Integrating order acceptance decisions with flexible due dates in a production planning model with load-dependent lead times

We consider a tactical planning problem, which integrates production planning decisions together with order acceptance decisions, while taking into account the dependency between workload and lead times. The proposed model determines which orders to accept and in which period they should be produced, so that they can be delivered to the customer within the acceptable flexible due dates. When the number of accepted orders increases, the workload and production lead time also increase, and this may result in the possibility of missing customer due dates. This problem is formulated as a mixed integer linear programme for which two relax-and-fix heuristic solution methods are proposed. The first one decomposes the problem based on time periods, while the second decomposes it based on orders. The performances of these heuristics are compared with that of a state-of-the-art commercial solver. Our results show that the time-based relax-and-fix heuristic outperforms the order-based relax-and-fix heuristic, and the solver solution as it yields better integrality gaps for much less CPU effort.     

Single machine multi-product capacitated lot sizing with sequence-dependent setups

In production planning in the glass container industry, machine-dependent setup times and costs are incurred for switch overs from one product to another. The resulting multi-item capacitated lot-sizing problem has sequence-dependent setup times and costs. We present two novel linear mixed-integer programming formulations for this problem, incorporating all the necessary features of setup carryovers. The compact formulation has polynomially many constraints, whereas the stronger formulation uses an exponential number of constraints that can be separated in polynomial time. We also present a five-step heuristic that is effective both in finding a feasible solution (even for tightly capacitated instances) and in producing good solutions to these problems. We report computational experiments.     

A priority rule-based constructive heuristic and an improvement method for balancing assembly lines with parallel multi-manned workstations

Assembly lines of big-size products such as buses, trucks and helicopters are very different from the lines studied in the literature. These products’ manufacturing processes have a lot of tasks most of which have long task times. Since traditional assembly line models including only one worker in each station (i.e. simple assembly lines) or at most two workers (two-sided assembly lines) may not be suitable for manufacturing these type of products, they need much larger shop floor for a number of stations and long product flow times. In this study, an assembly line balancing problem (ALBP) with parallel multi-manned stations is considered. Following the problem definition, a mixed integer programming formulation is developed. A detailed study of priority rules for simple ALBPs is also presented, and a new efficient constructive heuristic algorithm based on priority rules is proposed. In order to improve solutions found by the constructive heuristic, a genetic algorithm-based solution procedure is also presented. Benchmark instances in the literature are solved by using the proposed mathematical programming formulation. It has been seen that only some of the small-size instances can be solved optimally by this way. So the efficiency of the proposed heuristic method is verified in small-size instances whose optimal solutions are found. For medium- and big-size instances, heuristics’ results and CPU times are demonstrated. A comparative evaluation with a branch and bound algorithm that can be found in the literature is also carried out, and results are presented.     

An approach to integrate production-transportation planning and scheduling in an aluminium supply chain network

This article is based on a real-life problem of a global aluminium supply chain network driven by an aluminium smelter. At each echelon of the aluminium supply chain network, several members are involved which are scattered around the world. Producing aluminium begins with bauxite mining. Next, aluminium oxide is made from bauxite and finally aluminium is produced from aluminium oxide. A novel type of mixed-integer decision-making model, including a time-continuous representation of the planning period, is presented. The model enables coordination of production quantities and times of all supply chain members in order to minimise production and transportation costs of the whole supply chain minus bonus payments for early deliveries which are stipulated between the supply chain network and its customers. Material flows can take place with or without temporary storage of intermediate products at supplying and/or receiving sites. Furthermore, relax-and-fix heuristics are presented. A number of randomly generated scenarios are presented to demonstrate that the heuristics can find nearly optimal solutions along with drastically reduced computation times. The relax-and-fix heuristic enables iterative planning between centralised and decentralised decision makers.     

