The design of simple subcontracting rules for make-to-order shops: An assessment by simulation

Subcontracting can be an important means of overcoming capacity shortages and of workload balancing, especially in make-to-order companies characterized by high variety, high demand variation and a job shop configuration. But there is a lack of simple, yet powerful subcontracting rules suitable for such contexts. The few existing rules were developed for single work center shops and neglect the actual subcontracting lead time, meaning some subcontracted jobs are destined to become tardy. This study uses Workload Control theory on matching required and available capacity over time to propose four new rules that address these shortcomings. The new rules are compared against four existing rules using an assembly job shop simulation model where the final, assembled product consists of several sub-assemblies that either flow through an internal job shop or are subcontracted. The best new rules stabilize the direct load queuing in front of a work center and significantly improve performance compared to the existing rules. For example, when the workload exceeds capacity by 10%, a 50% reduction in percentage tardy can be achieved. By examining how the workload behaves over time, we reveal that improvements come from selectively subcontracting the sub-assemblies that would otherwise cause overloads, thereby cutting off peaks in the workload.     

A multi-period order selection problem in flexible manufacturing systems

We consider a multi-period order selection problem in flexible manufacturing systems, which is the problem of selecting orders to be produced in each period during the upcoming planning horizon with the objective of minimising earliness and tardiness costs and subcontracting costs. The earliness and tardiness costs are incurred if an order is not finished on time, while subcontracting cost is incurred if an order is not selected within the planning horizon (and must be subcontracted) due to processing time capacity or tool magazine capacity. This problem is formulated as a 0–1 integer program which can be transformed into a generalised assignment problem. To solve the problem, a heuristic algorithm is developed using a Lagrangian relaxation technique. Effectiveness of the algorithm is tested on randomly generated problems and results are reported.     

同类机下的供应链排序及转包策略

研究了一类工件排序与转包关联的模型,即工件既可以在制造商的同类机上加工,也可以较高费用转包给某个承包商加工.需要确定被转包的工件集,以及未转包工件的加工顺序,使得工件加工与转包费用在工件最大完工时间满足限制条件下达到极小.证明了该问题的NP困难性,用数学规划方法构造多项式时间近似算法,并分析算法性能比.     

Transportation planning in freight forwarding companies: Tabu search algorithm for the integrated operational transportation planning problem

The integrated operational transportation planning problem extends the traditional vehicle routing and scheduling problem by the possibility of outsourcing a part of the requests by involving subcontractors. The purpose of this paper is to present the integrated planning problem and to propose an approach for solving it by a tabu search heuristic. Existing approaches from literature which discuss vehicle routing combined with outsourcing regard only one specific type of subcontracting. This paper describes and explores the complex situation where an own fleet and several types of subcontracting are used for request fulfillment. As the approach contains new aspects, unknown to the literature so far, tabu search is extended to special types of moves. On the basis of computational results the cost structure is analyzed in order to investigate the long-term planning question whether and to what extend it is profitable to maintain an own fleet.     

Aggregate–disaggregate approach to an airfreight forwarder’s planning under uncertainty: a case study

Resource planning of airfreight forwarders is a complex endeavor, requiring decisions to be made in a dynamic and uncertain environment. Airfreight forwarders acquire airfreight spaces from three sources: allotment from carriers, retail from carriers and subcontracting to partners, all of which differ in terms of cost, flexibility and timing of booking. This real-life problem has many planning decisions (bookings in terms of carriers, route, time, ULDs, etc.). In this case study, we propose an aggregate–disaggregate approach and focus on the most critical decisions. A two-stage stochastic dynamic program first determines, in aggregates, the amount of allotment bookings, retail resources, and subcontracting or surplus co-loading. Then, a heuristic is used to disaggregate resource requirements into specific bookings. An analysis is provided to examine the relevant managerial issues. Based on real-life data, we show several patterns of aggregate resource bookings with respect to different levels of demand uncertainty and cost parameters. We show that resource disaggregation has to balance cost-effectiveness, capacity flexibility and routing flexibility of a resource plan.     

