An integrated modelling approach for raw material management in a steel mill

An integrated modelling approach combining optimisation models with simulation is proposed for coordinated raw material management at steel works throughout the whole supply chain management process. The integrated model is composed of three components: ship scheduling, yard operation simulation and material blending models. The ship scheduling model determines which brands, how much and when they should be arrived, and the problem is modelled as mixed integer linear programming. The simulation model is used to simulate the whole processes from ships’ arrivals to the retrieval of the materials through the berthing and unloading the raw materials. Finally, the raw material blending model is developed for determining the brand and quantity of raw materials to be used. The proposed integrated modelling approach for raw material management has been successfully implemented and applied at steelwork to provide shipping schedules and predict future inventory levels at stock yards. By coordinating all the activities throughout the entire raw material supply chain management process, this article proposes an integrated approach to the problem and suggests a guideline by the appropriate simplification. The quantitative nature of the optimisation model and simulation facilitates an assessment of the risk factors in the supply chain, leading to an evaluation of a wide variety of scenarios and the development of multiple contingency plans. Further research is expected to supplement the ship scheduling models with heuristics for the idiosyncratic constraints of maritime transportation.     

A MODEL-BASED DECISION SUPPORT SYSTEM FOR SCHEDULING LUMBER DRYING OPERATIONS

Raw lumber must be dried to a specified level of moisture content before it can be used to make furniture. This paper deals with a model-based decision support system (DSS) for a local furniture manufacturing company to assist its management in scheduling lumber drying operations. In addition to buying ready-to-use dried lumber from vendors at a premium, the company processes raw lumber in house using two production process that require various lengths of processing time in predryers and dry-kilns. Given the demand for various types of dried lumber over a specified planning horizon, the processing times and costs for each production process, technological restrictions, and management policies, the problem of interest is to satisfy the demand at a minimum cost. The DSS incorporates the mathematical formulation of this problem, is user friendly, maintains model and data independence, and generates the necessary reports, including loading and unloading schedules for the equipment.     

A joint economic lot size model for raw material ordering,manufacturing setup,and finished goods delivering

In this research we consider a single-manufacturer single-buyer supply chain problem where the manufacturer orders raw materials from its supplier, then using its manufacturing processes converts the raw materials to finished goods, and finally delivers the finished goods to its customer. The manufacturer produces the product in batches at a finite rate and periodically delivers the finished goods at a fixed lot size to its customer, who has a constant demand rate. An integrated inventory control model, making joint economic lot sizes of manufacturer's raw material ordering, production batch, and buyer's ordering, is developed to minimize the mean total cost per unit time of the raw materials ordering and holding, manufacturer's setup and finished goods holding, the buyer's ordering, and inventory holding. Numerical examples are also setup to illustrate that jointly considering the inventory costs above results in less mean total cost than that of considering them separately.     

Multicriteria decision making for optimal blending for beneficiation of coal: a fuzzy programming approach

Beneficiation of coal refers to the production of wash coal from raw coal with the help of some suitable beneficiation technologies. The processed coal is used by the different steel plants to serve their purpose during the manufacturing process of steel. The present paper deals with the optimal planning for blending raw coal of different grades used for beneficiation with a view to satisfy the requirements of the end users with desired specifications. The input specifications of coal samples are known whereas the output specifications are imprecise in nature. The aim of the work is to fix the level of the raw coal from different coal seams to be fed for beneficiation to meet the desired target of yield and ash percentage to maximum extent. Further, it is also desired by the decision-maker (DM) to restrict the input cost of raw coal to be fed for beneficiation. The problem is modeled as multicriteria decision-making problem with imprecise specifications. Fuzzy set theoretic approach has been used and a corresponding model has been developed. The solution of the problem would enable the DM to optimize the raw coal feed with existing available specifications from different collieries along with the overall degree of satisfaction.     