A branch-and-bound algorithm for the cell formation problem

The Cell Formation Problem (CFP) is an important optimisation problem in manufacturing. It has been introduced in the Group Technology (GT) and its goal is to group machines and parts processed on them into production cells minimising the movement of parts to other cells for processing and maximising for each cell the loading of its machines with operations on its parts. We consider one of the computationally hardest formulations of this problem – the CFP with a variable number of cells and the grouping efficacy objective, which is a fractional function. The CFP literature contains many heuristic algorithms, but only a small number of exact approaches especially for this formulation. In the current paper, we present an exact branch-and-bound algorithm for the same hard CFP formulation. To linearise the fractional objective function, we apply the Dinkelbach approach. We have been able to solve 24 of the 35 instances from the well known GT benchmark. For the remaining 11 instances, the difference in the grouping efficacy with the best known solutions is less than 2.6%.     

Job-shop like manufacturing system with variable power threshold and operations with power requirements

This paper addresses an important issue in manufacturing by considering the scheduling of a Job-shop like manufacturing system involving a power threshold that must not be exceeded over time. A power profile is attached to operations that must be scheduled. This power profile presents a consumption peak at the start of process in order to model most of real-world machining operations. These operations must be scheduled according to the instantly available power threshold. A mathematical formulation of the problem is proposed; its main goal is to minimise the total completion time of all operations. A set of instances is built based on classical format of instances for the Job-shop problem. As it is time-consuming to obtain exact solutions on these instances with the CPLEX solver, a Greedy Randomised Adaptive Search Procedure hybridised with an Evolutionary Local Search (GRASP × ELS) metaheuristic is designed. The GRASP × ELS is compared with two other metaheuristics: a Variable Neighbourhood Search and a Memetic Algorithm. The GRASP × ELS is also compared with several algorithms developed in the literature for the classical job-shop problem. Results show the relevancy of the metaheuristic approaches both in terms of computational time and quality of solutions.     

Multi-objective production scheduling with controllable processing times and sequence-dependent setups for deteriorating items

The production scheduling problem is to find simultaneously the lot sizes and their sequence over a finite set of planning periods. This paper studies a single-stage production scheduling problem subject to controllable process times and sequence-dependent setups for deteriorating items. The paper formulates the problem by minimising two objectives of total costs and total variations in production volumes simultaneously. The problem is modelled and analysed as a mixed integer nonlinear program. Since it is proved that the problem is NP-hard, a problem-specific heuristic is proposed to generate a set of Pareto-optimal solutions. The heuristic is investigated analytically and experimentally. Computational experiences of running the heuristic and non-dominated sorting genetic algorithm-I over a set of randomly generated test problems are reported. The heuristic possesses at least 56.5% (in the worst case) and at most 94.7% (in the best case) of total global Pareto-optimal solutions in ordinary-size instances.     

Improved heuristics and a genetic algorithm for finding short supersequences

In this paper several heuristics and a genetic algorithm (GA) are described for the Shortest Common Supersequence (SCS) problem, an NP-complete problem with applications in production planning, mechanical engineering and data compression. While our heuristics show the same worst case behaviour as the classical Majority Merge heuristic (MM) they outperform MM on nearly all our test instances. We furthermore present a genetic algorithm based on a slightly modified version of one of the new heuristics. The resulting GA/heuristic hybrid yields significantly better results than any of the heuristics alone, though the running time is much higher. Received: 1 April 1997 / Accepted: 11 September 1997     

Mixed-integer linear programming method for multi-degree and multi-hoist cyclic scheduling with time windows

Multi-degree cyclic hoist scheduling and multi-hoist cyclic scheduling are both capable of improving the throughput in an automatic electroplating line. However, previous research on integrated multi-degree and multi-hoist cyclic scheduling is rather limited. This article develops an optimal mixed-integer linear programming model for the integrated multi-degree and multi-hoist cyclic scheduling with time window constraints. This model permits overlap on hoist coverage ranges, and it proposes new formulations to avoid hoist collisions, by which time window constraints and tank capacity constraints are also formulated. A set of available benchmark instances and newly generated instances are solved using the CPLEX solver to test the performance of the proposed method. Computational results demonstrate that the proposed method outperforms the zone partition heuristic without overlapping, and the throughputs are improved by a significant margin using the proposed method, especially for large-size instances.     

