Determination of the number of containers,production kanbans and withdrawal kanbans; and scheduling in kanban flowshops - Part 1

In the first part of this paper, we consider a kanban-controlled flowshop and present recursive equations for time-tabling of containers in a given sequence. The flowshop is characterized by the following: a production batch of a part-type (or job) divided into kanban lots or containers; production kanbans to control the loading of containers on machines or workstations; withdrawal kanbans to regulate the movement of containers between two consecutive buffer storages; periodic material handling of containers; dual blocking mechanisms operative on workstations and material handling; and sequence-dependent set-up times of containers. Considering different types of problems, recursive equations have been developed for time-tabling of containers in a given sequence.     

Determining the number of kanbans: a step toward non-stock-production

Just-in-time (JIT) production is a philosophy that calls for reducing work-in-process (WIP) inventory to aid process improvement and reduce process variability. In some cases, JIT production has been misinterpreted as a method that would lead to zero or minimal WIP with a lot size of one. There are no models or theories to achieve the JIT goal, i.e. non-stock-production (NSP), and, in particular, to help determine when and where to maintain this minimal inventory. A kanban system acts as the nerve of a JIT production system whose functions are to direct materials just-in-time to workstations in stages of manufacturing, and to pass information as to what and how much to produce. Indeed, the number of kanbans between two adjacent workstations decides the inventory level of that pair of workstations. With the objective of minimizing WIP inventory level, one model dealing with three cases of production configuration is developed for deciding the optimum number of kanbans. The model is then solved using a Markov process approach which considers the demand of finished products as the departure rate and the production rates of stations as arrival rate. In this paper, the model and solution procedure are illustrated with a numerical example.     

Prioritization of kanbans in the case of a single station serving multiple downstream stations

When implementing the kanban method in non-serial production lines, an interesting prioritization problem arises. Often a single server station will be linked with M different downstream stations via M separate kanban loops. Then the K-priority problem may be described as determining which kanban card should be processed next, given that empty cards are waiting in more than one loop. The objective in prioritizing the kanbans is to reduce back order or shortage costs and inventory costs at the downstream stations. Utilizing the theory of Markovian decision process and dynamic programming concepts, a solution to the K-priority problem is developed. This solution is labelled the K-rule, and was found to outperform the first-come-first-served and longest queue rules, plus a cost inclusive heuristic rule, in experimental tests,     

Configuring layout in unidirectional loop manufacturing systems

This paper addresses the layout configuration problem of workstations in a unidirectional loop manufacturing system. In this popular unicyclic material handling facility, the material transporters depart from the input/output station, traverse each workstation exactly once, and then return to the input/output station. We show the important properties of this unidirectional material handling loop network. Based on these characterizations, both heuristic and branch-and-bound algorithms are proposed to solve such NP-complete layout problems. Computational experiments with problem sizes up to 100 workstations are reported. Both the problem size and the material flow density have been found to affect the solution quality and the computational efficiency. The proposed methods appear efficient and effective for solving these layout problems.     

Optimal method for changing the number of kanbans in the e -Kanban system and its applications

The Toyota Motor Corporation has recently developed a new kanban system called ‘e-Kanban’, which is a parts ordering information system that operates within the communications network established between Toyota and its suppliers. One of the goals for developing the e-Kanban system was to introduce an efficient means for properly changing the number of kanbans once the required number has been calculated, as changing the number of kanbans in the kanban system directly affects the order quantity. Consequently, it is very important to monitor carefully and control changes in the number of kanbans. The paper investigates and proposes an effective method for changing the number of kanbans using the e-Kanban system. Applying this method to three problems, it is shown that the e-Kanban system can be implemented more efficiently and effectively than the original kanban system.     

