Logistics Problems

A rough differentiation into two categories is possible:

  • Constituting economic decisions that determine the essence of business activity: the company’s strategic orientation (aspiration), its business proposal and operation method (activity pattern), and its chosen region of activity (business location).
  • Logistic choices of tactical/ operative orientation: The assignment of logistics locations (warehouses, reloading points) builds connections between sourcing, production, and retail. The supply path describes the assignment of commodity flows within this network. Thus, the tactically optimal way of transportation is determined. The supply modalities describe the means of transportation, the options that are offered. The transportation mode (flight, road, etc.), the quality of delivery (just in sequence, temperature, express, etc.) or the frequency can be specifications. Dispatching signifies the actual execution of the transportation, the operatively optimal realization. Questions concerning tour or lot size are typical for this stage.

The following five planning classes (and the forms related to them) are embedded within this hierarchy – in the given order

  • Facility location seeks to determine the according to an objective optimal geographic place of a set of facilities serving a set of demand points with respect to some constraints. Only operative and normative models with a focus on cost-minimal allocation have been examined. Typical examples are the p-median or the covering location problem.
  • Distribution system signifies the simultaneous optimization of multiple echelons regarding location and allocation in an environment of demand points; furthermore, it includes approaches of an integrated treatment of all participants, considering “procurement, production, inventory, distribution, and routing”. Models are usually labeled “production distribution”, “inventory distribution”, “supply chain”, or “multi-echelon inventory”.
  • Lot size describes the determination of the optimal replenishment strategy – usually balancing between fixed order costs (decreasing with amount) and variable inventory costs (proportional to amount). Variables which influence order size are usually demand and lead time. Therefore, the question of inventory policy is closely related. The models are often referred to as inventory problems in literature.
  • Bin packing is concerned with the creation of an optimal packing within a container. Due to capacitive restrictions in transportation and storage, as efficient a use of space as possible is required in order to secure minimum costs through the minimal number of containers. The knapsack problem, which considers multiple dimensions per item (often weight and value) is closely related to the bin-packing problem.
  • Vehicle routing strives for an optimal allocation (space and time) of assignments to vehicles under certain objectives (costs, service level, etc.) and constraints. Its execution is characterized by two steps: the tours – the division of the customer set into subsets – and the routes – the order in which the customers are served. Well-known (and well-researched) is the vehicle routing problem with its wide variety of characteristics as well as the ‘notorious’ traveling salesman problem.
Modeling and Optimization
Logistics Optimization

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