Container Scheduling: Complexity and Algorithms

We consider the transport of containers through a fleet of ships. Each ship has a capacity constraint limiting the total number of containers it can carry and each ship visits a given set of ports following a predetermined route. Each container has a release date at its origination port, and a due date at its destination port. A container has a size 1 or size 2; size 1 represents a 1 TEU (20‐foot equivalent unit) and size 2 represents 2 TEUs. The delivery time of a container is defined as the time when the ship that carries the container arrives at its destination port. We consider the problem of minimizing the maximum tardiness over all containers. We consider three scenarios with regard to the routes of the ships, namely, the ships having (i) identical, (ii) nested, and (iii) arbitrary routes. For each scenario, we consider different settings for origination ports, release dates, sizes of containers, and number of ports; we determine the computational complexity of various cases. We also provide a simple heuristic for some cases, with its worst case analysis. Finally, we discuss the relationship of our problems with other scheduling problems that are known to be open.     

价格下界随时间递增的占线采购问题

本文研究的是价格不确定且其下界随时间递增的原材料采购问题。在实际的原材料采购问题中,原材料的价格随时间的变动往往是不可预测的。之前的学者在研究价格不确定的占线采购问题时,假设价格在一个统一的常数上下界内,这没有考虑到经过时间的变化,价格的上下界可能也是变化的。本文提出并研究价格下界随时间递增的原材料占线采购问题。构建了相应数学模型,给出了相应的竞争采购策略并证明了竞争比,同时通过证明问题的匹配竞争比下界,说明给出的竞争采购策略是最优的,最后利用数值分析进一步说明竞争策略具有较好的竞争性能。     

A possibilistic aggregate production planning model for brass casting industry

This article discusses a possibilistic aggregate production planning (APP) model for blending problem in a brass factory; the problem computing optimal amounts of raw materials for the total production of several types of brass in a planning period. The model basically has a multi-blend model formulation in which demand quantities, percentages of the ingredient in some raw materials, cost coefficients, minimum and maximum procurement amounts are all imprecise and have triangular possibility distributions. A mathematical model and a solution algorithm are proposed for solving this model. In the proposed model, the Lai and Hwang's fuzzy ranking concept is relaxed by using ‘Either-or’ constraints. An application of the brass casting APP model to a brass factory demonstrates that the proposed model successfully solves the multi-blend problem for brass casting and determines the optimal raw material purchasing policies.     

A market regulation bilevel problem: A case study of the Mexican petrochemical industry

In this paper, a bilevel programming model is proposed to study a problem of market regulation through government intervention. One of the main characteristics of the problem herein analyzed is that the government monopolizes the raw material in one industry, and competes in another industry with private firms for the production of commodities. Under this scheme, the government controls a state-owned firm to balance the market; that is, to minimize the difference between the produced and demanded commodities. On the other hand, a regulatory organization that coordinates private firms aims to maximize the total profit by deciding the amount of raw material bought from the a state-owned firm. Two equivalent single-level reformulations are proposed to solve the problem. The first reformulation is based on the strong duality condition of the lower level and results in a continuous non-linear model. The second reformulation resorts to the complementarity slackness optimality constraints yielding a mixed-integer linear model. Additionally, three heuristic algorithms are designed to obtain good-quality solutions with low computational effort. In this problem, the feasible region of the dual problem associated to the follower is independent from the leader’s decision. Therefore, the proposed heuristics exploit this particular characteristic of the bilevel model. Moreover, the third heuristic hybridizes the other two algorithms to enhance its performance. Extensive computational experimentation is carried out to measure the efficiency of the proposed solution methodologies. A case study based on the Mexican petrochemical industry is presented. Additional instances generated from the case study are considered to validate the robustness of the proposed heuristic algorithms. Numerical results indicate that the hybrid algorithm outperforms the other two heuristics. However, all of them demonstrate to be good alternatives for solving the problem. Additionally, optimal solutions of all the instances are obtained by using good quality solutions (given by the hybrid algorithm) as initial solutions when solving the second reformulation via a general purpose solver.     

Integrated procurement- production system in a just-in-time environment-modelling and analysis

Classically, economic lot size models have been used separately for procurement and production subsystems. However, when the raw materials are used in production, the procurement policies are dependent on the schedule and the batch size for the product. Hence, it is necessary to unify the procurement and production policies. The just-in-time JIT environment provides an ideal setting for such a coordination between the procurement and production policies. The model proposed here is a traditional inventory model recast into a model for a JIT system for a single product, multistage batch environment aiming at the minimization of total variable cost and thereby determining the batch sizes for the product and raw material order sizes. A JIT system aims at minimizing setup time and this feature is captured in the proposed model. The computational experience reported in this paper is based on a number of simulated problem sets. The possible domain of application is also highlighted.     