A genetic algorithm for solving the economic lot scheduling problem in flow shops

In this study, we propose a hybrid genetic algorithm (HGA) to solve the economic lot scheduling problem in flow shops. The proposed HGA utilizes a so-called Proc PLM heuristic that tests feasibility for the candidate solutions obtained in the evolutionary process of genetic algorithm. When a candidate solution is infeasible, we propose to use a binary search heuristic to ‘fix’ the candidate solution so as to obtain a feasible solution with the minimal objective value. To evaluate the performance of the proposed HGA, we randomly generate a total of 2100 instances from seven levels of utilization rate ranged from 0.45 to 0.80. We solve each of those 2100 instances by the proposed HGA and the other solution approaches in the literature. Our experiments show that the proposed HGA outperforms traditional methods for solving the economic lot scheduling problem in flow shops.     

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.     

A robust bus evacuation model with delayed scenario information

Due to natural or man-made disasters, the evacuation of a whole region or city may become necessary. Apart from private traffic, the emergency services also need to consider transit-dependent evacuees which have to be transported from collection points to secure shelters outside the endangered region with the help of a bus fleet. We consider a simplified version of the arising bus evacuation problem (BEP), which is a vehicle scheduling problem that aims at minimizing the network clearance time, i.e., the time needed until the last person is brought to safety. In this paper, we consider an adjustable robust formulation without recourse for the BEP, the robust bus evacuation problem (RBEP), in which the exact numbers of evacuees are not known in advance. Instead, a set of likely scenarios is known. After some reckoning time, this uncertainty is eliminated and planners are given exact figures. The problem is to decide for each bus, if it is better to send it right away—using uncertain information on the evacuees—or to wait until the the scenario becomes known. We present a mixed-integer linear programming formulation for the RBEP and discuss solution approaches; in particular, we present a tabu search framework for finding heuristic solutions of acceptable quality within short computation time. In computational experiments using both randomly generated instances and the real-world scenario of evacuating the city of Kaiserslautern, Germany, we compare our solution approaches.     

Mathematical models and solution methods for optimal container terminal yard layouts

In this paper, we introduce an integer linear program for planning the layout of container yards. We concentrate on a special layout class of container yards which we call yard layout with transfer lanes. For those layouts typically rubber tired gantry cranes are used for stacking operations and trucks for horizontal transports. We show that the optimization model can be formulated as a special type of a resource constrained shortest path problem for which the LP relaxation always has at least one integer optimal solution. This model is restricted to a rectangular storage yard which allows a linear formulation. For an arbitrary shaped container yard we adopt the model and develop a variable neighborhood descent (VND) heuristic for solving non-rectangular instances. Concerning the rectangular case, we show that the VND heuristic achieves optimal solutions for 38% of the realistic test instances.     

A heuristic,dynamic programming-based approach for a two-dimensional cutting problem with defects

This paper deals with a two-dimensional cutting problem in which small rectangular items of given types are to be cut from a rectangular large object which contains several defects. It is assumed that the number of pieces of each small item type which can be cut from the large object is not limited. In addition, all cuts are restricted to be of the guillotine-type and the number of stages necessary to perform all cuts is not limited. Furthermore, no small item must overlap with a defective region. The objective is to maximize the value of the cut small items. For the solution of the above-described problem, a heuristic, dynamic programming-based approach is presented which overcomes the structural and computational limitations of previously-proposed methods. In the presence of defects, the representation of the defective regions and the definition of discretization sets are revisited. This allows for an improvement of the computational efficiency as well as of the storage space requirements for solving the given problem with any number of defects in this approach. We further analyze the computational complexity of the algorithm and identify the factors which affect its running time. The proposed method is evaluated by means of a series of detailed numerical experiments which are performed on problem instances extracted from the literature, as well as on randomly generated instances. The experiments do not only illustrate how the suggested method is able to identify optimal solutions of the test problem instances, but they also explain why already existing methods fail to do so. Furthermore, the computational results indicate that the proposed method, equipped with the newly-proposed discretization sets, is capable of efficiently generating a high percentage of optimal solutions to the corresponding problem with defects.     

