Optimal and heuristic algorithms for the multi-location dynamic transshipment problem with fixed transshipment costs

We consider centrally controlled multi-location systems, which coordinate their replenishment strategies through the use of transshipments. In a dynamic deterministic demand environment the problem is characterized by several locations, each of which has known demand for a single product for each period in a given finite horizon. We consider replenishment, transshipment and inventory holding costs at each location, where the first two have location-dependent fixed, as well as linear components, and the third is linear and identical to all locations. We prove that the resulting dynamic transshipment problem is NP-hard, identify a special structure which is satisfied by an optimal solution and develop, based on this structure, an exponential time algorithm to solve the problem optimally. In addition, we develop a heuristic algorithm, based on partitioning the time horizon, which is capable of solving larger instances than the optimal solution. Our computational tests demonstrate that the heuristic performs extremely well.     

Retrieval sequencing for unit-load automated storage and retrieval systems with multiple openings

Automated storage and retrieval systems (AS/RS) have made a dramatic impact on material handling and inventory control in warehouses and product systems. A unit-load AS/RS is generic and other AS/RS represent its variations. In this paper, we study a problem of sequencing retrieval requests in a unit-load AS/RS. In a unit-load AS/RS, there are usually multiple openings and a unit-load can be stored in any opening. Given a list of retrieval requests and the locations of openings, this problem seeks a sequence of dual cycles that minimizes total travel time taken by a storage/retrieval machine. Previous researchers believed that this problem is computationally intractable and provided greedy-style heuristic algorithms. In this paper, we present an algorithm that combines the Hungarian method and the ranking algorithm for the assignment problem with tour-checking and tour-breaking algorithms. We show that this algorithm finds either a verified optimal or near-optimal solution quickly for moderate size problems. Using this algorithm, we also evaluate the effectiveness of the existing simple heuristics. Computational results are reported.     

A HEURISTIC FOR THE DYNAMIC FACILITY LAYOUT PROBLEM

This paper presents a heuristic for the dynamic facility layout problem. All existing methods for solving this problem require the use of a dynamic programming model, the optimal solution of the quadratic assignment problem, or both. The proposed heuristic is based on the steepest-descent pairwise-interchange procedure to develop layouts utilizing material handling cost data from varying lengths of forecast windows as well as the explicit consideration of the corresponding rearrangement costs. Numeric results indicate that it typically performs as well as any existing methodology and only slightly worse than optimal.     

Analysis and solution to the single-level batch production smoothing problem

Many companies use mixed-model production systems running under the Just-in-Time philosophy in order to efficiently meet customer demands for a variety of products. Such systems require demand be stable and production sequence be leveled. The production smoothing problem aims at finding level schedules in which the appearances of products are dispersed over the horizon as uniformly as possible. In this paper, the production smoothing problem is extended to a more general manufacturing environment where a single machine can be identified as either the final or the bottleneck stage of the system and products may have arbitrary non-zero setup and processing time requirements on this single machine. An optimization model is built for the problem and a two phase solution methodology is developed. The first phase problem is shown to be NP-hard and a parametric heuristic procedure is proposed for its solution. In contrast, the second phase problem is shown to be efficiently solvable and currently available solution methods are adopted from the literature. A computational study is designed to test the proposed two phase solution methodology and also the parametric heuristic procedure. Computational results show that the proposed two phase solution methodology enables effective and efficient control of the studied manufacturing system, and the heuristic procedure developed for the first phase problem is time efficient and promises near optimal solutions for a variety of test instances.     

Single machine scheduling problem with batch setups involving positional deterioration effects and multiple rate-modifying activities

This article considers a single machine scheduling problem with batch setups, positional deterioration effects, and multiple optional rate-modifying activities to minimize the total completion time. This problem is formulated as an integer quadratic programming problem. In view of the complexity of optimally solving this problem, a two-phase heuristic algorithm is proposed where an optimal but non-integer solution is obtained in the first phase by solving a continuous relaxed version of the problem. This solution serves as a lower bound for the optimal value of the total completion time. The second phase of the algorithm generates an integer solution using a simple rounding scheme that is optimum or very close to optimum for this problem. Empirical evaluation and comparison with an existing heuristic algorithm show that the proposed heuristic algorithm is substantially more effective in solving large-size problem instances.     