A study of simple rules for subcontracting in make-to-order manufacturing

We study a low volume component manufacturing operation facing order arrival rate greater than the service rate, thus necessitating subcontracting of some of the orders, for the case where order lead times are exogenous and highly variable. The major objective of the firm is to maximize capacity utilization and minimize tardiness (so as to minimize cost and maximize delivery reliability). Limiting the focus to operational decisions, we develop four heuristic decision rules with varying informational needs and complexity to determine when and which orders should be subcontracted. The performance of the decision rules over a range of environments is examined first under the assumption of perfect information. Then, we investigate the robustness of the policies for up to ±50% error in parameter estimates. The results show that, compared to simpler rules that do not seek to use the shop-workload information in making the subcontracting decision, the performance of the shop-workload feedback based decision rules (1) produce a superior performance, especially when the target utilization is high, and (2) are robust with up to ±50% error in parameter estimates.     

A noniterative multiproduct multiperiod production planning method

Production planning for multiple products on a single production facility over a time horizon requires minimizing the sum of production costs (regular time, overtime and subcontracting) and inventory carrying costs for meeting the known demands of the products. It is shown that the problem can be formulated and solved by a simple and noniterative method of ‘column minima’ even for multiple product situations.     

Optimal control of a dual service rate M/M/1 production-inventory model

We analyse a dual-source, production-inventory model in which the processing times at a primary manufacturing resource and a second, contingent resource are exponentially distributed. We interpret the contingent source to be a subcontractor, although it could also be overtime production. We treat the inventory and contingent sourcing policies as decision variables in an analytical study and, additionally, allow the primary manufacturing capacity to be a decision variable in a subsequent numerical study. Our goal is to gain insight into the use of subcontracting as a contingent source of goods and whether it can fulfill real-world managers' expectations for improved performance. We prove that a stationary, non-randomised inventory and subcontracting policy is optimal for our M/M/1 dual-source model and, moreover, that a dual base-stock policy is optimal. We then derive an exact closed-form expression for one of the optimal base stocks, which to our knowledge is the first closed-form solution for a dual-source model. We use that closed-form result to advantage in a numerical study from which we gain insight into how optimal capacity, subcontracting, and inventory policies are set, and how effectively a contingent source can reduce total cost, capacity cost, and inventory cost. We find that (i) the contingent source can reduce total cost effectively even when contingent sourcing is expensive and (ii) contingent sourcing reduces capacity cost more effectively than it does inventory cost.     

A graph theory approach to subcontracting, machine duplication and intercell moves in cellular manufacturing

We address in this paper the problem of finding an optimal strategy for dealing with bottleneck machines and bottleneck parts in the cell formation process in group technology. Three types of economic decisions are considered: subcontracting, machine duplication and intercell moves. The problem is formulated as a minimum weighted node covering problem in a hypergraph, and we show that it can be solved in polynomial time by finding a maximum weighted stable set in a bipartite graph. We extend this result to cellular manufacturing systems in which the sequence of operations of each part is known in advance.     

Capacitated Lot Sizing for Injection Moulding: A Case Study

This paper considers the medium-term production smoothing problem for the injection moulding department of a Belgian firm. The problem is formulated as a series of one machine capacitated dynamic lot sizing problems, which are then solved by heuristic procedures. Computational results for real-life data are presented. It follows that the capacitated lot sizing approach succeeds in smoothing production such that subcontracting, which was often necessary with the E.O.Q. approach used by the firm, could be avoided in the future. Moreover, total set-up and inventory costs are reduced by about 20%.     