Flexible kanbans to enhance volume flexibility in a JIT environment: a simulation based comparison via ANNs

Kanbans play an important role in the information and material flows in a JIT production system. The traditional kanban system with a fixed number of cards does not work satisfactorily in an unstable environment. In the flexible kanban-type pull control mechanism the number of kanbans is allowed to change with respect to the inventory and backorder level. Based on the need for the flexible kanban, a method was proposed by (Husseini, S.M.M., O’Brien, C., and Hosseini, S.T., 2006. A method to enhance volume flexibility in JIT production control. International Journal of Production Economics, 104 (2), 653–665), using an integer linear programming technique, to flexibly determine the number of kanbans for each stage of a JIT production system, minimising total inventory cost for a given planning horizon. Here, the effectiveness of the method proposed by Husseini et al. is examined by a case study and compared with the results for the conventional method of fixed kanban determination. This is also confirmed by a simulation study using artificial neural networks (ANNs). The main aim of this paper is to show the cost advantage for Husseini et al.'s method over the conventional method in fluctuating demand situations, and especially to prove that simulation via ANNs ensures a simplified representation for this method and is time saving.     

A simulation study of container size in two-card kanban systems

Setting container sizes is one of the first decisions that users of kanban systems must address. Yet researchers have largely assumed container sizes to be given. This paper investigates the effect of container size on average inventory and customer service levels in a two-card kanban system processing multiple part types. Container size and the number of kanbans are varied in tandem so that total in-process inventory capacity remains constant. Simulation results show that smaller containers lead to smaller average total inventories. The surprise is that smaller containers do not always lead to poorer average customer service. Smaller container sizes can lead to better average customer service when the costs of greater total setup time are offset by the benefits of more frequent material handling, that is less frequent station material starvation, and improved finished goods part mix. This occurs primarily when container size is larger than average finished-goods order size and when setup times are relatively short.     

Effect of discrete batch WIP transfer on the efficiency of production lines

In this paper, the effect of discrete batch transfer of WIP between workstations on the efficiency of asynchronous production lines is analysed via a simulation model. The processing times are assumed to be random variables distributed according to specific distribution functions. The WIP transfer design problem involves determining the number of containers to allocate to each buffer location and the container capacity. Interesting and valuable information for practitioners has been obtained. It is found that loss in capacity occurs in the first few stations. Another finding is that an important portion of the lost capacity can be regained by allocating two containers to each buffer location, and if it is impossible to assign two containers to each location, then no single-container location should be adjacent to another single-container location.     

Integrated scheduling and self-reconfiguration for assembly job shop in knowledgeable manufacturing

The problems of integrated assembly job shop (AJS) scheduling and self-reconfiguration in knowledgeable manufacturing are studied with the objective of minimising the weighted sum of completion cost of products, the earliness penalty of operations and the training cost of workers. In AJS, each workstation consists of a certain number of teams of workers. A product is assumed to have a tree structure consisting of components and subassemblies. The assembly of components, subassemblies and final products are optimised with the capacity of workstations simultaneously. A heuristic algorithm is developed to solve the problem. Dominance relations of operations are derived and applied in the development of the heuristic. A backward insertion search strategy is designed to locally optimise the operation sequence. Once the optimal schedule is acquired, the teams are reconfigured by transferring them from workstations of lower utilisation to those of higher utilisation. Effectiveness of the proposed algorithm is tested by a number of numerical experiments. The results show that the proposed algorithm promises lower total cost and desirable simultaneous self-reconfiguration in accordance with scheduling.     

An effective heuristic for scheduling a yard crane to handle jobs with different ready times

In land-constrained port container terminals, yard cranes are commonly used for handling containers in a container yard to load containers onto or unload containers from trucks. However, yard cranes are bulky, slow and need to move frequently between their work locations. As it is common that the container flow in a terminal is bottlenecked by yard crane operations, effective work schedules of yard cranes are needed to increase the terminal’s throughput. This article studies the problem of scheduling a yard crane to perform a given set of container handling jobs with different ready times. The objective is to minimize the sum of job waiting times. It is noted that the scheduling problem is NP-complete. This research develops a heuristic to solve the scheduling problem and an algorithm to find lower bounds for benchmarking the schedules found by the heuristic. The performance of the heuristic is evaluated by a set of test problems generated on the basis of real-life terminal operations data. Indeed, the computational results show that the proposed heuristic can find effective solutions for the scheduling problem.     