Storage Decisions in Information Systems

The problem is to dynamically store different data records in different storage devices in each period so as to minimize the total expected discounted cost over a planning horizon. Each device has a fixed total capacity, each record has a given storage space requirement, while the number of requests for each record per period is changing stochastically through time. Given an allocation, the total cost per period consists of the storage cost (depending on the storage requirements and device), the access cost including update and retrieval costs (depending on the number of requests) and the transfer cost (depending upon the change of allocation from the previous period). A dynamic programming model is presented to yield optimal strategies. The special case of independent identically distributed demands is completely solved, using a generalized transportation algorithm while a heuristic procedure is indicated for the general problem using parametric analysis.     

Multi-product continuous plant scheduling: combination of decomposition,genetic algorithm,and constructive heuristic

We propose a polylithic method for medium-term scheduling of a large-scale industrial plant operating in a continuous mode. The method combines a decomposition approach, a genetic algorithm (GA) and a constructive MILP-based heuristic. In the decomposition, decisions are made at two levels, using the rolling horizon approach. At the upper level, a reduced set of products and the time period is chosen to be considered in the lower level. At the lower level, a short-term scheduling MILP-model with event-based representation is used. A heuristic solution to the lower level problem is found using a constructive Moving Window heuristic guided by a genetic algorithm. The GA is applied for finding efficient utilisation of critical units in the lower level problem. For solving the one unit scheduling problem, a parallel dynamic programming algorithm is proposed. Implementation of the dynamic programming algorithm for a graphics processing unit (GPU) is incorporated in the GA for improving its performance. The experimental study of the proposed method on a real case of a large-scale plant shows a significant improvement of the solution quality and the solving time comparing to the pure decomposition algorithm proposed in the earlier study, and confirmed suitability of the proposed approach for the real-life production scheduling. In particular, the reduction of the number of changeovers and their duration in the obtained solution as well as the CPU time of solving the problem was about 60% using the new approach.     

A two‐phase approach for single machine scheduling problems: Minimizing the total absolute deviation

Abstract

This paper presents a heuristic for solving a single machine scheduling problem with the objective of minimizing the total absolute deviation. The job to be scheduled on the machine has a processing time, p_i , and a preferred due date, d_i . The total absolute deviation is defined as the sum of the earliness or tardiness of each job on a schedule 5. This problem is proved to be NP‐complete by Garey et al. [8]. As a result, we developed a two‐phase procedure to provide a near‐optimal solution to this problem. The two‐phase procedure includes the following steps: First, a greedy heuristic is applied to the set of jobs, N, to generate a “good” initial sequence. According to this initial sequence, we run Garey's local optimization algorithm to provide an initial schedule. Then, a pairwise switching algorithm is adopted to further reduce the total deviation of the schedule. The effectiveness of the two‐phase procedure is empirically evaluated and has been found to indicate that the solutions obtained from this heuristic procedure are often better than other heuristic approaches.     

Environment conscious manufacturing edited by S.M. Gupta and A.J.D. Lambert

The dynamic facility layout problem (DFLP) aims to minimise the sum of handling and re-layout costs by devising an individual layout for each distinctive production period. In this paper, a hybrid particle swarm optimisation (HPSO) algorithm is proposed to find near-optimal solutions of DFLP. We use a coding and decoding technique that permits a one to one mapping of a solution in discrete space of DFLP to a PSO particle position in continuous space. The proposed PSO will further use this coding technique to explore the continuous solution space. For further enhancement, the proposed PSO is hybridised with a simple and fast simulated annealing. The developed algorithm is capable of being extended to more general cases although equal area machines and standardised handling equipments with identical unit costs are assumed for the time being. Computational results show the efficiency of the proposed algorithm compared to other heuristics.     

Initial allocation compensation algorithm for redundancy allocation: The scanning heuristic

The tiny feature size in current semiconductor integrated circuits naturally requires redundancy strategies to improve manufacturing yield and operating reliability. To find an optimal redundancy architecture that provides maximum yield and reliability is a trade-off problem. In the reliability optimization field, this type of problem is generally called a redundancy allocation problem. In this paper, we propose a new iterative algorithm, the scanning heuristic, to solve the redundancy allocation problem. The solution quality of conventional iterative heuristics is highly dependent on the initial starting point of the algorithm employed. To overcome this weakness, the scanning heuristic systematically divides the original solution space into several small bounded solution spaces. The local optimum in each divided solution space then becomes a candidate for the final solution. The experimental results demonstrate that the proposed heuristic, and subsequently some combinations of heuristics, are superior to existing heuristics in terms of solution quality.     

