Dynamic Programming and Hill-Climbing Techniques for Constrained Two-Dimensional Cutting Stock Problems

In this paper we propose an algorithm for the constrained two-dimensional cutting stock problem (TDC) in which a single stock sheet has to be cut into a set of small pieces, while maximizing the value of the pieces cut. The TDC problem is NP-hard in the strong sense and finds many practical applications in the cutting and packing area. The proposed algorithm is a hybrid approach in which a depth-first search using hill-climbing strategies and dynamic programming techniques are combined. The algorithm starts with an initial (feasible) lower bound computed by solving a series of single bounded knapsack problems. In order to enhance the first-level lower bound, we introduce an incremental procedure which is used within a top-down branch-and-bound procedure. We also propose some hill-climbing strategies in order to produce a good trade-off between the computational time and the solution quality. Extensive computational testing on problem instances from the literature shows the effectiveness of the proposed approach. The obtained results are compared to the results published by Alvarez-Valdés et al. (2002).     

Single‐Period Two‐Product Assemble‐to‐Order Systems with a Common Component and Uncertain Demand Patterns

We consider a single‐period assemble‐to‐order system that produces two types of end products to satisfy two independent and stochastic customer orders. Each type of product is used to fulfill a particular customer order and these two products share a common component. Furthermore, one customer may confirm her order before the other one, and the manufacturer needs to make a commitment immediately upon the receipt of each customer order on how many products to be delivered. We propose a model for optimizing the inventory and production decisions under the above ATO environment. We also extend our model to the situation where the manufacturer can fulfill the unsatisfied low‐priority demand using the left‐over inventories after fulfilling the high‐priority demand, in case the low‐priority customer arrives first. Numerical experiments are conducted, which provide some interesting insights on the impact of uncertain demand pattern.     

Triple-solution approach for the strip packing problem with two-staged patterns

A triple-solution approach for the rectangular level strip packing problem is presented, where m item types with specified demands are packed in levels into a strip with definite width and infinite height to minimize the occupied height, with the constraint that the items in the same level cannot be placed one on top of the other. The approach contains two phases and considers three types of solutions. In phase one, two types of solutions, obtained respectively from solving residual problems using column generation and from looking ahead, are considered and the best is selected as phase-one solution. In phase two, an integer programming model is solved over the levels generated in phase-one to obtain phase-two solution. Finally the better one of the phase-one and phase-two solutions are selected. Computational results indicate that the approach is effective for both the instances with strongly heterogeneous items and those with weakly heterogeneous items.     

The nearest neighbor Spearman footrule distance for bucket, interval, and partial orders

Comparing and ranking information is an important topic in social and information sciences, and in particular on the web. Its objective is to measure the difference of the preferences of voters on a set of candidates and to compute a consensus ranking. Commonly, each voter provides a total order of all candidates. Recently, this approach was generalized to bucket orders, which allow ties. In this work we further generalize and consider total, bucket, interval and partial orders. The disagreement between two orders is measured by the nearest neighbor Spearman footrule distance, which has not been studied so far. For two bucket orders and for a total and an interval order the nearest neighbor Spearman footrule distance is shown to be computable in linear time, whereas for a total and a partial order the computation is NP-hard, 4-approximable and fixed-parameter tractable. Moreover, in contrast to the well-known efficient solution of the rank aggregation problem for total orders, we prove the NP-completeness for bucket orders and establish a 4-approximation.     

An association-based clustering approach to order batching considering customer demand patterns

Research on warehousing systems has gained interest since the 1980s, reflecting the fact that supply chain management has pursued a demand-driven organization with high product variety, small order sizes, and reliable short response times throughout the supply chain. This market trend has affected warehouse management and operations tremendously. Order batching in a warehouse attempts to achieve high-volume order processing operations by consolidating small orders into batches. Order batching is an essential operation of order processing in which several orders are grouped into batches. This paper describes the development of an order batching approach based on data mining and integer programming. It is valuable to discover the important associations between orders such that the occurrence of some orders in a batch will cause the occurrence of other orders in the same batch. An order-clustering model based on 0–1 integer programming can be formulated to maximize the associations between orders within each batch. From the results of several test problems, the proposed approach shows its ability to find quality solutions of order batching problems.     

Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts

This paper presents an approach for solving a new real problem in cutting and packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cutting and packing problems that include guillotine cuts deal with rectangles only, where all cuts are orthogonal to the edges of the stock sheet and a maximum of two angles of rotation are permitted. The literature tackling packing problems with irregular shapes largely focuses on strip packing i.e. minimizing the length of a single fixed width stock sheet, and does not consider guillotine cuts. Hence, this problem combines the challenges of tackling the complexity of packing irregular pieces with free rotation, guaranteeing guillotine cuts that are not always orthogonal to the edges of the stock sheet, and allocating pieces to bins. To our knowledge only one other recent paper tackles this problem. We present a hybrid algorithm that is a constructive heuristic that determines the relative position of pieces in the bin and guillotine constraints via a mixed integer programme model. We investigate two approaches for allocating guillotine cuts at the same time as determining the placement of the piece, and a two phase approach that delays the allocation of cuts to provide flexibility in space usage. Finally we describe an improvement procedure that is applied to each bin before it is closed. This approach improves on the results of the only other publication on this problem, and gives competitive results for the classic rectangle bin packing problem with guillotine constraints.     

A multiple criteria decision-making model for justifying the acceptance of rush orders

Rush orders are immediate customer demands that exceed the expectation of a currently effective MPS (master production schedule). Decision-makers are often hesitant in the decision of accepting such orders. This paper presents a multiple criteria decision-making model for justifying the acceptance of rush orders for an assembly-to-order production system. Four criteria or production objectives are simultaneously considered and a multiple objective programming technique, the e-constraints approach, is adopted to solve the decision-making problem. This model could give the cost estimation for producing a rush order under various combinations of production objectives. The computed cost value could serve as a valuable reference for justifying the economics of accepting the rush order, and help to determine its pricing strategy.     

Optimal Production and Admission Policies in Make‐to‐Stock/Make‐to‐Order Manufacturing Systems

In this article, we study optimal production and admission control policies in manufacturing systems that produce two types of products: one type consists of identical items that are produced to stock, while the other has varying features and is produced to order. The model is motivated by applications from various industries, in particular, the automobile industry, where a part supplier receives orders from both an original equipment manufacturer and the aftermarket. The product for the original equipment manufacturer is produced to stock, it has higher priority, and its demands are fully accepted. The aftermarket product is produced to order, and its demands can be either accepted or rejected. We characterize the optimal production and admission policies with a partial‐linear structure, and using computational analysis, we provide insights into the benefits of the new policies. We also investigate the impact of production capacity, cost structure, and demand structure on system performance.     

The Effects of Computerized Visual Feedback Using Flashing Lights on Order Selection in Large Industrial Settings: Productivity,Accuracy, and Cost Justifications

This report from the field concerns a pilot study that used computerized visual feedback in the form of flashing lights to inform order selectors in an auto parts distribution center to fulfill store orders. Compared to paper pick lists, order selection performance and accuracy reliably increased when the delivery method was the flashing lights. The role of the organizational behavior management participant in industrial settings in designing interventions that increase accuracy and productivity was examined. More than just the intervention, the cost justification was part of the decision-making process about whether to continue with the intervention.     

专利保护下闭环供应链的再制造策略研究

在专利完善市场,受专利保护的原制造商享有产品再制造的专有权利,只有获得原制造商的专利许可,第三方再制造商才能进行旧产品的回收再制造。本文分析了受专利保护下原制造商所采取的不同再制造策略:阻止旧产品再制造(N策略)、原制造商自己再制造(O策略)和许可第三方再制造商进行再制造(A策略),并建立了由零售商负责旧产品回收的闭环供应链模型。通过比较发现,只有在第三方再制造商处理旧产品的节省成本足够低时,受专利保护的原制造商才会选择许可第三方再制造商进行旧产品再制造。     

Mitigating the environmental and social footprint of brownfields: The case for a peripheral CSR approach

Industrial plant closures create a largely unexplored challenge for corporate social responsibility (CSR) strategy. Such plant closures lead to brownfield sites: economic assets and large pieces of land that often cannot be redeployed for alternative purposes, except by incurring significant costs. The direct effects of plant closures typically include a rise in unemployment and value chain disturbance (or dismantling), but brownfields are usually also associated with additional social effects and environmental pollution. Here, a proactive CSR strategy means reducing or mitigating the joint, negative social and environmental footprint of industrial plant closures beyond what is mandated by law (which has tended primarily to address direct effects). We assess the various strategies firms can pursue to mitigate negative, post-closure footprints and we distinguish between two alternative strategic options beyond the ‘legal obligations’ approach, namely the ‘core business related’ (core) CSR approach, and the ‘peripheral CSR’ approach. We explore the case of a plant closure by Bekaert S.A., a large, Belgian industrial firm, which adopted a peripheral CSR approach to manage and redevelop a brownfield site. In this context, we identify four enabling conditions for peripheral CSR to be implemented effectively.     

