A scheduling model of logistics service supply chain based on the time windows of the FLSP’s operation and customer requirement

Abstract

In the scheduling problem of logistics service supply chain (LSSC), the uncertainties of the functional logistics service provider’s (FLSP’s) operation time and customer requirement time will directly influence the logistics service integrator’s (LSI’s) time scheduling plan. In this paper, we explored the influences of time windows of the FLSP’s operation and customer requirement on the scheduling decision. A multi-objective programming model of the LSSC time scheduling is established, aiming to minimize total order operation cost of the LSSC, minimize the difference between the total expected operation time and customer requirement time, and maximize the satisfaction of functional logistics service providers. To simplify the model solution, this multi-objective model is changed into a single-objective model with ideal point method. In the following numerical analysis for a specific example, genetic algorithm is applied. The influences of some relevant parameters on the scheduling performance are discussed. Firstly, with the increases of FLSPs’ operation time range and the postponement proportionality coefficient of customer requirement time, the optimal scheduling performance of LSSC will increase and then tend to be stable. Secondly, the customer requirement time could not be compressed too much and have a minimum in order to obtain a feasible solution. Thirdly, the time windows of the FLSP’s operation and customer requirement have significant interactions. The time window of customer requirement will expand with the increase of the time window of the FLSP’s operation.

Appendix: Integration deployment process of objective \(Z_1 \)

(1) When $T_i^{\exp } <a_i$ or $T_i^{\exp } >b_i ,f_{2i} = T_i^{ext} \times C_i^{ext} =| {E( {t_i } )-T_i^{\exp } } |\times C_i^{ext} =C_i^{ext} | {\frac{a_i +b_i }{2}-T_i^{\exp } } |, f_{3i} =T_i^{ext} \times P_i =| {E( {t_i } )-t_i } |\times P_i =\frac{P_i (b_i -a_i )}{4}$.

(2) When $a_i \le T_i^{\exp } \le b_i , f_{2i} =0, f_{3i} =T_i^{ext} \times P_i =| {T_i^{\exp } -t_i } |\times P_i =\frac{( {T_i^{\exp } -a_i } )^{2}}{2}\times \frac{P_i }{b_i -a_i }+\frac{( {b_i -T_i^{\exp } } )^{2}}{2}\times \frac{P_i }{b_i -a_i}$.

Similarly,

(1) When $T_{ij}^{\exp } <a_{ij}$ or $T_{ij}^{\exp } > b_{ij} ,f_{5i} = T_{ij}^{ext} \times C_{ij}^{ext} =| {E( {t_{ij}})-T_{ij}^{\exp } } |\times C_{ij}^{ext} =C_{ij}^{ext} | {\frac{a_{ij} +b_{ij} }{2}-T_{ij}^{\exp } } |, f_{6i} =T_{ij}^{ext} \times P_{ij} =| {E( {t_{ij} } )-t_{ij} } |\times P_{ij} =\frac{P_{ij} (b_{ij} -a_{ij} )}{4}$.

(2) When $a_{ij} \le T_{ij}^{\exp } \le b_{ij} , f_{5i} =0, f_{6i} = T_{ij}^{ext} \times P_{ij} = | {T_{ij}^{\exp } -t_{ij} } |\times P_{ij} = \frac{( {T_{ij}^{\exp } -a_{ij} } )^{2}}{2}\times \frac{P_{ij} }{b_{ij} -a_{ij} }+ \frac{( {b_{ij} -T_{ij}^{\exp } } )^{2}}{2}\times \frac{P_{ij} }{b_{ij} -a_{ij}}$.