Simulation optimization iteration approach on traffic integrated yard allocation problem in transshipment terminals

Abstract

To improve the efficiency of the container terminals, we propose a simulation optimization iteration approach to integrate the yard allocation problem (YAP) with the vehicle congestion problem. YAP is formulated as a mixed integer programming model to reduce the total job travel time. A discrete event simulation model is developed to simulate the terminal operation and traffic movement within the terminal. The approach solves two models iteratively to improve the allocation decisions. Experiment results show that this approach can effectively generate yard allocation decisions, which reduce the overall traffic time comparing with traditional intuitive rules.

Appendices

Appendix 1: YAP with high-low workload protocol constraints

1.1 Additional parameter

$H_{b}$ :

The threshold of high-low workload for sub-block $b$

1.2 Additional decision variable

$\beta_{bt}$ :

Binary variable, $\beta_{bt} = 1$ indicates that the sub-block $b$ is high in loading or unloading workload at shift t, $t = 1 \ldots T$

$${\text{Objective}}:\quad \quad \quad \quad \quad \hbox{min} \;\;\;\sum\limits_{{n \in {\mathbf{N}}}} {\sum\limits_{{b \in {\mathbf{B}}}} {\alpha_{nb} d_{nb} W_{nb} } }$$

(16)

Subject to:

Constraint (3) to (11)

$$\beta_{b,t} + \sum\limits_{{a \in {\mathbf{A}}_{b} }}^{{}} {\beta_{a,t} } \le 1,\;\;\;\;\;b \in {\mathbf{B}},t \in {\mathbf{T}}$$

(17)

$$M \cdot \beta_{{b,t_{n}^{d} }} \ge W_{nb}^{{}} - H_{b} ,\;\;\;\;\;n \in {\mathbf{N}},b \in {\mathbf{B}}$$

(18)

$$M \cdot \beta_{{b,t_{n}^{l} }} \ge W_{nb}^{{}} - H_{b} ,\;\;\;\;\;n \in {\mathbf{N}},b \in {\mathbf{B}}$$

(19)

Constraint (17) ensures that high unloading workload cannot be allocated to two sub-blocks that are neighbors of each other in the same shift. Constraint (18) and (19) define low and high handling capacity boundary of each sub-block.

Appendix 2: YAP with penalty on high workload

2.1 Additional parameter

$H_{b}$ :

The threshold of high workload for sub-block $b$

$\lambda$ :

The penalty time added to travel time, if the high workload is achieved

Additional decision variable

$\beta_{bt}$ :

Binary variable, $\beta_{bt} = 1$ indicates that the sub-block $b$ is high in loading or unloading workload at shift t, $t = 1 \ldots T$

$${\text{Objective}}:\quad \quad \quad \quad \hbox{min} \;\;\;\sum\limits_{{n \in {\mathbf{N}}}} {\sum\limits_{{b \in {\mathbf{B}}}} {\left( {\alpha_{nb} d_{nb} W_{nb} + \sum\limits_{{t \in \left\{ {t_{n}^{d} ,t_{n}^{l} } \right\}}} {\lambda \cdot \beta_{bt} } } \right)} }$$

(20)

Subject to:

Constraint (3) to (11)

$$M \cdot \beta_{{b,t_{n}^{d} }} \ge W_{nb}^{{}} - H_{b} ,\;\;\;\;\;n \in {\mathbf{N}},b \in {\mathbf{B}}$$

(21)

$$M \cdot \beta_{{b,t_{n}^{l} }} \ge W_{nb}^{{}} - H_{b} ,\;\;\;\;\;n \in {\mathbf{N}},b \in {\mathbf{B}}$$

(22)

Objective function (20) represents that a penalty time (delay caused by congestion) will be added to the job if the sub-block is under high workload condition. Constraint (21) and (22) define the condition of high workload in each sub-block.