Optimization of Transfer Baggage Handling in a Major Transit Airport

Abstract

We consider the handling of baggage from passengers changing aircraft at an airport. The transfer baggage problem is to assign the bags from each arriving aircraft to an infeed area, from where a network of conveyor belts will bring them to the corresponding outbound flight. The main objective is to minimize the number of missed bags, but in order to reach this goal, we introduce some auxiliary objectives that minimize the transportation time of bags, while ensuring robustness and avoiding overload of the handling facilities. We first present a static mixed integer programming model for the transfer baggage problem. However, the transfer baggage process is subject to uncertainty related to aircraft arrival time, transportation time from aircraft to baggage handling facility, and capacity use in the baggage handling system. In order to handle this uncertainty, a stochastic model is developed, optimizing over a finite set of scenarios. Although the model in theory should lead to more balanced and stable decisions, it suffers of long solution times. Therefore, a semi-stochastic model is presented, where short-term decisions are stochastic, while long-term decisions are deterministic. Computational experiments on real-life data from a major European hub airport are reported, demonstrating that each of the three models has its advantages. In particular, the semi-stochastic model shows promising results both with respect to robustness and solution times.

Appendices

Appendix A: List of Symbols

In this section, we give an overview of all sets, parameters and variables used in the various models.

Sets

• A, set of feasible assignments of trips.

• B, set of trips.

• I, set of infeed areas.

• $A_b \subseteq A$, subset of feasible assignments for a specific trip $b \in B$.

• $A_i \subseteq A$, subset of feasible assignments for a specific infeed area $i \in I$.

• $A^{STO} \subseteq A$, subset of assignments, defining the stochastic assignments.

• $Bs \subseteq B$, subset of trips, where only one container is used in the trip.

• $N_{b'} \subseteq B$, subset of trips, defining neighboring trips of $b'\in B$.

• T, set of time-steps.

• $T^{STO} _i \subseteq T$, subset of time-steps, defining the time-steps where a capacity use for stochastic assignment exists for area $i \in I$.

• $T^{last} _i \subseteq T^{STO} _i$, subset of stochastic time-steps for area $i \in I$. Defines the last time-step for each area included in $T^{STO} _i$.

• $T'_i = \{t \in T \mid k_{i,t}>0 \}$, set of time-steps where the baggage infeed area $i \in I$ is active.

• $T^*_i = \{t \in T^{STO} _i \mid k_{i,t}>0 \}$, set of time-steps where the baggage infeed area $i \in I$ is active and where capacity use exists for any stochastic assignment for that area.

• S, set of scenarios in the stochastic optimization.

Parameters

• $C^{des} _i$, desired maximum capacity at infeed area $i \in I$.

• $C^{tech} _i$, technical capacity at infeed area $i \in I$.

• $C^{queue1} _i$, workload limit of extended capacity at infeed area $i \in I$. First step of overwork function.

• $C^{queue2} _i$, workload limit of additionally extended capacity at infeed area $i \in I$. Second step of overwork function.

• $u_{a,t}$, amount of capacity used in timeslot $t \in T$ of assignment $a \in A$.

• $u^{late} _a$, number of late bags for assignment $a \in A$.

• $u^{missed} _a$, total connecting/missed probability of all bags in assignment $a \in A$.

• $u^{drive} _a$, transportation time from the parking position to the infeed area for assignment $a \in A$, in seconds.

• $u^{BHS} _a$, total combined transportation time for each bag in assignment $a \in A$ through the baggage handling system (BHS), given in seconds.

• $\upsilon _{s,a,t}$, stochastic capacity use, amount of capacity used for scenario $s \in S$ in timeslot $t \in T$ of assignment $a \in A$.

• $\upsilon ^{missed} _{s,a}$, total missed probability of all bags in assignment $a \in A$ for scenario $s \in S$.

• $w^{late}$, weight of cost term for late bags.

• $w^{missed}$, weight of cost term for connecting/missed probability.

• $w^{drive}$, weight of cost term for apron transportation time.

• $w^{BHS}$, weight of cost term for transportation through the BHS.

• $w^{des}$, weight of cost term for capacity use, between desired and technical capacity.

• $w^{queue1}$, weight of cost term for capacity use, between technical and queue1.

• $w^{queue2}$, weight of cost term for capacity use, between queue1 and queue2.

• $w^{penalty}$, weigh of cost term for capacity use above queue2.

• $k_{i,t}$, number of bags infeed area $i \in I$ can service when working at technical capacity in time-step $t \in T$. Reflects the amount of workers assigned. If the infeed area is closed at a given time-step then $k_{i,t} = 0$.

• $L_{i,t}$, indicator parameter for $T^{last} _i$, equal 1 for $t \in T^{last} _i$ and 0 otherwise.

• $\Omega$, timespan defining the stochastic assignments.

• $\lambda _0$, initial increase rate.

• $\tau$, tolerance value.

Variables

• $x_a \in \{0,1\}$, denotes whether assignment $a \in A$ is chosen.

• $y^{des} _{i,t} \in \mathbb {R}_+$, use of capacity exceeding the desired capacity use $C^{ des }_i$ at infeed area $i \in I$ in time-step $t \in T$.

• $y^{queue1} _{i,t} \in \mathbb {R}_+$, workload stretched above technical capacity up to $C_i^{ queue1 }$ at infeed area $i \in I$ in time-step $t \in T$.

• $y^{queue2} _{i,t} \in \mathbb {R}_+$, workload stretched above technical capacity between $C_i^{ queue1 }$ and $C_i^{ queue2 }$ at infeed area $i \in I$ in time-step $t \in T$.

• $y^{penalty} _{i,t} \in \mathbb {R}_+$, ensures feasibility even if workload exceeds $C_i^{ queue2 }$ at infeed area $i \in I$ in time-step $t \in T$.

• $y_{i,t} \in \mathbb {R}_+$, denotes the deterministic capacity use for area $i \in I$ in time-step $t \in T$.

• $\gamma ^{des} _{s,i,t} \in \mathbb {R}_+$, like $y^{des} _{i,t}$, but used for stochastic capacity use, defined for each scenario $s \in S$.

• $\gamma ^{queue1} _{s,i,t} \in \mathbb {R}_+$, like $y^{queue1} _{i,t}$, but used for stochastic capacity use, defined for each scenario $s \in S$.

• $\gamma ^{queue2} _{s,i,t} \in \mathbb {R}_+$, like $y^{queue2} _{i,t}$, but used for stochastic capacity use, defined for each scenario $s \in S$.

• $\gamma ^{penalty} _{s,i,t} \in \mathbb {R}_+$, like $y^{penalty} _{i,t}$, but used for stochastic capacity use, defined for each scenario $s \in S$.

• $q^{avg} \in \mathbb {R}_+$, average load of all infeed areas.

• $q^{plus} _i \in \mathbb {R}_+$, positive deviation from average load at infeed area $i \in I$.

• $q^{minus} _i \in \mathbb {R}_+$, negative deviation from average load at infeed area $i \in I$.

• $q \in \mathbb {R}_+$, total deviation from average load at infeed area.