Risk-Based Integration of Strategic and Tactical Capacity Planning

We consider capacity management with a long-term strategic choice, such as the number of production lines to install before demand is known, and short-term tactical decisions relating to production, inventory, and subcontracting (recourse actions made after demand is known). We present an integrated scenario-based mathematical modeling and solution framework. For a single-product environment, we examine properties of total profit as a function of demand and the long-term capacity z. We investigate two measures of risk (profit variance and mean downside risk) and their corresponding profit-risk frontiers. Computational experiments are used to illustrate parameter sensitivity results obtained from the model.     

Operational transportation planning of freight forwarding companies in horizontal coalitions

In order to improve profitability, freight forwarding companies try to organize their operational transportation planning systematically, considering not only their own fleet but also external resources. Such external resources include vehicles from closely related subcontractors in vertical cooperations, autonomous common carriers on the transportation market, and cooperating partners in horizontal coalitions. In this paper, the transportation planning process of forwarders is studied and the benefit of including external resources is analyzed. By introducing subcontracting, the conventional routing of own vehicles is extended to an integrated operational transportation planning, which simultaneously constructs fulfillment plans with overall lowest costs using the own fleet and subcontractors’ vehicles. This is then combined with planning strategies, which intend to increase the profitability by exchanging requests among members in horizontal coalitions. Computational results show considerable cost reductions using the proposed planning approach.     

工件可转包加工的排序问题研究

研究工件可以转包加工的单台机排序问题: 有n个工件, 在零时刻已经到达一个单台机处, 每个工件可以由加工者自有的单台机器加工或者转包给其他机器加工. 如果工件被转包加工, 那么其完工时间等于在自有机器上的加工时间, 而产生的加工费用与在自有机器上加工的费用不同. 假设被转包加工的工件的完工时间和加工费用与转包加工机器的总负载没有关系.目标函数是最小化工件最大完工时间与总加工费用的加权和. 该问题已经被证明是NP-难的. 最后给出该问题的伪多项式时间最优算法, 并且提出一个完全多项式时间近似方案(FPTAS).     

A novel approach for considering layout problem in cellular manufacturing systems with alternative processing routings and subcontracting approach

In this paper a new integrated approach is presented for designing cellular manufacturing system and its inter- and intra-cell layouts. Various production factors such as part demands, alternative processing routings, operation sequences, processing times, capacity of machines, etc. are incorporated in the problem in order to extend its applicability. To increase the accuracy of the inter- and intra-cell layout design, the material handling cost is calculated in terms of the actual position of machines within the cells and regarding the dimensions of the machines and aisle distances. Also, a subcontracting approach is proposed to determine the production volume of parts within the CF and layout design process regarding the production, material handling and outsourcing costs and under demand and machine capacity constraints. To the best of our knowledge, this is the first study that addresses all these design features simultaneously. As the proposed problem is NP-hard, an efficient GA is employed to solve it. Finally, numerical examples adopted from the literature are used to verify the proposed approach.     

Contribution of simulation to the optimization of maintenance strategies for a randomly failing production system

This paper compares two strategies for operating a production system composed of two machines working in parallel and a downstream inventory supplying an assembly line. The two machines, which are prone to random failures, undergo preventive and corrective maintenance operations. These operations with a random duration make the machines unavailable. Moreover, during regular subcontracting operations, one of these machines becomes unavailable to supply the downstream inventory. In the first strategy it is assumed that the periodicity of preventive maintenance operations and the production rate of each machine are independent. The second strategy suggests an interaction between the periods of unavailability and the production rates of the two machines in order to minimize production losses during these periods. A simulation model for each strategy is developed so as to be able to compare them and to simultaneously determine the timing of preventive maintenance on each machine considering the total average cost per time unit as the performance criterion. The second strategy is then considered, and a multi-criteria analysis is adopted to reach the best cost-availability compromise.     

