†*** *** *** ****
*
**
***
****
(2000 2 9 , 2000 11 10 )
Optimal Scheduling of Quality Controlled Product Storage
Gyeongbeom Yi†, Dongil Sin*, Ho-Kyung Lee**, Bom Sock Lee***, Jin-Kuk Ha**** and Euy Soo Lee****
Dept. of Chem. Eng., Pukyong National Univ., Pusan 608-739, Korea
*School of Chem. Eng., Seoul National Univ., Seoul 151-742, Korea
**Automation Research Center, Dept. of Chem. Eng., POSTECH, Pohang 790-784, Korea
***Dept. of Chem. Eng., Kyunghee Univ., Yongin 449-701, Korea
****Dept. of Chem. Eng., Dongguk Univ., Seoul 100-715, Korea (Received 9 February 2000; accepted 10 November 2000)
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Abstract−The mixed integer linear programming model has been developed for the production scheduling of liquid state polymer process such as a Polybutene(PB). The example process is composed of one reactor, twelve storage tanks and two package types. The reactor produces 9 liquid state products. The products are reserved in tanks and then, packaged into drum or isocontainer. The drum products are stored in a warehouse before they are shipped out to customers but the isocontainer prod- ucts are shipped directly out to customers. Two major products use multiple tanks. Most tanks are dedicated to a certain prod- uct but basically any tank can be shared by any product. The reactor is operated on block mode. The unique characteristic of this scheduling problem exists on the fact that the product in a tank should be locked for 3-15 days in order to check the quality specifications after run-down from the reactor. The primary objective of scheduling is reducing the number of quality checking processes because it causes great loss in production time and tank utilization. The model is composed of about 1,500-2000 inte- ger variables. The branching priorities are adjusted according to the importance of variables based on current manual sched- uling practice and it greatly enhanced the convergence of the mixed integer model.
Key words: Optimal Scheduling Quality Storage Block
†E-mail: [email protected]
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no.
Number of equations
Number of variables
Number of binary variables
CPU time (sec)
1 17880 7856 2202 1432
2 13280 5009 1526 2932
3 12416 5848 1999 5465
4 12130 5451 1725 4322
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i : index for reactor products p : index for packaged products k : index for tanks
t : index for time periods
BLpt : the backlogging quantity of packaged product p at the end of period t
CAPt : is the drumming capacity of period t
Dpt : the customer demand of packaged product p at period t DRUM(i) : the subset of reactor products with drum package FIikt : the inventory hold-up of product i in tank k at the end of period t FHikt : the discharge quantity of product i from tank k at period t FQikt : the quantity of product i moved from reactor into the tank
k at t period
ISOCON(i) : the subset of reactor products with isocontainer LAG(i) : is the quality checking period for product i LAG(p) : the time delay for drumming
NTC(i, i') : the set of pairs of reactor products that can not be produced in sequence
PACK(i, p) : the connection between reactor product and package product PQpt : the drumming quantity of packaged product p at period t RXMAX : maximum daily production rate of reactor
RXMIN : minimum daily production rate of reactor
SHpt : the shipping quantity of packaged product p at period t TKMXik : the maximum storage size of tank k for product i wδ,..., wBL : the weighting factors for infeasibility of relevant constraints Yit : is set to 1 if product i is produced in reactor at t period,
otherwise 0
YFIikt : is set to 1 if FIikt is positive, otherwise 0 YFHikt : YFHikt is set to 1 if FHikt is positive, otherwise 0 YFQikt : is set to 1 if FQikt is positive, otherwise 0
YSikt : is set to 1 if product i is continuously fed from reactor to tank k at period t and period t+1, otherwise it is set to 0 YHFit : is set to 1 if product i is packaged into drum at period t,
otherwise 0
δ, γ : the infeasibility of the relevant constraints
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