A New MILP Approach for the Facility Layout Design Problem with Rectangular and L/T Shaped Departments

In this paper we propose a new approach for the facility layout problem (FLP) and suggest new mixed-integer linear programming (MILP) formulations. The proposed approach considers simultaneously the location of the departments within the facility and the internal arrangement of the machines. Two models are suggested, where the first addresses the rectangular department case and the second allows nonrectangular departments defined by an L/T shape. New regularity constraints are developed to avoid irregular department shapes

An efficient MILP formulation for the parallel load retrieval in puzzle based storage systems with simultaneous load movements

Puzzle-based storage (PBS) is one of the most spaceefficient types of storage systems. In a PBS unit, loads are stored in a grid of cells, where each cell may be empty or contain a load. A load can move only to adjacent empty cells using four-way conveyors. When loads are requested for retrieval, a sequence of load movements is performed in order to bring them to the input/output (I/O) points of the unit. In this paper, we present a time-expanded-graph based integer-linear-programming (MILP) formulation that aims to minimize the time to retrieve a set of target loads (makespan). Note that other objectives, such as the flowtime or the number of moves, can be minimized as well. Experiments show that the proposed formulation can solve small to medium size instances, especially when the storage density is not extremely high. Additionally, we show that parallel load retrieval significantly decreases the makespan compared to serial load retrieval

Throughput Rate of a Two-worker Stochastic Bucket Brigade

Work-sharing in production systems is a modern approach that improves throughput rate. Work is shifted between cross-trained workers in order to better balance the material now in the system. When a serial system is concerned, a common work-sharing approach is the Bucket-Brigade (BB), by which downstream workers sequentially take over items from adjacent upstream work- ers. When the workers are located from slowest-to-fastest and their speeds are deterministic, it is known that the line does not suffer from blockage or starvation, and achieves the maximal theoretical throughput rate (TR). Very little is known in the literature on stochastic self-balancing systems with work-sharing, and on BB in particular. This paper studies the basic BB model of Bartholdi & Eisenstein (1996) under the assumption of stochastic worker speeds. We identify settings in which conclusions that emerge from deterministic analysis fail to hold when speeds are stochastic, in particular relating to worker order assignment as a function of the problem parameters

Using Buffers and Work-sharing for Minimizing Makespan of Small Batches in Assembly Lines Under Learning Effects

The effect of workers’ learning curve on production rate in manual assembly lines is significant when producing relatively small batches of different products. This research analyzes this effect and suggests applying work-sharing among the workers in such an environment to improve the time to complete the batch, namely, the makespan. Work-sharing refers to a situation where adjacent workers help each other in order to reduce idle times caused by blockage and starvation. The effect of work-sharing and existence of buffers on the makespan is examined and compared to a baseline situation, with no work-sharing and buffers. We present mixedinteger linear-programing (MILP) formulations, which minimize the makespan and provides optimal work allocation. A numerical study is conducted and the results along with some operational insights are presented

A multi-objective optimization approach for exploring the cost and makespan trade-off in additive manufacturing

Additive manufacturing (AM) suggests promising manufacturing technologies, which complement traditional manufacturing in multiple areas, such as biomedical, aerospace, defense, and automotive industries. This paper addresses the production planning problem in multi-machine AM systems. We consider all relevant physical and technological parameters of the machines and the produced parts, for using direct metal laser sintering (DMLS) technology. In DMLS technology, each machine produces jobs, where each job consists of several parts arranged horizontally on the build tray. Starting a new job requires a setup operation. We address the simultaneous assignment of parts to jobs and jobs to the machines, while considering the cost and makespan objectives. A unified mixed-integer linear-programming (MILP) formulation that can minimize the above objectives separately and simultaneously is suggested, along with analytical bounds and valid inequalities. Experimentation demonstrates the effectiveness of the proposed formulation with single objectives versus similar formulations from the literature. An efficient frontier approach is applied to the multi-objective problem while generating a diverse set of exact non-dominated solutions. The trade-off between the objectives is analyzed via experimentation. Results show that when identical machines are used, the trade-off is relatively small, and hence the decision-maker can use any of the single objectives. However, when non-identical machines are used, it is important to consider both objectives simultaneously. Moreover, the trade-off increases with the number of machines and heterogeneity of the system, with respect to the size and settings of the machines

Decentralization Cost in Scheduling: A Game-Theoretic Approach

Decentralized organizations may incur inefficiencies because of scheduling issues associated with competition among decision makers (DMs) for limited resources. We analyze the decentralization cost (DC), i.e., the ratio between the Nash equilibrium cost and the cost attained at the centralized optimum. Solution properties of a dispatching-sequencing model are derived and subsequently used to develop bounds on the DC for an arbitrary number of jobs and DMs. A scheduling-based coordinating mechanism is then provided, ensuring that the centralized solution is obtained at equilibrium.game theory, scheduling, decentralization, noncooperative games, incentives, contracting