Joint supplier selection and scheduling of customer orders under disruption risks: Single vs. dual sourcing

This paper presents a stochastic mixed integer programming approach to integrated supplier selection and customer order scheduling in the presence of supply chain disruption risks, for a single or dual sourcing strategy. The suppliers are assumed to be located in two different geographical regions: in the producer's region (domestic suppliers) and outside the producer's region (foreign suppliers). The supplies are subject to independent random local disruptions that are uniquely associated with a particular supplier and to random semi-global (regional) disruptions that may result in disruption of all suppliers in the same geographical region simultaneously. The domestic suppliers are relatively reliable but more expensive, while the foreign suppliers offer competitive prices, however material flows from these suppliers are more exposed to unexpected disruptions. Given a set of customer orders for products, the decision maker needs to decide which single supplier or which two different suppliers, one from each region, to select for purchasing parts required to complete the customer orders and how to schedule the orders over the planning horizon, to mitigate the impact of disruption risks. The problem objective is either to minimize total cost or to maximize customer service level. The obtained combinatorial stochastic optimization problem will be formulated as a mixed integer program with conditional value-at-risk as a risk measure. The risk-neutral and risk-averse solutions that optimize, respectively average and worst-case performance of a supply chain are compared for a single and dual sourcing strategy and for the two different objective functions. Numerical examples and computational results are presented and some managerial insights on the choice between the two sourcing strategies are reported.     

Scheduling professionals in the retail pharmacy chain

To control operating costs, a zero-one integer programming model is developed to assist pharmacy staff scheduling decisions. Variable scheduling needs are met by the assignment of relief (mobile) pharmacists to help or temporarily replace full-time pharmacists. Assignments of relief pharmacists over a two-week planning horizon are determined with consideration given to variations in wage rates and travel costs together with the underlying corporate, contractual and operating constraints. The developed model has been applied with considerable success using data collected from a business district in the US located in northern Louisiana related to a national retail chain pharmacy. Forecasting the number of chain retail outlets in the near future has been also performed and the results obtained argue in favor of adopting the model by the entire chain.     

Product mix in the TFT-LCD industry

As operational costs and equipment depreciation in the TFT-LCD (thin film transistor-liquid crystal display) industry are a high percentage of the total cost, most manufacturers usually fully utilise their production capacity to reduce the average unit cost. However, when the market demand is less than the supply the stock of panels increases; this forces manufacturers to instigate a price war to reduce levels of stock and results in a wide fluctuation in panel prices. Inventory stocks of panels could be decreased by optimising the product mix. This will help manufacturers to reduce the risk of holding stocks, increase profit, and improve competitive advantage. This study uses mixed integer linear programming (MILP) to construct a product mix for the TFT-LCD industry given the conditions of profit, productivity, raw materials supply, and market demand. A case study shows that this model is proven to be effective in generating product mix for the TFT-LCD industry while improving profit. The product mix generated by this model can provide a reference for the sales department for orders and shipping, for the production department for the order quantity, and for master production scheduling for each product.     

中小呼叫中心月度排班优化模型与算法

国内中小呼叫中心制定坐席人员月度排班表时,通常考虑劳动法规合同约束和体现企业自身用工管理诉求。构建坐席人员月度排班优化问题的二次整数规划模型。鉴于问题模型难解性,依据调研企业需求和模型逻辑结构分析,把问题分解成三个子问题。通过构建整数规划模型和提出启发式算法来求出子问题解,从而生成排班问题优化解。问题实例计算表明,模型算法能够有效控制人力成本和兼顾员工同班次管理目标。与周排班方法比较,该方法能够充分体现月度排班人力灵活性来实现人力优化配置。     

A harmony search-based memetic optimization model for integrated production and transportation scheduling in MTO manufacturing

This paper investigates an integrated production and transportation scheduling problem in an MTO supply chain. A harmony search-based memetic optimization model is developed to handle this problem, in which certain heuristic procedures are proposed to convert the investigated problem into an order assignment problem. A novel improvisation process is also proposed to improve the optimum-seeking performance. The effectiveness of the proposed model is validated by numerical experiments. The experimental results show that (1) the proposed model can solve the investigated problem effectively and that (2) the proposed memetic optimization process exhibits better optimum-seeking performance than genetic algorithm-based and traditional memetic optimization processes.     

