In this paper, we propose a formulation of DEA with constraints of weight intervals given by a group of decision makers. The importance grades of items are considered as probability measures whose sum is equal to one. In order to make weights in DEA represent importance grades given by decision makers, all the given data are divided by respective input/output data. The efficiency values obtained from the normalized data and the original data are the same. In DEA, the product of data and weight is considered as the importance grade of each item rather than the weight itself. By the normalization, the product of data and weight becomes equal to the weight itself. Therefore, the optimal weights obtained from the normalized data naturally represent the importance grades of decision makers. The sum of the optimal weights for inputs obtained in DEA becomes one and the sum of the optimal weights for outputs comes out to be the efficiency value in DEA. Assuming a group of decision makers, the interval importance grade is formed from many decision makers' importance grades, which can be obtained through AHP. If the given information with respect to the evaluation contains partial ignorance, the importance grades are assumed as semi-mobile probability mass in the setting of Dempster-Shafer theory. Both of these probabilistic weights are easily included as weight constraints in CCR model of DEA with normalized data.

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For optimally designing layouts of a factory or a shop, we have to consider constraint with respect to a site or a building, i.e., floor constraint. Also, we have to adapt shapes of plants or shops to be placed in the site or the building. Then, it is important to decrease both initial cost, e.g., site and building costs, and running cost, e.g., material handling costs. In this paper, we deal with layout problems with floor constraint. First, we formulate the problems as bicriteria problems. The bicriteria functions consist of a total of distances between shops weighted by an inter-station flow cost respectively and a dead space area in a floor. In the formulation, we introduce a variable aspect ratio for each rectangular shop. We propose two algorithms for solving the problems, i.e., a Simulated Annealing algorithm (SA) and an improved Genetic Algorithm adopting the idea of the Evolution Strategy (ES-GA). Based on numerical experiments, we clarify the effect of introducing variable aspect ratios on improving optimality of layout design. Then, we show that ES-GA performance is superior to that of SA. Also, we propose a method for generating Pareto solutions for multi-objective problems based on Data Envelopment Analysis (DEA). This method extracts the candidates of Pareto solutions using the ES-GA, and finally generates Pareto solutions using DEA. We clarify the effectiveness of the proposed method, based on numerical experiments. Finally, by tuning the weight for bicriteria, obtaining a compact layout that has a lower total weighted distance and a smaller dead space is possible.

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This paper proposes a heuristic algorithm to minimize makespan in a machineunfixed, Machining-Assembly Flow Shop (MAFS) scheduling problem, where parts of each job are machined on any unprespecified parallel machining-centers at the machining stage and then assembled by one robot at the assembly stage after all parts have been completed. This problem is more complex than the machine-fixed MAFS scheduling problem, because both assignments of all parts on parallel machines and scheduling jobs should be simultaneously determined in an optimal manner. Since this problem is strongly NP-complete like a machine-fixed MAFS problem, a large-sized problem can not be solved through any optimal method such as a branch and bound methed. Therefore, a heuristic algorithm is proposed in this paper by converting the original "machine-unfixed" problem into a "machine-fixed" problem, and then by applying the current best heuristic algorithm proposed for a machine-fixed case to the converted problem. The problem conversion can be implemented by assigning parts on parallel machines, but a simple balanced-loading method does not work well, because it does not incorporate the basic idea used in scheduling jobs. In the proposed part-assignment method, a sort of unbalanced-loading method is employed as long as the completion time at the machining stage does not increase. Numerical experiments are performed in comparison with a branch and bound method (B&B), showing that the proposed heuristic algorithm can provide solutions very close to optimal solutions for a small-sized problem and that it is superior to the one-hour truncated B&B for a large-sized problem.