A similarity score-based two-phase heuristic approach to solve the dynamic cellular facility layout for manufacturing systems

The dynamic cellular facility layout problem (DCFLP) is a well-known NP-hard problem. It has been estimated that the efficient design of DCFLP reduces the manufacturing cost of products by maintaining the minimum material flow among all machines in all cells, as the material flow contributes around 10–30% of the total product cost. However, being NP hard, solving the DCFLP optimally is very difficult in reasonable time. Therefore, this article proposes a novel similarity score-based two-phase heuristic approach to solve the DCFLP optimally considering multiple products in multiple times to be manufactured in the manufacturing layout. In the first phase of the proposed heuristic, a machine–cell cluster is created based on similarity scores between machines. This is provided as an input to the second phase to minimize inter/intracell material handling costs and rearrangement costs over the entire planning period. The solution methodology of the proposed approach is demonstrated. To show the efficiency of the two-phase heuristic approach, 21 instances are generated and solved using the optimization software package LINGO. The results show that the proposed approach can optimally solve the DCFLP in reasonable time.     

A genetic algorithm heuristic approach to general outsourcing capacitated production planning problems

This paper addresses a dynamic capacitated production planning (CPP) problem with consideration of outsourcing. Specifically, the outsourcing problem considered in this paper has the following features: (1) all demands are met by production or outsourcing without postponement or backlog, (2) production, inventory, and outsourcing levels all have a limit, and (3) the cost functions are considered arbitrarily and time-varying. These features come together, leading to a so-called general outsourcing CPP problem. In our previous work, an algorithm with pseudo-polynomial time complexity was developed, which includes a formation of a feasible solution region and then a search procedure using dynamic programming techniques. Due to the computational complexity with such an approach, only small and medium problems can be solved in a practical sense. In this paper, we present a genetic algorithm (GA) approach to the same problem. The novelty of this GA approach is that the idea of the feasible solution region is used as a heuristic to guide the searching process. We present a computational experiment to show the effectiveness of the proposed approach.     

Tool path optimisation method for large thin-wall part of spacecraft

Roughing tool path of panel machining, which is a bottleneck of spacecraft production, should be optimised rapidly to shorten process time. This problem has a large solution space, and surface quality should be taken into account. The decision variables are cavity machining order, feed point and cutting direction of each cavity. Our problem is presented as an asymmetric general travelling salesman problem (AGTSP). A cluster optimisation-based hybrid max–tmin ant system (CO-HMMAS) is proposed, which solves two sub-problems as a whole. The oriented pheromone and dynamic heuristic information calculating methods are designed. We analyse the differences between one-stage and two-stage AGTSP local search heuristics and combine CO-HMMAS with them properly. An improved Global 3-opt heuristic suitable for both symmetric and asymmetric cases is proposed with sharply reduced time complexity. Comparison experiments verified that, two-stage local search heuristics decrease solution error significantly and rapidly when the error is great, and one-stage ones improve a near-optimal solution costing much more computing time. Benchmarks tests show that, CO-HMMAS outperforms the state-of-the-art algorithm on several technical indexes. Experiments on typical panels reveal that all algorithm improvements are effective, and CO-HMMAS can obtain a better tool path than the best algorithm within less CPU time.     

Unrelated parallel machine scheduling with job splitting

Scheduling jobs on unrelated parallel machines is an activity that is very much a part of industrial scheduling. We report a methodology for minimizing the total weighted tardiness of all jobs intended to be processed on unrelated parallel machines in the presence of dynamic job releases and dynamic machine availability. More importantly, the mixed (binary) integer linear programming model formulated for the problem incorporates a couple of “hard” operational constraints to ensure that just-in-time manufacturing practices are followed by controlling the work-in-process and/or finished goods inventories generated by split jobs mandated by a tight due date, a high priority, and/or a high workload. Four different methods based on simple and composite dispatching rules are used to identify an initial solution, which is then used by the tabu-search-based heuristic solution algorithm to ultimately find the best solution. Incorporating the various tabu search features led to the development of six different heuristics that were tested on eight small problem instances to compare the quality of their solutions to the optimal solutions. The results show that the proposed heuristics are capable of obtaining solutions of good quality in a remarkably short computation time with the best performer among them recording a percentage deviation of only 1.18%. A factorial experiment based on a split-plot design is performed to test the performance of the heuristics on problem structures, ranging from nine jobs and three machines to 60 jobs and 15 machines. The results show that the newly developed composite dispatching heuristic, referred to as the modified apparent tardiness cost, is capable of obtaining initial solutions that significantly accelerate the tabu-search-based heuristics to attain the best solution. The use of a long-term memory function is proven to be advantageous in solving all problem structures. In addition, the variable tabu list size is preferred for solving the small problem structure, while the fixed tabu list size is preferred as the problem size grows from small to medium and then large.     

