Parallel Batch Processing Machine Scheduling Under Two-Dimensional Bin-Packing Constraints

A new MILP model and fast heuristics for the variable-sized bin packing problem with time windows

Two new continuous-time MILP (Mixed Integer Linear Programming) models are developed for resource constrained project scheduling problems in which activities can be conducted in different (multi) modes. There are efficient and flexible MILP models for this problem in which time is represented by a number of discrete time intervals. However, they require to use large numbers of binary variables as the number of activities increases and time horizon stretches. Hence efforts have been made to formulate MILP models based on continuous-time representation and therefore to speed up the solution process. We propose two novel MILP models based on the event and resource flow concepts. The models are verified by solving benchmark problems in the literature.

MILP and MINLP models for the optimal scheduling of multi-energy systems accounting for delivery temperature of units, topology and non-isothermal mixing

Passive Optical Network (PON) deployments have recently been aiming to combine the capacity of metro and access networks in the last mile of the Internet service provisioning. Deployment of PONs by running fiber to the premises introduces the advantage of huge capacity but at the same time, it calls for a robust design in order to avoid long service outage durations in case of network failures where survivable network design is mostly limited to the deployment budget. In this paper, we propose three mixed integer linear programming (MILP) models for various survivability policies to deploy reliable long-reach PONs under the budget limitations. Each MILP model aims to place the ONUs in optimal locations so that the covered area is maximized while availability requirements of the users are satisfied within the deployment budget. We solve the MILP models under the uniform and heterogeneous availability requirement scenarios and show that service availability and coverage introduce a trade-off so as the coverage and deployment cost do. Two out of the three survivability policies can guarantee 99.99% service availability while the third one is able to guarantee 99.999% by running the proposed MILP models. However, the first two schemes are able to cover larger area when compared to the third scheme which is the most reliable protection policy.

Purpose: The main purpose of the paper is to evaluate the impact of diverse personnel policies around personnel promotion in the design of the strategic staff plan for a public university. The strategic staff planning consists in the determination of the size and composition of the workforce for an organization.Design/methodology/approach: The staff planning is solved using a Mixed Integer Linear Programming (MILP) model. The MILP model represents the organizational structure of the university, the personnel categories and capacity decisions, the demand requirements, the required service level and budget restrictions. All these aspects are translated into a set of data, as well as the parameters and constraints building up the mathematical model for optimization. The required data for the model is adopted from a Spanish public university.Findings: The development of appropriate policies for personnel promotion can effectively reduce the number of dismissals while proposing a transition towards different preferable workforce structures in the university.Research limitations/implications: The long term staff plan for the university is solved by the MILP model considering a time horizon of 8 years. For this time horizon, the required input data is derived from current data of the university. Different scenarios are proposed considering different temporal trends for input data, such as in demand and admissible promotional ratios for workers.Originality/value: The literature review reports a lack of formalized procedures for staff planning in universities taking into account, at the same time, the regulations on hiring, dismissals, promotions and the workforce heterogeneity, all considered to optimize workforce size and composition addressing not only an economic criteria, but also the required workforce expertise and the quality in the service offered. This paper adopts a formalized procedure developed by the authors in previous works, and exploits it to assess the impact of various personnel policies in the staff planning for a particular university case, and this is the principal contribution of the paper.

Mixed integer linear programming for the design of solar thermal energy systems with short-term storage

To support the selection of food items for FFQs in such a way that the amount of information on all relevant nutrients is maximised while the food list is as short as possible. Selection of the most informative food items to be included in FFQs was modelled as a Mixed Integer Linear Programming (MILP) model. The methodology was demonstrated for an FFQ with interest in energy, total protein, total fat, saturated fat, monounsaturated fat, polyunsaturated fat, total carbohydrates, mono- and disaccharides, dietary fibre and potassium. The food lists generated by the MILP model have good performance in terms of length, coverage and R 2 (explained variance) of all nutrients. MILP-generated food lists were 32-40 % shorter than a benchmark food list, whereas their quality in terms of R 2 was similar to that of the benchmark. The results suggest that the MILP model makes the selection process faster, more standardised and transparent, and is especially helpful in coping with multiple nutrients. The complexity of the method does not increase with increasing number of nutrients. The generated food lists appear either shorter or provide more information than a food list generated without the MILP model.

An improved MILP model for scheduling crude oil unloading, storage and processing

Knowledge representation of mathematical optimization problems and constructs for modeling

Modeling side slopes in vertical alignment resource road construction using convex optimization

This paper integrates two-dimensional bin packing with facility layout concepts to address scenarios in which items must not only fit within a confined space but also be arranged according to spatial priorities. We embed a prioritization matrix into the bin packing framework, enabling items to be clustered with one another or pulled toward certain bin access points based on assigned priority weights. Unlike traditional bin packing, which focuses on space utilization alone, our approach balances proximity to bin access points and adjacency among functionally related items, extending the utility of bin packing to applications requiring more nuanced layout preferences. We introduce a single mixed-integer linear programming (MILP) model and a complementary sliding window decomposition method that scales effectively to larger problem instances. Numerical experiments illustrate that this decomposition approach consistently outperforms a direct MILP solve with a commercial solver in both runtime and solution quality. This computational study underscores the flexibility and effectiveness of embedding multi-level priorities into bin packing.

Solving a large-scale industrial scheduling problem using MILP combined with a heuristic procedure

With the availability of advanced MPSoC and emerging Dynamic RAM (DRAM) interface technologies, an optimal allocation of logical data buffers to physical memory cannot be handled manually anymore due to the huge design space. An allocation does not only need to decide between an on-or off-chip memory, but also needs to take an increasing number of available memory channels, different bandwidth capacities and several routing possibilities into account. We formalize this problem and introduce a Mixed Integer Linear Programming (MILP) model based on two different optimization criteria. We implement the MILP model into a retargetable tool and present a case study with representative data of the Long-Term-Evolution (LTE) standard to show the real-life applicability of our approach.

Due to the large size of open-pit mines’ long-term production scheduling (OPMPS) problem in large-scale deposits, it is challenging to solve that problem as the mixed integer linear programming (MILP) model. This study used an approach of the genetic algorithm (GA) to tackle this challenge. So, in a small hypothetical deposit, based on the blocks in the ultimate pit limit and scenarios with 2–6 phases, net present values (NPV) and computational times obtained from the GA and MILP model were compared to evaluate the GA. Also, the GA was applied to a large-scale deposit to determine the efficiency of the GA in real deposits. The maximum NPV was obtained for the four-phase scenario in the hypothetical deposit and the six-phase scenario in the large-scale deposit. Although the GA’s NPV decreased slightly compared to the global optimum solution from the MILP model, the computational time was significantly reduced.

To design a cellular manufacturing system, many decisions have to be taken into consideration; grouping machines into cells, determining the system and intracellular layouts, and dividing the resources between the cells. In this paper, a novel mixed integer linear programming (MILP) model is proposed for the integrated cell formation, cellular layout and worker assignment problem. The workers are assumed to have different skill levels, and worker load is based on manual workload and material handling tasks. A genetic algorithm (GA) is further proposed to solve the problem, where the GA chromosome represents locations of machines and assignment of workers to machines. A numerical study is finally conducted to evaluate the performance of the proposed GA with regards to solutions attained by solving the MILP model. Results demonstrate the efficiency of the proposed GA in solving the integrated problem, as well as the competence in the developed MILP model.