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Dock Assignment in the warehouses of KLM Cargo at Schiphol Airport

Along with their widely known passenger services, KLM moves a significant amount of cargo shipments in the cargo compartments of passenger and full freighter aircraft. KLM is hired by logistics companies such as DHL, Amazon and PostNL to move shipments by air.

Thus, logistics companies dispatch trucks to deliver and pick up shipments from/to KLM Cargo that are transported by air. To receive and (un)load those trucks, KLM Cargo has a warehouse with a total of 22 docks. Twelve docks are currently assigned to receive trucks delivering outbound cargo that will later be loaded into the aircraft, whereas ten docks are assigned to receive trucks picking up inbound cargo, which has been unloaded from the aircraft and placed in the warehouse waiting to be picked up. To perform the (un)loading activities, it is necessary to use one (un)loading dock and a crew of 3 persons for the whole duration of the (un)loading activities. Crews are organized in three 8-hour shifts starting at 6:00 AM.

Truck arrivals depend on the day of the week and the hour of the day as Thursdays, Fridays and Saturdays have a much higher flow than other days. Outbound truck arrivals have a different pattern and higher rate than inbound truck arrivals (see Table 1 and Table 2 in the Appendix). The maximum weight capacity of a truck is 10 metric tons but the actual weight of consolidated shipments carried by a single truck is a random variable, which can be represented by a triangular distribution with parameters min = 0 tons, mode = 5 tons, max = 10 tons.

Your goal is to find the dock assignments (per 8-hour shifts) that reduce as much as possible the total costs incurred by KLM Cargo. The only constraint that you have for assigning docks in each shift is that, in an 8-hour shift, a dock cannot be used simultaneously to load and unload trucks, i.e. receive both inbound and outbound shipments. For example, you could assign a dock for the whole week to unload outbound shipments or you can assign on Mondays that dock to process outbounds for the first two shifts and then for inbounds for the last shift. You can also elect to close a dock for any number of 8-hour shifts. Shifts need to be 8-hour shifts.

They have identified three main costs in these operations:

1. Cost of personnel working at the (un)loading docks: each person is paid two times the minimum wage per hour in the Netherlands.

2. Cost of truckers’ waiting times. To consider the service provided to the truckers, KLM Cargo has decided to assign a cost per every minute that a truck is waiting in line to be received at a dock. Assume that the cost per hour associated with a trucker that is waiting is directly proportional to their hourly wage, which is two times the minimum wage per hour in the Netherlands. Note that this cost is only incurred when the trucker is waiting in line. When the trucker is parked in the dock (or doing maneuvers to park), then the truck is being serviced and this cost is not incurred.

3. 10% of the outbound shipments (irrespective of day and hour) need to be handled in less or equal than 90 minutes as these are critical shipments, e.g., pharmaceuticals or livestock. If these shipments are processed in more than 90 minutes (waiting time plus (un)loading time) KLM Cargo will incur a penalty of 500 euros per metric ton, irrespective of the magnitude of the lateness, i.e. either a 91 or a 1000 handling time (waiting time plus (un)loading time) will incur in a penalty of 500 euros per metric ton. Thus, the third cost associated with this system is a penalty cost. Note that the maximum penalty incurred by a late handling of a critical shipment is 5000 euros (500 euros/ton * 10 tons).

To reduce the penalties of processing critical shipments late you also have two options:

A. Assign a (set of) dedicated dock(s) to handle only critical outbound shipments. Similar to non-dedicated docks, you can assign a dedicated dock for the whole week or on a shift-byshift basis. If you elect to use a dedicated dock, then the crew assigned to the dedicated dock will be paid 2.5 times the minimum wage, as they have an increased pressure to perform. It is worth noting that, currently, all outbound docks share one waiting queue for outbound shipments, whereas all inbound docks share one waiting queue for inbound shipments. This means that, by assigning a dedicated dock for critical shipments, this dock will have a dedicated queue in which only critical shipments can queue.

B. Assign a priority for critical outbound shipments. This means that, if a critical outbound shipment arrives at the system, then it will be placed at the front of the queue to be able to be processed much quicker. This option does not have an extra cost associated and can be used in combination with option A. For instance, you can assign 2 dedicated docks, 2 docks with priority for critical shipments, and the remaining docks as non-dedicated, non-priority docks.

Assume that truck arrivals are time-varying Poisson arrivals (a Poisson with changing arrival rates) and that (un)loading times have a linear relationship with the weight to be (un)loaded. The minimum (un)loading time is 5 minutes (considering parking maneuvers) and the maximum (un)loading time is 60 minutes. Thus, a truck carrying (or picking up) 0 tons will need 5 minutes to be (un)loaded, whereas a truck with 10 tons (the maximum) will need 60 minutes to be (un)loaded, and a truck with 5 tons (the mean) will need 32.5 minutes.

Prepare a report for KLM Cargo analyzing the current situation and suggesting a schedule consisting of 8-hour shifts for the docks (outbound, inbound, dedicated) and their associated priority policy. The main objective is to reduce as much as possible the total costs incurred by this system of (un)loading docks.

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