Integrated scheduling and inventory management of an oil products distribution system

The oil supply chain is facing new challenges due to emerging issues such as new alternative energy sources, oil sources scarcity, and price variability with high impact on demand and production and profit margins reduction. Additionally, the existence of large, complex and world wide spread businesses implies a complex system to be managed where distribution can be seen as one of the key areas that needs to be efficiently and effectively managed. Different types of distribution modes characterize the oil supply chain where the pipeline mode is one of the most complex to operate when having multiproduct characteristics. This paper addresses the planning of a generic oil derivatives transportation system characterized by a multiproduct pipeline that connects a single refinery to a storage tank farm. Two alternative mixed integer linear programming models (MILP) that aim to attain a set of planning objectives such as fulfilling costumers’ demands (which is mandatory) while minimizing the medium flow rate are developed. Additionally, final inventory levels are avoided to be excessively low. A real world scenario of a Portuguese company is used to validate and compare the two alternative MILP models developed in this paper.     

Integrated supply,production and distribution scheduling under disruption risks

This paper presents a bi-objective stochastic mixed integer programming approach for a joint selection of suppliers and scheduling of production and distribution in a multi-echelon supply chain subject to local and regional disruption risks. Two conflicting problem objectives are minimization of cost and maximization of service level. The three shipping methods are considered for distribution of products: batch shipping with a single shipment of different customer orders, batch shipping with multiple shipments of different customer orders and individual shipping of each customer order immediately after its completion. The stochastic combinatorial optimization problem is formulated as a time-indexed mixed integer program with the weighted-sum aggregation of the two objective functions. The supply portfolio is determined by binary selection and fractional allocation variables while time-indexed assignment variables determine the production and distribution schedules. The problem formulation incorporates supply–production, production–distribution and supply–distribution coordinating constraints to efficiently coordinate supply, production and distribution schedules. Numerical examples modelled after an electronics supply chain and computational results are presented and some managerial insights are reported. The findings indicate that for all shipping methods, the service-oriented supply portfolio is more diversified than the cost-oriented portfolio and the more cost-oriented decision-making, the more delayed the expected supply, production and distribution schedules.     

A heuristic framework for the bi-objective enhanced index tracking problem

The index tracking problem is the problem of determining a portfolio of assets whose performance replicates, as closely as possible, that of a financial market index chosen as benchmark. In the enhanced index tracking problem the portfolio is expected to outperform the benchmark with minimal additional risk. In this paper, we study the bi-objective enhanced index tracking problem where two competing objectives, i.e., the expected excess return of the portfolio over the benchmark and the tracking error, are taken into consideration. A bi-objective Mixed Integer Linear Programming formulation for the problem is proposed. Computational results on a set of benchmark instances are given, along with a detailed out-of-sample analysis of the performance of the optimal portfolios selected by the proposed model. Then, a heuristic procedure is designed to build an approximation of the set of Pareto optimal solutions. We test the proposed procedure on a reference set of Pareto optimal solutions. Computational results show that the procedure is significantly faster than the exact computation and provides an extremely accurate approximation.     

Theory of integer-valued data envelopment analysis under alternative returns to scale axioms

Kuosmanen and Kazemi Matin [Theory of integer valued data envelopment analysis. European Journal of Operational Research 2009;192:658–67] developed an axiomatic foundation for a data envelopment analysis (DEA) model that assumes subsets of input and output variables to be integer valued. In this paper we extend and generalize the axiomatic foundation for the integer DEA under variable, non-decreasing and non-increasing returns to scale. These model variants are achieved by introducing new axioms of natural convexity and natural augmentability. We also develop mixed integer linear programming (MILP) formulations for computing efficiency scores in these environments. An empirical example illustrates the approach.     

Scheduling Methods for Efficient Stamping Operations at an Automotive Company

We consider scheduling issues at Beyçelik, a Turkish automotive stamping company that uses presses to give shape to metal sheets in order to produce auto parts. The problem concerns the minimization of the total completion time of job orders (i.e., makespan) during a planning horizon. This problem may be classified as a combined generalized flowshop and flexible flowshop problem with special characteristics. We show that the Stamping Scheduling Problem is NP‐Hard. We develop an integer programming‐based method to build realistic and usable schedules. Our results show that the proposed method is able to find higher quality schedules (i.e., shorter makespan values) than both the company's current process and a model from the literature. However, the proposed method has a relatively long run time, which is not practical for the company in situations when a (new) schedule is needed quickly (e.g., when there is a machine breakdown or a rush order). To improve the solution time, we develop a second method that is inspired by decomposition. We show that the second method provides higher‐quality solutions—and in most cases optimal solutions—in a shorter time. We compare the performance of all three methods with the company's schedules. The second method finds a solution in minutes compared to Beyçelik's current process, which takes 28 hours. Further, the makespan values of the second method are about 6.1% shorter than the company's schedules. We estimate that the company can save over €187,000 annually by using the second method. We believe that the models and methods developed in this study can be used in similar companies and industries.     

