effect in various areas, especially for the warehousing problem in the supply chain management (SCM) [12]. In fact, the warehousing problem, a strategic activity in the SC, that consists in finding the best storage configuration in the available warehouses and the allocation of customers' orders to be delivered from the different warehouses. This challenging activity in the SC, once optimized, can offer cost saving solutions [3]. A warehousing variant of great relevance in the SC takes into account the possibility of incompatibilities between items by avoiding joint packing of such items the same warehouse [13].

In this paper, we show the ability of the BPPC concept to handle the Warehousing Problem with Conflict (WPC) where conflicts can be assumed in the storage of items. As such, the set of bins in the BPPC represent the set of warehouses in the WPC. The main objective of the WPC is to minimize the number of warehouses while avoiding joint storage of items in conflict. Such problems handle chemical and pharmaceuticals storage instead stocking.

Since the WPC is $\mathcal{NP}$-hard, numerous approximate methods were developed and compared to achieve concurrential solution quality [8], [14]. As it is the case, our incentive in this paper is to develop a Multi-start Tabu Search (MTS) that performs advanced features in order to well approximate the optimal solution that reports, in our case, the number of used bins. A Decision Support System (DSS), for the WPC, is also developed to solve the storage problems. The proposed DSS often present in storage applications. In fact, optimization tools used in the resolution step can either be accomplished by CPLEX or MTS, depending on the problem size. In fact, extensive computational experiments across a variety of problem sizes and different storage ratios are reported. A comparison to a state-of-the-art approach is performed to check the validity of the proposed MTS algorithm. The obtained results show that the MTS algorithm is computationally effective in generating optimal storage solutions.

This paper is structured as follows: The WPC is described and stated mathematically in Section 2. Section 3 describes the DSS and details the MTS algorithm for the WPC. Experimental results and computational study are reported in section 4 in order to provide the efficiency of our proposed algorithm.