A Multifactory Integrated Production and Distribution Scheduling Problem with Parallel Machines and Immediate Shipments Solved by Improved Whale Optimization Algorithm
Table 1
Definition of sets, indexes, parameters, and variables.
Sets
Definition
Set of customers
Set of orders
Order set for customer
Set of factories
Machine set for factory
Indexes
Definition
,
Order indexes
,
Customer indexes
Factory index
Machine index
Parameters
Definition
Number of orders/batches/factories/machines
The size for order of customer
The due date for order of customer
Late delivery cost for each unit of order of customer
Processing time for order of customer at factory
Distance between customer and factory
Mean vehicle speed in a unit of distance
Transportation cost for order of customer per unit of distance
Production cost for order of customer at factory
Decision variables
Definition
1 if the order of customer is processed at factory on machine ; 0 otherwise
1 if the order of customer is processed before the order of customer at factory on machine ; 0 otherwise
1 if the order of customer is scheduled as the first job at factory on machine ; 0 otherwise
1 if the order of customer is processed as the last job at factory on machine ; 0 otherwise
1 if the order of customer is the first job delivered from factory ; 0 otherwise
1 if the order of customer is the last job delivered from factory ; 0 otherwise
1 if the order of customer is delivered before the order of customer at factory ; 0 otherwise
Nonnegative variables for production start time of order of customer
Nonnegative variables for transportation start time of order of customer
Intermediate variables
Definition
Nonnegative variables for production completion time of the order of customer
Nonnegative variables for traveling time of the order of customer
Nonnegative variables for delivering time of the order of customer
Maximum of production completion time and vehicle available time to transport order of customer when it is transported immediately after order of customer