Optimised loading patterns for intermodal trains

This paper considers one important aspect of operations planning referred to hereafter as train planning. Train planning is the process of spatially assigning containers to specific wagons (also known as railcars) on an intermodal train. The spatial arrangement of containers on a train can have a significant influence over the amount of time and energy consumed in the handling of containers. Efficient train planning can also maximise utilisation of wagon carrying capacity. This study proposes a mixed-integer programming model to determine the arrangement of containers on a train to minimise a weighted sum of number of wagons required and equipment working time. Due to the large number of variables, the proposed model cannot be solved in a timely manner for practical problems. This is addressed by applying heuristic algorithms local search and simulated annealing. Discrete-event simulation of an intermodal terminal is used to evaluate the proposed methods and to illuminate various properties of the model.     

Joint lot-sizing and scheduling for multi-stage multi-product flow shops

Here we consider a multi-product flow shop under capacity constraints and develop an efficient heuristic procedure to determine joint lot sizes, production sequence and production schedule. We treat setup costs as fixed in the short run and thus independent of the number of setups. Loss of production capacity due to setup times is explicitly accounted for and the transfer of portions of a production lot between stages is permitted. The procedure is based on identifying the bottleneck workcentre and synchronizing production schedules at all other workcentres with the bottleneck workcentre such that product throughput requirements are met with minimal inventory costs. A compact procedure for constructing the Gantt charts is also presented. Conversion of the lot si2es and transfer batches into an information control system with kanbans is also presented.     

A decomposition-based approach for the selection of standardized modular containers

The standardisation of packaging and containers for product handling has potential benefits from transportation, material handling and environmental perspectives. Likewise, standardised modular containers play an important role in the Physical Internet (PI). To support implementation of standard modular containers, we introduce a mathematical model to select a requisite number of modular containers to pack a set of products to maximise space utilisation. A decomposition-based solution methodology is developed and presented. Computational results from industry-based problem instances indicate that using standardised modular containers results in increased space utilisation at the unit load level. This finding substantiates the use of modular containers in moving toward the PI.     

Data envelopment analysis of AGV fleet sizing at a port container terminal

A decision-making approach based on Data Envelopment Analysis (DEA) for determining the efficient container handling processes (considering the number of employed Automated Guided Vehicles (AGVs)) at a port container terminal (PCT) is presented in this paper. Containers are unloaded from the ship by quay cranes and transported to the storage area by AGVs. We defined performance measures of proposed container handling processes and analysed the effects when changing the number of AGVs. The values of performance measures were collected and/or calculated from simulation. Container handling process, with a fixed number of quay cranes, when a different number of AGVs is used to transport containers from berth to assigned locations within storage area, represents a decision-making unit (DMU). We applied the basic CCR (Charnes, Cooper and Rhodes) DEA model with two inputs: average ship operating delay costs and average operating costs of employed equipment at a PCT, and two outputs: average number of handled import containers per ship and weighted average utilisation rate of equipment at a PCT. DEA method proved to be useful when testing different DMUs and when determining efficient DMUs for planning purposes. This study shows that efficiency evaluation of AGV fleet sizing and operations is useful for planning purposes at PCTs.     

Improving the equality of workload assignments in assembly lines

Most heuristic and optimal methods for assembly line balancing are designed either to minimize the number of workstations required given a production rate, or to maximize the production rate given a fixed number of workstations. This singular focus on line design efficiency typically results in an imbalanced allocation of tasks among the stations. This paper presents a new procedure that rebalances a given solution to level the allocation of tasks. Characteristics of dominant levelled solutions are identified and incorporated into this heuristic procedure. Computational results indicate that the procedure is very effective in levelling workloads.     

