drivliftsproblem

Drivliftsproblem is a term used in puzzle and optimization communities to denote a family of combinatorial optimization problems that couple routing with lifting tasks. In its simplest form, a set of jobs must be processed in a chosen order, where each job requires moving an agent between locations and performing a lifting action to handle an item. The objective is typically to minimize makespan or total energy, subject to constraints such as machine capacity, precedence relations, and time windows.

Formalization: The problem can be modeled as a two-stage scheduling problem. Each job j has a travel time d_j representing the drive time to reach its operating location and a lift time l_j representing the time to perform the lifting operation. A feasible schedule specifies an order of jobs and, if applicable, an assignment to machines. Depending on the variant, drive and lift operations may be performed sequentially or overlapped. The common objective is to minimize C_max, the total completion time, or a weighted combination of time and energy.

Variants and complexity: Variants differ in whether a single agent performs all tasks or multiple agents share tasks, whether driving and lifting can occur simultaneously, and whether there are release dates or due dates. The problem is typically NP-hard, even in simplified forms. Solution approaches include exact methods for small instances and heuristics such as local search, tabu search, simulated annealing, and genetic algorithms. In practice, drivlifts problems appear in robotics, automated warehouses, and manufacturing where routing and manipulation must be coordinated.

History and usage: The term appears mainly in informal problem collections, teaching materials, and online discussions rather than in formal optimization literature. It is often used as a didactic example to illustrate coupling of routing and manipulation in scheduling contexts.

See also: Scheduling, job shop scheduling, flow shop, two-machine scheduling, robotics, logistics.