工业原材料期货价格指数研制与功能的实证分析

本文探讨了开发国内工业原材料期货价格指数的意义,并提出了符合中国实际情况的编制方法和修正方法,研制出我国上海期货交易所的工业原材料期货价格指数。实证结果表明:在样本区间内其先行时间达到3个月,能反映出我国生产资料价格的未来价格走势,这为我国宏观价格政策的制定具有重要的意义。     

Scheduling Truck Arrivals at an Air Cargo Terminal

We consider the scheduling of truck arrivals at an air cargo terminal. By coordinating arrivals of cargo delivery trucks with outbound flight departure schedules, some of the shipments can be transferred directly to the departing flights, while others will be stored at the terminal's storage facility and incur extra handling and storage costs. The objective is to obtain a feasible schedule so as to minimize the total cost of operations. We formulate the problem as a time‐indexed integer program and show that, even with limited number of unloading docks at the terminal, the problem is non‐trivial (NP‐hard in the strong sense). Our solution method includes an exact solution procedure to determine an optimal unloading sequence for the shipments carried by each truck, together with a Lagrangian relaxation‐based heuristic for assigning trucks to truck docks and determining truck arrival times. We conducted computational experiments to test the performance of our solution method. Computational results show that our method can generate near‐optimal solutions efficiently. Our simulation results indicate that the scheduling approach proposed in this paper has the potential to generate significant cost savings over a first‐come, first‐served approach currently used at the air cargo terminal that we observed.     

Transportation Approach to Locating Plants in Relation to Potential Markets and Raw Material Sources

Proximity to the market place has been considered the most important locational factor in the literature so far. However, the growing need for frequent deliveries of materials in smaller lot sizes for just-in-time (JIT) manufacturing prefers plants closer to the raw materials sources. Locating plants for JIT manufacturing is, therefore, a problem of finding the right balance between the requirements of procurement and distribution. A comprehensive model is proposed in this paper to solve this problem. The model is solved by using the transportation algorithm and produces simultaneous decisions on procurement, production, and distribution. The model does not require plant sizes to be known a priori, but it allows upper limits to be placed on the size of each plant and raw material source. As such, optimal plant capacities along with the corresponding procurement and distribution quantities are all determined by the model solution.     

基于“前港后厂”模式的进口铁矿石采购物流成本优化

作为钢铁产量大国，国内铁矿石资源品位低、开采难度大、选矿成本高，需要大量进口国外优质铁矿石，导致钢铁企业采购物流成本居高不下；长期大批量远距离的铁矿石海运历史，促使了我国"港-钢"企业的发展紧密相连。因此，本文基于"前港后厂"模式，构建了以船型、供应商和接卸港的选择为变量，以最小化铁矿石采购物流成本为目标的组合优化模型。运用免疫遗传算法和MATLAB进行求解与仿真验证，结果表明"前港后厂"模式较传统模式在优化采购物流系统上更优，为推行"前港后厂"模式提供了理论依据。     

价格柔性合同下的原材料采购策略及风险分析

为了降低原材料价格波动给采购-供应双方企业带来的风险,供应链企业通常采用签订价格合同的方式来共同分担原材料价格波动的风险。本文通过设计价格柔性合同,利用Stackelberg主从博弈模型研究了由一个供应商和一个制造商组成的采购系统的最优采购策略及原材料价格波动风险的分担机制。研究表明,通过实施价格柔性合同可以降低供应双方的风险,且通过设置合理的价格柔性系数可以提高双方的收益。     

Order consolidation for hierarchical product lines

We consider the batch production of hierarchical product lines in raw material industry where the whole or parts of multiple customer orders may be consolidated and processed in the same batch if their product specifications are compatible. The objective of the problem is to find maximum possible number of batches completely filled up to their capacity. The compatibility relationship among product specifications is represented by a graph called the compatibility graph. If the compatibility graph is an arbitrary graph, the problem is proven to be NP-hard and belongs to Max SNP-hard class. We develop an optimum algorithm for an important subclass of the problem where the graph is a quasi-threshold graph which in fact is the case for producing hierarchical product lines that are often found in raw materials industry.     

