Integrated optimization approach to order allocation and delivery problem of online supermarket

Transcription

1 JOURNAL OF SYSTEMS ENGINEERING Vol.30 No.2 Apr , 2, 1 (1., ; 2., ) :,,,.,,,,. C W,.. : ; ; ; - (LRP); : TP273 : A : (2015) doi: /j.cnki.jse Integrated optimization approach to order allocation and delivery problem of online supermarket Zhang Yuankai 1, Huang Minfang 2, Hu Xiangpei 1 (1. Faculty of Management and Economics, Dalian University of Technology, Dalian , China; 2. School of Economics and Management, North China Electric Power University, Beijing , China) Abstract: From the perspective of integrated optimization, this paper studies order allocation and delivery problems of online supermarket with multiple warehouses in one city. A nonlinear mixed integer programming model with the objective of minimizing the delivery cost is built, and a heuristic algorithm is constructed to solve it. In the heuristic algorithm by introducing the state-space search theory in artificial intelligence and utilizing key influencing factors for delivery cost as the order assignment rules, an improved width-first search method is applied to generate better order allocation scheme set, which greatly reduces the solution space. C W saving algorithm and local search algorithm are used to optimize the delivery schemes and adjust the allocation schemes. Finally, a numerical example is constructed to demonstrate the efficiency of the solution algorithm. Key words: online supermarket; order allocation; delivery; location routing problem (LRP); integrated optimization 1,., NP-hard., : ; : : ( ; ).

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3 2 : 253 n ws O ws ; Q ; F ; T ; c ij i j(i,j V,i j) ; t ij i j(i,j V,i j) ; a os 0 1, o(o O) s(s S),a os = 1, a os = 0., ; b ow 0 1, o(o O) w(w W),b ow = 1, b ow = 0; y k 0 1, k, y k = 1, y k =0; x kij 0 1, k(k K) i j(i,j V,i j), x kij = 1 x kij = 0. Min z = Fy k + k K k K s.t. c ij x kij, (1) i V j V 1 b ow 3, o O, (2) w W b ow = n ws, (3) o O w W w W s S n ws = a os b ow, w W, s S, (4) o O x kij = x kji, j S, k K, (5) i V i S n ws x kij Q, k K, (6) i V j V t ij x kij T, k K, (7) i V j V x kij 1, j S, (8) i V k K x kij 1, k K, j S, (9) i V (1) ; (2), ( ); (3) ; (4) w s ; (5) ; (6) ; (7) ; (8) ; (9).,,. 3,.,

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6 min, 200, 60 km / h., 1. 16, Table 1 Results of numerical case ( ) ( ) R 1 W 4 W 1 S 17 S 2 S 18 S 15 S R 2 W 3 S 16 S 13 S 4 S 5 S 14 S R 3 W 2 S 13 S 16 S 1 S 14 S 5 S R 4 W 2 S 8 S 10 S 11 S 12 S 19 S R 5 W 3 S 6 S 19 S 12 S 11 S 10 S R 6 W 4 W 1 S 12 S 19 S R 7 W 4 W 1 S 11 S 10 S 9 S 3 S R 8 W 1 S 11 S R 9 W 4 W 1 S 1 S 16 S R 10 W 4 S 4 S 5 S 14 S R 11 W 3 S 9 S 7 S 15 S 17 S 2 S R 12 W 1 S 5 S R 13 W 2 S 15 S 7 S 9 S 3 S R 14 W 3 S 20 S R 15 W 1 S 1 S 14 S R 16 W 2 S 18 S 2 S Table 2 Comparison results of 10 cases from Method A and Method B ( ) ( ) ( ) A B % A B % A B % A B % A B % A B % A B % A B % A B % A % B % : = ( B A ) / A 100%,,. 10 ( 1 10), ( A) ( B). 2, 1 10, 8.19% 17.32% ( )..

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