Baggage Carousel Assignment at Airports: Model and Case Study

Abstract

Baggage operations at an airport are split into several different sub problems. The problem of assigning baggage carousels to each arriving flight is part of the important passenger arrival process. This article presents a mixed integer formulation for the underlying decision problem which aims at balancing customer satisfaction with operational needs. We introduce a static model that fulfills the different real-world requirements and balances the different objective criteria. It is shown how the model can be used in the dynamic environment of an airport. Because of the high degree of uncertainty at an airport, the issue of stability is discussed in detail. In a case study several scenarios with different time horizons and times of decision were studied. The model was verified with data from Frankfurt Airport and is successfully running as part of the decision support system at Frankfurt Airport.

Appendices

Appendix 1. Notation

All parameters and variables are defined in the main text, but for ease of reference, an overview is given in Tables 6, 7, and 8.

Table 6 List of indices and sets

Table 7 List of parameters

Table 8 List of variables

Appendix 2. Complete Model

For the sake of completeness we here present the complete model as described in the paper:

$$ \begin{array}{@{}rcl@{}} &\min& \underset{a\in{A}_, c\in{C}}{\sum} n_{c} \cdot w_{c} \cdot o_{a,c} \cdot x_{a} + \underset{s\in{S}}{\sum} w_{s} \underset{r\in{R_{s}}, t\in{T}}{\sum} y_{r, t}+ w^{BH} \underset{h\in{H}}{\sum} y_{h}^{BH} \\&&+ w^{BC} \underset{h\in{H}}{\sum} {y}_{h}^{BC} \end{array} $$

(15)

$$ \begin{array}{@{}rcl@{}} &\text{s.t.}& \underset{a\in A_{f}}{\sum} x_{a} = 1 \forall{f\in{F}} \end{array} $$

(16)

$$ \begin{array}{@{}rcl@{}} &&\underset{a\in{A}}{\sum} u_{a, r, t} \cdot x_{a} \leq CAP_{r,t} + y_{r, t} \quad \forall{r\in{R_{s}}}, \forall{t\in{T}} \end{array} $$

(17)

$$ \begin{array}{@{}rcl@{}} &&y^{BH,mean} = \frac{{\sum}_{a\in{A}, h\in{H}, t\in{T}} u_{a, h, t} \cdot x_{a} }{{\sum}_{h\in{H}, t\in{T}}CAP_{h,t}} \end{array} $$

(18)

$$ \begin{array}{@{}rcl@{}} &&y^{BH,mean} + {y}_{h}^{BH,+} - {y}_{h}^{BH,-} = \frac{{\sum}_{a\in{A}, {t\in{T}}} u_{a, h, t} \cdot x_{a} } {{\sum}_{{t\in{T}}} CAP_{h,t}} \quad \forall{h\in{H}} \end{array} $$

(19)

$$ \begin{array}{@{}rcl@{}} &&{y}_{h}^{BH} = {y}_{h}^{BH,+} + {y}_{h}^{BH,-} \quad \forall{h\in{H}} \end{array} $$

(20)

$$ \begin{array}{@{}rcl@{}} &&{y}_{h}^{BC,max} \geq \frac{{\sum}_{a\in{A}, t\in{T}} u_{a, b, t} \cdot x_{a}}{{\sum}_{t\in{T}} CAP_{b, t}}\quad \forall{h\in{H}}, {b\in{B_{h}}} \end{array} $$

(21)

$$ \begin{array}{@{}rcl@{}} &&{y}_{h}^{BC,min} \leq \frac{{\sum}_{a\in{A}, t\in{T}} u_{a, b, t} \cdot x_{a}}{{\sum}_{t\in{T}} CAP_{b, t}} \quad \forall{h\in{H}}, {b\in{B_{h}}} \end{array} $$

(22)

$$ \begin{array}{@{}rcl@{}} &&{y}_{h}^{BC} = {y}_{h}^{BC,max} - {y}_{h}^{BC,min} \forall{h\in{H}} \end{array} $$

(23)

$$ \begin{array}{@{}rcl@{}} &&\underset{a\in{A}}{\sum} u_{a, b, t, bl} \cdot x_{a} \leq 1 + y_{b, t, bl} \quad \forall{h\in{H}},{b\in{B_{h}}}, {t\in{T}}, {bl\in{Bl}} \end{array} $$

(24)

$$ \begin{array}{@{}rcl@{}} &&y^{BH,mean} \geq 0 \end{array} $$

(25)

$$ \begin{array}{@{}rcl@{}} &&{y}_{h}^{BH} \geq 0, \quad {y}_{h}^{BH,+} \geq 0, \quad {y}_{h}^{BH,-} \geq 0 \quad \forall{h\in{H}} \end{array} $$

(26)

$$ \begin{array}{@{}rcl@{}} &&{y}_{h}^{BC} \geq 0, \quad {y}_{h}^{BC,max} \geq 0, \quad {y}_{h}^{BC,min} \geq 0 \quad \forall{h\in{H}} \end{array} $$

(27)

$$ \begin{array}{@{}rcl@{}} &&x_{a}\in{\{0,1\}} \quad \forall{a\in{A}} \end{array} $$

(28)