局内动态配送车调度管理及其竞争策略

提出了动态物流配送车辆调度优化问题——配送车在一度量空间中进行服务,度量空间中的任何一节点可能在任何时间提出服务请求,要求配送车将该点处的货物运送到另一点,每一个服务请求都有一个服务期限,若在规定的时间内某一服务请求不能被满足则将被取消,在考虑装/卸货所用时间的情况下,决策者如何以局内方式确定调度策略,使配送车完成的服务请求数最多.针对该不确定性条件下的管理决策问题,给出了两种局内管理策略,并利用局内问题及竞争分析理论,给出了不同载重量下(Q=1和Q=∞)的两种策略的竞争比.     

The closed-loop supply chain network with competition,distribution channel investment,and uncertainties

In this paper, a closed-loop supply chain network is investigated with decentralized decision-makers consisting of raw material suppliers, retail outlets, and the manufacturers that collect the recycled product directly from the demand market. We derive the optimality conditions of the various decision-makers, and establish that the governing equilibrium conditions can be formulated as a finite-dimensional variational inequality problem. We establish convergence of the proposed algorithm that can allow for the discussion of the effects of competition, distribution channel investment, yield and conversion rates, combined with uncertainties in demand, on equilibrium quantity transactions and prices. Numerical examples are provided for illustration.     

Multi-echelon supply chain network design in agile manufacturing

In this paper, we consider a supply chain network design problem in an agile manufacturing scenario with multiple echelons and multiple periods under a situation where multiple customers have heavy demands. Decisions in our supply chain design problem include selection of one or more companies in each echelon, production, inventory, and transportation. We formulate the problem integrating all decisions to minimize the total operational costs including fixed alliance costs between two companies, production, raw material holding, finished products holding, and transportation costs under production and transportation capacity limits. A Lagrangian heuristic is proposed in this paper. Optimizing a Lagrangian relaxation problem provides a lower bound, while a feasible solution is generated by adjustment techniques based on the solution of subproblems at each iteration. Computational results indicate the high quality solutions with less than 5% optimality gap are provided quickly by the approach in this paper. Further, compared to initiative managerial alternatives, an improvement of 15% to 25% is not unusual in certain cases for the proposed approach.     

An Industrial Ocean-Cargo Shipping Problem

This paper reports the modeling and solution of an industrial ocean-cargo shipping problem. The problem involves the delivery of bulk products from an overseas port to transshipment ports on the Atlantic Coast, and then over land to customers. The decisions made include the number and the size of ships to charter in each time period during the planning horizon, the number and location of transshipment ports to use, and transportation from ports to customers. The complexity of this problem is compounded by the cost structure, which includes fixed charges in both ship charters and port operations. Such a large scale, dynamic, and stochastic problem is reduced to a solvable stationary, deterministic, and cyclical model. The process of modeling the problem and the solution of the resultant mixed integer program are described in detail. Recommendations from this study have been implemented.     

Multi-echelon supply chain network design in agile manufacturing

In this paper, we consider a supply chain network design problem in an agile manufacturing scenario with multiple echelons and multiple periods under a situation where multiple customers have heavy demands. Decisions in our supply chain design problem include selection of one or more companies in each echelon, production, inventory, and transportation. We formulate the problem integrating all decisions to minimize the total operational costs including fixed alliance costs between two companies, production, raw material holding, finished products holding, and transportation costs under production and transportation capacity limits. A Lagrangian heuristic is proposed in this paper. Optimizing a Lagrangian relaxation problem provides a lower bound, while a feasible solution is generated by adjustment techniques based on the solution of subproblems at each iteration. Computational results indicate the high quality solutions with less than 5% optimality gap are provided quickly by the approach in this paper. Further, compared to initiative managerial alternatives, an improvement of 15% to 25% is not unusual in certain cases for the proposed approach.