In two-stage warehouse location problem, goods are moved from plants to warehouses at stage-1 (which are larger sized warehouses), and from there to warehouses at stage-2 (which are smaller sized warehouses);and final...In two-stage warehouse location problem, goods are moved from plants to warehouses at stage-1 (which are larger sized warehouses), and from there to warehouses at stage-2 (which are smaller sized warehouses);and finally to the markets. We aim to minimize the sum of location costs of the warehouses at stage-1 and stage-2;plus the total distribution cost of goods to the markets. In this paper two-stage capacitated warehouse location problem (TSCWLP) is vertically decomposed into the smaller problems, which is attained by relaxing the associated flow balance constraints. This leads to three different versions of Capacitated Plant Location Problem (CPLP) referred as RHS_CPLP, MID_CPLP and LHS_CPLP (Verma and Sharma REF _Ref387068711 \r \h [1]). In this paper MID_CPLP is reduced to RHS_CPLP and a single constraint 0-1 Knapsack problem by relaxing a difficult constraint. Interesting results and conjectures are given. Later two more valid constraints are added to MID_CPLP which are relaxed further to get additional results.展开更多
In the past, researchers have applied Bender’s decomposition to distribution problem and used feasibility constraint to speed up the performance of Bender’s decomposition. Further, the application of Branch and Boun...In the past, researchers have applied Bender’s decomposition to distribution problem and used feasibility constraint to speed up the performance of Bender’s decomposition. Further, the application of Branch and Bound to single-stage multi-commodity single-period warehouse location problem (SSMCSPWLP) with strong constraints has shown that they are more effective. It was also shown in the previous research (in the context of Branch and Bound Methodology) that hybrid formulation for the single-stage single-period multi-commodity warehouse location problem yielded superior results. In this paper we apply Benders’ decomposition to strong and weak formulations of single-stage multi-commodity multi-period warehouse location problem (SSMCMPWLP). As suggested in the previous literature we put feasibility constraints in the pure integer sub- problem to speed up the performance of Benders’ decomposition. We also develop an additional cut (constraint that is again added to pure integer sub-problem) and show that it further speeded up Benders’ Decomposition. This research led to the possibility of applying Benders’ Decomposition to the hybrid formulation of SSMCMPWLP in future.展开更多
文摘In two-stage warehouse location problem, goods are moved from plants to warehouses at stage-1 (which are larger sized warehouses), and from there to warehouses at stage-2 (which are smaller sized warehouses);and finally to the markets. We aim to minimize the sum of location costs of the warehouses at stage-1 and stage-2;plus the total distribution cost of goods to the markets. In this paper two-stage capacitated warehouse location problem (TSCWLP) is vertically decomposed into the smaller problems, which is attained by relaxing the associated flow balance constraints. This leads to three different versions of Capacitated Plant Location Problem (CPLP) referred as RHS_CPLP, MID_CPLP and LHS_CPLP (Verma and Sharma REF _Ref387068711 \r \h [1]). In this paper MID_CPLP is reduced to RHS_CPLP and a single constraint 0-1 Knapsack problem by relaxing a difficult constraint. Interesting results and conjectures are given. Later two more valid constraints are added to MID_CPLP which are relaxed further to get additional results.
文摘In the past, researchers have applied Bender’s decomposition to distribution problem and used feasibility constraint to speed up the performance of Bender’s decomposition. Further, the application of Branch and Bound to single-stage multi-commodity single-period warehouse location problem (SSMCSPWLP) with strong constraints has shown that they are more effective. It was also shown in the previous research (in the context of Branch and Bound Methodology) that hybrid formulation for the single-stage single-period multi-commodity warehouse location problem yielded superior results. In this paper we apply Benders’ decomposition to strong and weak formulations of single-stage multi-commodity multi-period warehouse location problem (SSMCMPWLP). As suggested in the previous literature we put feasibility constraints in the pure integer sub- problem to speed up the performance of Benders’ decomposition. We also develop an additional cut (constraint that is again added to pure integer sub-problem) and show that it further speeded up Benders’ Decomposition. This research led to the possibility of applying Benders’ Decomposition to the hybrid formulation of SSMCMPWLP in future.