Ant colony optimisation algorithm for distribution-allocation problem in a two-stage supply chain with a fixed transportation charge

In a fixed charge transportation problem, each route is associated with a fixed charge (or a fixed cost) and a transportation cost per unit transported. The presence of the fixed cost makes the problem difficult to solve, thereby requiring the use of heuristic methods. In this paper, an algorithm based on ant colony optimisation is proposed to solve the distribution-allocation problem in a two-stage supply chain with a fixed transportation cost for a route. A numerical study on benchmark problem instances has been carried out. The results obtained for the proposed algorithm have been compared with that for the genetic algorithm-based heuristic currently available in the literature. It is statistically confirmed that the proposed algorithm provides significantly better solutions.     

On the worst case performance of TESSA

TESSA is a facility layout heuristic for obtaining a maximal planar adjacency graph (MPG) from relationship chart data. Computational experiments performed by Boswell (1992b) have shown that the algorithm produces good quality solutions, almost all of which are above 90% of the often unattainable upper bound. In this paper we show that the heuristic displays arbitrarily bad theoretical worst case performance.     

Sequence based heuristics for two-dimensional bin packing problems

This article addresses several variants of the two-dimensional bin packing problem. In the most basic version of the problem it is intended to pack a given number of rectangular items with given sizes in rectangular bins in such a way that the number of bins used is minimized. Different heuristic approaches (greedy, local search, and variable neighbourhood descent) are proposed for solving four guillotine two-dimensional bin packing problems. The heuristics are based on the definition of a packing sequence for items and in a set of criteria for packing one item in a current partial solution. Several extensions are introduced to deal with issues pointed out by two furniture companies. Extensive computational results on instances from the literature and from the two furniture companies are reported and compared with optimal solutions, solutions from other five (meta)heuristics and, for a small set of instances, with the ones used in the companies.     

A mixed-integer programming formulation and Lagrangean relaxation for the cross-dock door assignment problem

In a cross-dock, goods are unloaded from incoming trucks, consolidated according to their destinations, and then, loaded into outgoing trucks with little or no storage in between. In this paper, we study the cross-dock door assignment problem in which the assignment of incoming trucks to strip doors, and outgoing trucks to stack doors is determined, with the objective of minimising the total material handling cost. We present a new mixed integer programming formulation which is embedded into a Lagrangean relaxation that exploits the special structure of the problem to obtain bounds on the optimal solution value. A primal heuristic is used at every iteration of the Lagrangean relaxation to obtain high quality feasible solutions. Computational results obtained on benchmark instances (with up to 20 origins and destinations, and 10 strip and stack doors) and on a new and more difficult set of instances (with up to 50 origins and destinations, and 30 strip and stack doors) confirm the efficiency of the algorithm.     

A vulcanising decision planning as a particular one-dimensional cutting stock problem with limited part-related tooling in make-to-order industrial environments

A specialised case of the classical one-dimensional cutting stock problem (1D-CSP) with six main additional features is adapted in this paper to model and solve planning unit operations with limited resources in the make-to-order industrial environment, generating a new decision-making problem. The objective is to satisfy demand using the minimum number of manufacturing cycles. Although there is a large number of applications, this paper proposes a decision model directed at the vulcanising operation during the manufacturing of rubber curved hoses in the automotive industry. Because each vulcanising cycle (VC) uses a considerable amount of resources, the need to minimise the total number of VCs is of importance due to its direct relationship with lead time and productivity. An integer-programming model based on a network optimisation formulation is proposed to solve the problem to optimality and allows for construction of the mathematical model. In addition, due to the limited capacity of computers to solve large instances, a heuristic is developed to obtain near-optimal solutions. Scheduling issues are found in the optimal solution of the integer-programming model, but the heuristic overcomes such obstacles. Numerical experiments demonstrate the efficiency of the 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.