基于状态依赖Hawkes过程的我国股市限价指令簿事件激励效应研究

指令驱动市场中,交易者对委托指令的提交和撤销往往表现出非平稳性和集聚性特征。量化评价限价指令簿事件间的激励关系,是探究限价指令簿动态演化的基础,指导交易者行为决策的重要参照。本文利用我国股票逐单委托数据重建了实时演化的限价指令簿,基于状态依赖Hawkes过程分析了不同市场状态下各类限价指令簿事件的自激励和互激励效应。共采用三种不同设定的状态依赖Hawkes过程模型进行实证分析,并探讨了我国股市中交易者的行为特征。实证结果表明,总体上我国股市中限价指令簿事件的自激励效应强于互激励效应,且不同市场状态下存在显著差异。激进事件所产生的互激励效应更为强烈,通过激进程度划分事件类型更能反映事件冲击和交易者的信息学习行为。     

Adjusting MRP for dynamic differentiation of identical items for process customisation

In the make-to-order (MTO) environment, different customer orders often require similar products that share identical basic features but require different customisation processes. To achieve efficiency, these products are often manufactured in a group at the initial stages. A significant issue then emerges as to how to differentiate identical items at the intermediate stages so that they can be dispatched to different kinds of work centres for process customisation. This article adjusts the current material requirements planning (MRP) approach for the MTO mode. A yield-allocating approach is then proposed for adjusting the material demand plans according to real-time process quality information. An approach for dynamically differentiating identical customised items at intermediate stages is then presented. How to implement the proposed methodology in a computer-based environment is also briefly introduced. A case study demonstrates that the proposed methodology can fulfil the dynamical differentiation task and can result in more reasonable differentiation decisions than the traditional MRP approach.     

Production quantity allocation for order fulfilment in the supply chain: a neural network based approach

In the current global business environment, it is very important to know how to allocate products from the producer to buyers (or distributors). If products are not appropriately distributed due to absence of an effective allocation policy, the producer and buyers cannot expect to increase customer satisfaction and financial profit. Sometimes some buyers can order more than the actual demand due to inappropriately forecasting customer orders. This is the big obstacle to the effective allocation of products. If the producer can become aware of buyers’ actual demands, it is possible to realise high-level order fulfilment through the effective allocation of products. In this study, new allocation policies are proposed considering buyers’ demands. The back propagation algorithm, one of the learning algorithms in neural network theory, is used to recognise actual demands from the previous buyers’ orders. After excluding surplus demands included in buyers’ demands, products are allocated to buyers according to one of the existing allocation policies depending on the company's decision. In the numerical examples, new allocation policies reducing buyers’ surplus demands outperform previous allocation policies with respect to average amount of backorder.     

On Disjunctive Cuts for Combinatorial Optimization

In the successful branch-and-cut approach to combinatorial optimization, linear inequalities are used as cutting planes within a branch-and-bound framework. Although researchers often prefer to use facet-inducing inequalities as cutting planes, good computational results have recently been obtained using disjunctive cuts, which are not guaranteed to be facet-inducing in general.A partial explanation for the success of the disjunctive cuts is given in this paper. It is shown that, for six important combinatorial optimization problems (the clique partitioning, max-cut, acyclic subdigraph, linear ordering, asymmetric travelling salesman and set covering problems), certain facet-inducing inequalities can be obtained by simple disjunctive techniques. New polynomial-time separation algorithms are obtained for these inequalities as a by-product.The disjunctive approach is then compared and contrasted with some other general-purpose frameworks for generating cutting planes and some conclusions are made with respect to the potential and limitations of the disjunctive approach.     

Interactive Job Shop Scheduling: An Experiment

An experiment is discussed in which three computer-aided, interactive job shop scheduling approaches are compared using an interactive job shop scheduling simulator (JOB) developed for the project. All three approaches use a combination of computer and human capabilities to develop job shop schedules, but differ in terms of the timing and degree of human involvement required. The three scheduling approaches are (1) the successive approach, (2) the interactive approach, and (3) the semi-interactive approach. The successive approach is characterized by the computer scheduling all work orders without any human intervention. The interactive approach is distinguished by the human scheduling one work order at a time until all work orders are scheduled. The schedule is developed interactively by the person who must simultaneously consider work-order scheduling needs and machine group load capacities. The semi-interactive approach may be viewed as a combination of the successive and interactive approaches. Work orders are automatically scheduled one at a time using the successive approach criteria, but with prespecified machine-group load thresholds. As long as the load threshold is not exceeded, the successive approach is used to schedule work orders. When a threshold is exceeded, the algorithm (successive approach) pauses and human rescheduling (interactive approach) is required to rectify the overload situation. A second (reallocation) phase, identical for all three approaches, is used to overcome any scheduling problems generated in phase one. Experimental results based on nine different performance criteria (including scheduling time, makespan, machine group utilization, and work-in-process inventory) and 45 experimental runs indicate that there are differences between the results produced by the three scheduling approaches. The interactive approach yields the best overall scheduling results, but the other two approaches are clearly better than the interactive approach in some situations. The success of the interactive approach indicates that it is usually best for the human scheduler to become involved early in the computer-based job shop scheduling process.     