Book review of Global Strategic Management,by P. Lasserre,Palgrave Macmillan,Basingstoke, 2003, xx + 454 pp., £24.99, softcover (ISBN 0 333 79375 7)

This paper considers the simultaneous scheduling of material handling transporters (such as automatic guided vehicles or AGVs) and manufacturing equipment (such as machines and workcentres) in the production of complex asembled product. Given the shipping schedule for the end-items, the objective of the integrated problem is to minimize the cumulative lead time of the overall production schedule (i.e. total makespan) for on-time shipment, and to reduce material handling and inventory holding costs on the shop-floor. The problem of makespan minimization is formulated as a transportation integrated scheduling problem, which is NP-hard. For industrial size problems, an effective heuritsic is developed to simultaneouly schedule manufacturing and material handling operations by exploting the critical path of an integrated operation network. The performance of the proposed heuristic is evaluated via extensive numerical studies and compared with the traditional sequential scheduling approach. The superiority of the integrated heuristic is well documented.     

Solving cell formation and task scheduling in cellular manufacturing system by discrete bacteria foraging algorithm

We consider a joint decision model of cell formation and task scheduling in cellular manufacturing system under dual-resource constrained (DRC) setting. On one hand, machines and workers are multi-functional and/or multi-skilled, and they are grouped into workstations and cells. On the other hand, there is a processing sequence among operations of the parts which needs to be dispatched to the desirable workstations for processing. Inter-cell movements of parts can reduce the processing times and the makespan but will increase the inter-cell material handling costs. The objective of the problem is to minimise the material handling costs as well as the fixed and operating costs of machines and workers. Due to the NP-hardness of the problem, we propose an efficient discrete bacteria foraging algorithm (DBFA) with elaborately designed solution representation and bacteria evolution operators to solve the proposed problem. We tested our algorithm using randomly generated instances with different sizes and settings by comparing with the original bacteria foraging algorithm and a genetic algorithm. Our results show that the proposed DBFA has better performance than the two compared algorithms with the same running time.     

The effect of sudden material handling system breakdown on the performance of a JIT system

In this paper we explore the impact of sudden breakdown of the material handling system on the performance of a traditional kanban system (TKS). TKS, which is an element of the just-in-time system, is designed to operate in an ideal environment such as constant processing times and uninterrupted processing. However, in a real life environment, the TKS could be subjected to various unpredictable factors including stochastic processing times and process interruption due to equipment failure. These factors would seriously strain the performance of TKS. We consider a TKS in which some stations are dependent on a material handling system to move parts between them. We study the effect of a sudden breakdown of such a material handling system on the performance of the TKS. In addition, we also study a newly developed kanban system (which dynamically and systematically manipulates the number of kanbans in order to offset the blocking and starvation caused by these factors during a production cycle) under the same conditions. We refer to the new system as the 'flexible kanban system' (FKS). We compare the overall performances of the TKS and FKS by considering a variety of cases. We present the solution procedure, results and discussion for these cases.     

A mixed integer linear programming formulation for optimal balancing of mixed-model U-lines

The mixed-model U-line balancing problem was first studied by Sparling and Miltenburg (Sparling, D. and Miltenburg, J., 1998. The mixed-model U-line balancing problem. International Journal of Production Research, 36(2), 485–501) but has not been mathematically formulated to date. This paper presents a mixed integer programming formulation for optimal balancing of mixed-model U-lines. The proposed approach minimises the number of workstations required on the line for a given model sequence. The proposed formulation is illustrated and tested on an example problem and compared with an existing approach. This paper also proposes a new heuristic solution procedure to handle large scale mixed-model U-line balancing problems. A comprehensive experimental analysis is also conducted to evaluate the performance of the proposed heuristic. The results show the validity and usefulness of the proposed integer formulation and effectiveness of the proposed heuristic procedure.     

Control of Material Handling Transporter in Automated Manufacturing

This paper presents a real time routing method for material handling transporters in automated manufacturing shops where the performance criterion is to maximize throughput The static version of the routing problem is identified as a one machine due date problem with sequence dependent processing times and sequence dependent due dates. For real time application, a heuristic method is proposed, and its performance is evaluated and compared to other currently known rules using discrete simulation on hypothetical cell operations.