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A mathematical programming model and Solution for Scheduling Production Orders in Shanghai Baoshan Iron and Steel Complex 1. Problem description In our project the quantities of the production orders are centralized as Q1: U[100, 500], Q2: U[500,1000], Q3: U[1000, 1500].The steel sheet manufacturing process studied in this paper mainly consists of 34 operations. Those operations and 708 technology routings constructed by them are depicted. The unit of time used in the model is one day. The decision horizon is 90 days. Each production order only involves one product. Only one technology routing is assigned for each production order. Production orders should be allowed to be split, which is helpful to smooth operation workloads over time. Each production order must be completed before its fixed delivery date. Available production capacity of each operation must not be exceeded. Technology routings must be observed. The average duality gaps and running times tables are below. The main task is when each production order on each operation should start processing so that the promised delivery dates for all orders are met and the sum of weighted completion times of all orders is minimized? Average duality gaps (%) Q1:U[100,500] Q2:U[500,1000] Q3:U[1000,1500] Qtotal:U[100,1500] LRp1 1,352407 1,281581 1,194258 1,239393 LRp2 1,352407 1,39092 1,204024 1,276996 LRp3 2,439522 2,119476 1,392493 1,375323 LRp4 2,544115 2,029682 0,916286 0,965775 Average running times (seconds) Q1:U[100,500] Q2:U[500,1000] Q3:U[1000,1500] Qtotal:U[100,1500] LRp1 180,4557 184,9544 261,553 202,1989 LRp2 180,6507 184,6623 239,506 198,3487 LRp3 166,4254 171,4977 237,3244 182,9604 LRp4 166,5109 137,8469 192,3358 133,9383 2. Parameters : 3. Decision variables: dij: the production cycle for production order i on operation j, i.e., the time for one unit slab (or coil) of order i to go through operation j; a graphic representation of di4, the production cycle for production order i on hot rolling, is given in Fig. 5 as an example. Note that ddije stands for the minimal integer larger than or equal to dij; Rjt: available production capacity of operation j during period t; rij: the total amount of the production capacity of operation j needed to complete production order i; lij:the earliest possible starting period of operation j for production order i; it is the earliest possible period that the materials of operation j for production order i is available; uij:the absolute due date of operation j for production order i; the iterative formulae used in this paper to define uij are described as follows. (Suppose j = Q i(k)) Ui,Qi(Ki) = G Ui,Qi(k+1) = Ui,Qi(k+1) – di,Qi(k+1) , k = 1, . . . , Ki – 1. It is obvious that each operation of production order i must be completed before its absolute due date.Otherwise the entire production order will be late.
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