From time representation in scheduling to the solution of strip packing problems

Abstract

We propose two mixed-integer linear programming based approaches for the 2-D orthogonal strip packing problem. Using knowledge from the alternative forms of time representation in scheduling formulations, we show how to efficiently combine three different concepts into the x-and ydimensions. One model features a discrete representation on the x-axis (strip width) and a continuous representation with general precedence variables on the y-axis (strip height). The other features a full continuous-space representation with the same approach for the y-axis and a single non-uniform grid made up of slots for the x-axis. Through the solution of a set of twenty nine instances from the literature, we show that the former is a better approach, even when compared to three alternative MILP models ranging from a pure discrete-space to a pure continuous-space with precedence variables in both dimensions. All models are available in www.minlp.org.

Incorporating Timesharing Scheme in Ecoindustrial Multiperiod Chilled and Cooling Water Network Design

“…There is one cross-plant pipeline from Plant 1 to Plant 3 (stream F 1,14,1 ), and the possible cross-plant flows such as streams F 19,7,1 , F 19,11,13 , and F 20,11,1 could be shared with either stream F 14,9,2 or F 14,10,2 in the common pipelines from Plant 3 to Plant 2. Next, total five common cross-plant pipelines are built as shown by stream flows F 1,9,1 , F 1,14,1 , F 5,11,1 , F 14,9,2 , and F 14,10,2 (see Figure 9).…”

“…In practice, both batch and continuous processes are influenced by process- and market-related uncertainties including seasonal product demand, scheduled plant shutdown, and expansion plans of plant capacity. In adaptation to the above transient scenarios, several methods such as Petri-net based, timed automata, S-graph, strip packing, and mathematical programming techniques have been proposed to achieve an optimum scheduling plan for the transient production. These scheduling plans would result in the change of the process demand as the total demand could be increased, be decreased, or remain unchanged.…”

Improved layout structure with complexity measures for the Manufacturer’s Pallet Loading Problem (MPLP] using a Block approach

“…Castro and Oliveira (2011) proposed a formulation based on a hybrid discrete and continuous-space, inspired by scheduling models. In a similar approach of time representation, Castro and Grossmann (2012) proposed a new hybrid discrete and continuous-space formulation which was able to find and prove more optimal solutions than the previous DCS proposed by Castro and Oliveira (2011). Block heuristics have also been considered and developed in the area of pallet loading, including G4-and G5-structures as in Lim, Ma, Xu and Zhang (2012) and Scheithauer and Terno (1996b).…”

Integrated Proactive and Reactive Scheduling for Refinery Front-End Crude Movement with Consideration of Unit Maintenance

“…Historically, mathematical programming techniques were widely employed to determine optimal schedules and plans in a variety of engineering fields, such as plant production, job manufacturing, product transportation, process safety, and so on. − As to unit maintenance management, the proactive scheduling of PM is to determine the integrated schedule of production and maintenance prior to failure emerging, in which PM is well coordinated with normal operations. According to different maintenance policies, proactive scheduling has been extensively investigated.…”