An efficient local search heuristic for the double row layout problem with asymmetric material flow

The double row layout problem (DRLP) consists of arranging a number of rectangular machines of varying widths on either side of a corridor to minimize the total cost of material handling for products that move between these machines. This problem arises in the context of many production environments, most notably semiconductor manufacturing. Because the DRLP contains both combinatorial and continuous aspects, traditional solution approaches are not well suited to obtain solutions within a reasonable time. Moreover, previous approaches to this problem did not consider asymmetric flows. In this paper, an effective local search procedure featuring linear programming is proposed for solving the DRLP with asymmetric flows (symmetric flows being a special case). This approach is compared against several constructive heuristics and solutions obtained by a commercial mixed integer linear programming solver to evaluate its performance. Computational results show that the proposed heuristic is an effective approach, both in terms of solution quality and computational effort.     

Integrated scheduling of a container handling system with simultaneous loading and discharging operations

The integrated scheduling of container handling systems aims to optimize the coordination and overall utilization of all handling equipment, so as to minimize the makespan of a given set of container tasks. A modified disjunctive graph is proposed and a mixed 0–1 programming model is formulated. A heuristic algorithm is presented, in which the original problem is divided into two subproblems. In the first subproblem, contiguous bay crane operations are applied to obtain a good quay crane schedule. In the second subproblem, proper internal truck and yard crane schedules are generated to match the given quay crane schedule. Furthermore, a genetic algorithm based on the heuristic algorithm is developed to search for better solutions. The computational results show that the proposed algorithm can efficiently find high-quality solutions. They also indicate the effectiveness of simultaneous loading and discharging operations compared with separate ones.     

Design of flexible assembly line to minimize equipment cost

In this paper we develop an optimal and a heuristic algorithm for the problem of designing a flexible assembly line when several equipment alternatives are available. The design problem addresses the questions of selecting the equipment and assigning tasks to workstations, when precedence constraints exist among tasks. The objective is to minimize total equipment costs, given a predetermined cycle time (derived from the required production rate). We develop an exact branch and bound algorithm which is capable of solving practical problems of moderate size. The algorithm's efficiency is enhanced due to the development of good lower bounds, as well as the use of some dominance rules to reduce the size of the branch and bound tree. We also suggest the use of a branch-and-bound-based heuristic procedure for large problems, and analyze the design and performance of this heuristic.     

A two-dimensional bin-packing problem with conflict penalties

In this paper, we address the two-dimensional bin-packing (2BP) problem with variable conflict penalties, which incur if conflicting items are loaded into the same bin. Such a problem is observed in applications such as supermarket chains and automobile components transportation. The problem not only focuses on minimisation of number of bins used, but also deals with the conflict penalties at the same time. We propose a heuristic method based on the IMA algorithm and adapt it to solve this problem. A local search procedure is also designed to further improve the solutions. For instances derived from benchmark test data, the computational results indicate that the adapted IMA heuristic algorithm with local search effectively balances the number of bins used and the conflict penalties. The algorithm outperforms several adapted approaches that are well known for the 2BP problems.     

New Tabu search heuristics for the dynamic facility layout problem

A manufacturing facility is a dynamic system that constantly evolves due to changes such as changes in product demands, product designs, or replacement of production equipment. As a result, the dynamic facility layout problem (DFLP) considers these changes and is defined as the problem of assigning departments to locations during a multi-period planning horizon such that the sum of the material handling and re-arrangement costs is minimised. In this paper, three tabu search (TS) heuristics are presented for this problem. The first heuristic is a simple TS heuristic. The second heuristic adds diversification and intensification strategies to the first, and the third heuristic is a probabilistic TS heuristic. To test the performances of the heuristics, two sets of test problems from the literature are used in the analysis. The results show that the second heuristic out-performs the other proposed heuristics and the heuristics available in the literature.     

A heuristic procedure for solving the Lexicographic Bottleneck Assembly Line Balancing Problem (LB-ALBP)

The Lexicographic Bottleneck Assembly Line Balancing Problem (LB-ALBP) is a new assembly-line balancing problem recently defined in the literature. The LB-ALBP hierarchically minimises the workload of the most heavily loaded workstation, followed by the workload of the second most heavily loaded workstation, followed by the workload of the third most heavily loaded workstation, and so on. The original study presents two mixed-integer linear programming (MILP) models designed to solve the LB-ALBP optimally, together with three heuristic procedures based on these MILPs. In this paper, we propose and test new algorithms that combine a heuristic procedure for obtaining an initial solution and several local search procedures, which are an improvement upon the heuristic procedures published to date.