MRP Planned Orders in a Multiple‐Supplier Environment with Differing Lead Times

This study examines a deterministic material requirements planning (MRP) problem where lead times at subsequent ordering moments differ. Adequate replenishment methods that can cope with lead time differences are lacking because of the order crossover phenomenon, that is, replenishment orders are not received in the sequence they are ordered. This study specifies how to handle order crossovers and recalculate planned order releases after an update of gross requirements. The optimal (s, S) policy is based on dynamic programing. The state space is kept to a minimum due to three fundamental insights. The performance of the optimal solution approach is compared with two heuristics based on relaxations and a benchmark approach in which order crossovers are ignored. A numerical analysis reveals that average cost savings up to 25% are possible if the optimal policy is used instead of the benchmark approach. The contribution of this study is threefold: (1) it generalizes theory on MRP ordering, allowing for lead time differences and order crossovers; (2) it develops new fundamental insights and an optimal solution procedure, leading to substantial cost saving; and (3) it provides good‐performing heuristics for a general and realistic replenishment problem that can replace the current replenishment methods within MRP.     

Approximate and Exact Algorithms for Constrained (Un) Weighted Two-dimensional Two-staged Cutting Stock Problems

In this paper we propose two algorithms for solving both unweighted and weighted constrained two-dimensional two-staged cutting stock problems. The problem is called two-staged cutting problem because each produced (sub)optimal cutting pattern is realized by using two cut-phases. In the first cut-phase, the current stock rectangle is slit down its width (resp. length) into a set of vertical (resp. horizontal) strips and, in the second cut-phase, each of these strips is taken individually and chopped across its length (resp. width).First, we develop an approximate algorithm for the problem. The original problem is reduced to a series of single bounded knapsack problems and solved by applying a dynamic programming procedure. Second, we propose an exact algorithm tailored especially for the constrained two-staged cutting problem. The algorithm starts with an initial (feasible) lower bound computed by applying the proposed approximate algorithm. Then, by exploiting dynamic programming properties, we obtain good lower and upper bounds which lead to significant branching cuts. Extensive computational testing on problem instances from the literature shows the effectiveness of the proposed approximate and exact approaches.     

Coordinating Supply Chains via Advance‐Order Discounts,Minimum Order Quantities,and Delegations

To avoid inventory risks, manufacturers often place rush orders with suppliers only after they receive firm orders from their customers (retailers). Rush orders are costly to both parties because the supplier incurs higher production costs. We consider a situation where the supplier's production cost is reduced if the manufacturer can place some of its order in advance. In addition to the rush order contract with a pre‐established price, we examine whether the supplier should offer advance‐order discounts to encourage the manufacturer to place a portion of its order in advance, even though the manufacturer incurs some inventory risk. While the advance‐order discount contract is Pareto‐improving, our analysis shows that the discount contract cannot coordinate the supply chain. However, if the supplier imposes a pre‐specified minimum order quantity requirement as a qualifier for the manufacturer to receive the advance‐order discount, then such a combined contract can coordinate the supply chain. Furthermore, the combined contract enables the supplier to attain the first‐best solution. We also explore a delegation contract that either party could propose. Under this contract, the manufacturer delegates the ordering and salvaging activities to the supplier in return for a discounted price on all units procured. We find the delegation contract coordinates the supply chain and is Pareto‐improving. We extend our analysis to a setting where the suppliers capacity is limited for advance production but unlimited for rush orders. Our structural results obtained for the one‐supplier‐one‐manufacturer case continue to hold when we have two manufacturers.     

A Dynamic Disaggregation Approach to Approximate Linear Programs for Network Revenue Management

The linear programming approach to approximate dynamic programming has received considerable attention in the recent network revenue management (RM) literature. A major challenge of the approach lies in solving the resulting approximate linear programs (ALPs), which often have a huge number of constraints and/or variables. Starting from a recently developed compact affine ALP for network RM, we develop a novel dynamic disaggregation algorithm to solve the problem, which combines column and constraint generation and exploits the structure of the underlying problem. We show that the formulation can be further tightened by considering structural properties satisfied by an optimal solution. We prove that the sum of dynamic bid‐prices across resources is concave over time. We also give a counterexample to demonstrate that the dynamic bid‐prices of individual resources are not concave in general. Numerical experiments demonstrate that dynamic disaggregation is often orders of magnitude faster than existing algorithms in the literature for problem instances with and without choice. In addition, adding the concavity constraints can further speed up the algorithm, often by an order of magnitude, for problem instances with choice.