Solving the capacitated lot-sizing problem with backorder consideration

In this research, we formulate and solve a type of the capacitated lot-sizing problem. We present a general model for the lot-sizing problem with backorder options, that can take into consideration various types of production capacities such as regular time, overtime and subcontracting. The objective is to determine lot sizes that will minimize the sum of setup costs, holding cost, backorder cost, regular time production costs, and overtime production costs, subject to resource constraints. Most existing formulations for the problem consider the special case of the problem where a single source of production capacity is considered. However, allowing for the use of alternate capacities such as overtime is quite common in many manufacturing settings. Hence, we provide a formulation that includes consideration of multiple sources of production capacity. We develop a heuristic based on the special structure of fixed charge transportation problem. The performance of our algorithm is evaluated by comparing the heuristic solution value to lower bound value. Extensive computational results are presented.     

A new approach towards integrated cell formation and inventory lot sizing in an unreliable cellular manufacturing system

This paper presents a comprehensive mathematical model for integrated cell formation and inventory lot sizing problem. The proposed model seeks to minimize cell formation costs as well as the costs associated with production, while dynamic conditions, alternative routings, machine capacity limitation, operations sequences, cell size constraints, process deterioration, and machine breakdowns are also taken into account. The total cost consists of machine procurement, cell reconfiguration, preventive and corrective repairs, material handling (intra-cell and inter-cell), machine operation, part subcontracting, finished and unfinished parts inventory cost, and defective parts replacement costs. With respect to the multiple products, multiple process plans for each product and multiple routing alternatives for each process plan which are assumed in the proposed model, the model is combinatorial. Moreover, unreliability conditions are considered, because moving from “in-control” state to “out-of-control” state (process deterioration) and machine breakdowns make the model more practical and applicable. To conquer the breakdowns, preventive and corrective actions are adopted. Finally, a Particle Swarm Optimization (PSO)-based meta-heuristic is developed to overcome NP-completeness of the proposed model.     

Machine duplication and part subcontracting in the presence of alternative cell locations in manufacturing cell design

In this paper a model and a solution algorithm are reported to simultaneously deal with the processes of machine duplication and part subcontracting in the presence of two significant design issues in cellular manufacturing systems: (i) alternative cell locations; and (ii) the maximum number of machines assigned to a cell. As the problem, formulated as a polynomial programming model, is shown NP-hard in the strong sense, a higher-level heuristic algorithm based upon a concept known as ‘tabu search’ is presented. An example (small) problem is solved to demonstrate the functionality of the algorithm. Additionally, the small problem is solved for its optimal solution under different scenarios, both with linear single-row and linear double-row layout arrangements, and the solutions obtained are shown to match with those obtained with the heuristic algorithm. A comparison of six different versions of tabu search-based heuristics (TSH 1–TSH 6) is performed to investigate the impact of long-term memory and the use of fixed versus variable tabu-list sizes. A carefully constructed statistical experiment, based on randomised complete-block design, is used to test the performance on three different problem structures, classified as small, medium and large. The results show that TSH 6 with variable tabu-list size and long-term memory based on minimal frequencies is preferred for the single-row layout, while TSH 4 with variable tabu-list size and no long-term memory is preferred for the double-row layout. When subject to budgetary restrictions, the proposed approach can be used by parts manufacturing companies to determine which of the following three actions should be undertaken for each bottleneck part: bottleneck part left as in the initial solution, all the bottleneck machines connected to it are duplicated, or the part subcontracted.     

Community operational research issues and public art practice: the art director system

The key issues of community operational research, outlined in a paper by Ritchie, have relevance to community projects in general and, we argue, a particular relevance to public art. We illustrate this relevance by describing eight case studies in public art, four in Japan and four in the west, and by considering the projects in a three-way factorial design, make a case for the art director system in the management of public art projects.     

零维理想关于变元正常与一般位置

设k[x_1,…,x_n]是域k上关于变量x_1,…,x_n的多项式环,I是k[x_1,x_2,…,x_n]中的零维理想.本文对I关于某个变元x_i正常与一般位置之同的关系进行探讨,并证明了零维理想对于变元x_i正常与一般位置在某种情况下的等价性.