Abstract
Most classical scheduling models assume a job is delivered to a customer immediately after job processing is complete. In numerous practical situations, however, multiple delivery dates exist, and the time interval between any two consecutive delivery dates is constant. A finished job is supplied to a customer by truck on the earliest date in a series of fixed delivery dates, typically at or after processing is complete. This fixed delivery strategy results in substantial cost savings when delivery is expensive or complex. The goal of this study is to minimize the sum of due-date cost and earliness penalty associated with jobs scheduling in a dynamic job shop environment. The due date cost for a job is incurred for time spent delivering a job to a customer. Earliness penalty is incurred if a job is completed before the delivery date. This study identifies three dispatching rules, and proposes nine new rules by explicitly considering different due date costs per time unit and the earliness penalty per time unit of a job. The proposed rules are simple and easily implemented without preliminary runs for parameter estimation. Simulation results show that the proposed dispatching rules are significantly superior to their counterparts.
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Abbreviations
- J :
-
Set of jobs, \( J = \left\{ {J_{1} ,\;J_{2} ,\; \ldots ,\;J_{n} } \right\} \)
- M :
-
Set of machines, \( M = \left\{ {M_{1} ,\;M_{2} ,\; \ldots ,\;M_{m} } \right\} \)
- \( N_{i} \) :
-
Number of operations in job i
- \( A_{i} \) :
-
Arrival time of job i
- \( P_{ij} \) :
-
Processing time for operation j of job i
- τ :
-
Length of each delivery interval
- \( C_{i} \) :
-
Completion time of job i
- α :
-
Due date cost per unit time of job i
- β :
-
Earliness penalty per unit time of job i
- \( TC_{i} \) :
-
Total cost of job i
- \( C_{i,j - 1} \) :
-
Completion time of the previous operation (i.e., operation j − 1) of job i
- \( RP_{ij} \) :
-
Remaining processing time required to complete job i after operation j
- \( T_{now} \) :
-
Time instant at which dispatching decision is made
- \( Z_{i} \) :
-
Priority index of job i at instant T now
- λ :
-
Number of completed deliveries
- R :
-
A ratio of the achieved rate to the next delivery date
- \( G_{1} \) :
-
Set of jobs whose current operation is the final operation
- \( G_{2} \) :
-
Set of jobs whose current operation is not the final operation
- \( P_{ij}^{(1)} \) :
-
Processing time of operation j of the first job in Set G 1
References
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Liu, CH., Hsu, CI. Dynamic job shop scheduling with fixed interval deliveries. Prod. Eng. Res. Devel. 9, 377–391 (2015). https://doi.org/10.1007/s11740-015-0605-z
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DOI: https://doi.org/10.1007/s11740-015-0605-z