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This study considers the effectiveness of TOC scheduling by developing an extended algorithm so as to be applicable even in a job shop environment. TOC originated from a scheduling technique named Drum-Buffer-Rope (DBR). The DBR technique is based on following steps. (1) Identify the primary bottleneck resource, (2) Exploit the bottleneck by scheduling it first, (3) Subordinate scheduling of all other resources to that of bottleneck resource. TOC scheduling seems appropriate for flow shop environments, and has been shown to be quite effective in such kind of production system. But as production systems become more complicated, like a job shop, it becomes increasingly difficult to identify a single resource as a constraint. A few past studies have speculated on the effectiveness of DBR in non-flow shop environments, but none has attempted to analyze its actual use and application range. In order to investigate the application range of the TOC scheduling technique, an extended TOC scheduling technique is proposed, and a criterion, Fd, is defined to classify several kinds of production systems. The extended algorithm is then compared to Tabu search, which is one of the most promising meta-heuristics for considering the critical path as a system constraint. The results show the application range of extended DBR algorithm which considers a single resource as the constraint and suggest that outside this range it is more appropriate to consider the critical path as the constraint.

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An aborescent inventory system consists of one central depot and m retailers(regional warehouses) is considered. The depot is replenished by outside suppliers regularly with a fixed length of replenishment cycle. When inventory arrives, the depot ships out the bulk of inventories immediately to retailers while keeping system safety stocks at the depot. The remaining safety stock is allocated to proper retailers later, to balance inventories and minimize total stock out. The problems in the allocation are, (1) how to determine the allocation quantity for each retailer, and (2) how to determine allocation instance. Many approaches such as "fair share allocation", "complete redistribution", and "optimal allocation" have been presented for the problem (1), and we adopted "complete redistribution", and optimal allocation" in this research. For problem (2), two approaches can be considered. The first approach is to allocate the safety stock at a fixed instance in each cycle which can minimize average shortages compared to other fixed allocation periods. The second approach analyzes shortages in each cycle, and dynamically determines the allocation instance for each cycle. Obviously, the second approach may yield better performance than the first approach. However, there are two difficulties in the second approach. The first one is that because demand is stochastic, we can not calculate the exact number of future stock out, and consequently are unable to predetermine optimal allocation instance. The traditional dynamic programming technique is also inappropriate for this difficulty, because we can not identify which retailer needs the centralized safety stock to be allocated. To cope with these difficulties, a heuristic for the second approach is proposed in this paper. The proposed heuristic has an indicator to determine immediate allocation, comparing average shortages between immediate allocation and next period allocation. If immediate allocation results in less average shortage, then allocate immediately, and otherwise do not allocate. Average shortage of the proposed approach is compared with the first approach. Computational results show that the proposed heuristic may reduce stock out more than 35% without increasing inventories compared to the first approach. Sensitivity analyses are also presented varying coefficient of variance, cycle length, number of retailers and allocation policy.

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This paper deals with the problem of designing a production system for a combination of made-to-stock (MTS) and make-to-order (MTO) products where the production facility is common for these two types of products. A hierarchical production planning model is introduced in order to design the production system. The buffer capacity is set as a decision variable for determining production capacity at a higher planning level, and the rule for allocating the production capacity to types of products is adopted as a decision variable at a lower level. Individual production quantities of MTS and MTO products cannot be determined in the production system for a combination of MTO and MTS products because the production capacity is common for the two different types of products. Additionally, routing and processing time for MTO products are specified by to customer's specifications, i.e., to order. The difference in routing and processing time between MTS and MTO products affects the manufacturing performance. In this paper, we present a method for designing an efficient production system for a combination of MTS and MTO products. The unfilled rate of the market demand for MTS products and the manufacturing time of MTO products are used as measures of manufacturing performance. The following points were clarified through a series of numerical experiments. (1) How will such manufacturing performance factors as unfilled rate of the market demand for MTS products and the manufacturing time of MTO products be affected by the differences in order quantity, routing and unit processing time between MTS and MTO products? (2) How will these manufacturing performances be affected by the assigned rules of production capacity and priority options for processing of MTS and MTO products? (3) What relationships are there between buffer production capacity of MTS products and manufacturing time of MTO products? (4) How much buffer capacity for production is required to control the manufacturing time of MTO products and the buffer inventory of MTS products within their acceptable levels?

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