Reducing Boarding in a Post‐Anesthesia Care Unit

When operating room schedules in hospitals are produced, the constraints and preferences of surgeons and hospital workers are a primary consideration. The downstream impact on post‐operative bed availability is often ignored. This can lead to the boarding of patients overnight in the post‐anesthesia care unit (PACU) because intensive care unit beds are unavailable. In this paper, we apply integer programming and simulation to develop improved surgical scheduling assignments. We want to balance new surgeries with hospital discharges in order to reduce the variability of occupied beds from one day to the next and, as a result, to reduce boarding in the PACU.     

Scheduling aerial resource operations for the extinction of large-scale wildfires

The significant increase in large-scale wildfire events in recent decades, caused primarily by climate change, has resulted in a growing number of aerial resources being used in suppression efforts. Present-day management lacks efficient and scalable algorithms for complex aerial resource allocation and scheduling for the extinction of such fires, which is crucial to ensuring safety while maximizing the efficiency of operations. In this work, we present a Mixed Integer Linear Programming (MILP) optimization model tailored to large-scale wildfires for the daily scheduling of aerial operations. The main objective is to achieve a prioritized target water flow over all areas of operation and all time periods. Minimal target completion across individual areas and time periods and total water output are also maximized as secondary and ternary objectives, respectively. An efficient and scalable multi-start heuristic, combining a randomized greedy approach with simulated annealing employing large neighborhood search techniques, is proposed for larger instances. A diverse set of problem instances is generated with varying sizes and extinction strategies to test the approaches. Results indicate that the heuristic can achieve (near)-optimal solutions for smaller instances solvable by the MILP, and gives solutions approaching target water flows for larger problem sizes. The algorithm is parallelizable and has been shown to give promising results in a small number of iterations, making it applicable for both night-before planning and, more time-sensitive, early-morning scheduling.     

Staff rostering in call centers providing employee transportation

We address the staff rostering problem in call centers with the goal of balancing operational cost, agent satisfaction and customer service objectives. In metropolitan cities such as Istanbul and Mumbai, call centers provide the transportation of their staff so that shuttle costs constitute a significant part of the operational costs. We develop a mixed integer programming model that incorporates the shuttle requirements at the beginning and end of the shifts into the agent-shift assignment decisions, while considering the skill sets of the agents, and other constraints due to workforce regulations and agent preferences. We analyze model solutions for a banking call center under various management priorities to understand the interactions among the conflicting objectives. We show that considering transportation costs as well as agent preferences in agent-shift assignments provides significant benefits in terms of both cost savings and employee satisfaction.     

Staffing and scheduling flexible call centers by two-stage robust optimization

We study the shift scheduling problem in a multi-shift, flexible call center. Differently from previous approaches, the staffing levels ensuring the desired quality of service are considered uncertain, leading to a two-stage robust integer program with right-hand-side uncertainty. We show that, in our setting, modeling the correlation of the demands in consecutive time slots is easier than in other staffing approaches. The complexity issues of a Benders type reformulation are investigated and a branch-and-cut algorithm is devised. The approach can efficiently solve real-world problems from an Italian call center and effectively support managers decisions. In fact, we show that robust shifts have very similar costs to those evaluated by the traditional (deterministic) method while ensuring a higher level of protection against uncertainty.     

WISCHE: A DSS for water irrigation scheduling

In this paper we present the models and the algorithms which are being used in a decision support system (DSS) to determine water irrigation scheduling. The DSS provides dynamic scheduling of the daily irrigation for a given land area by taking into account the irrigation network topology, the water volume technical conditions and the logistical operations. The system has been validated by the Agriculture Community of Elche (Spain) and annexed to their Supervisory Control and Data Acquisition system (SCADA). We present two heuristic approaches to solve the mixed 0–1 separable nonlinear program for irrigation scheduling implemented with free software.     

An improved MIP heuristic for the intermodal hub location problem

Optimization methods have been commonly developed for the intermodal hub location problem because it has a broad range of practical applications. These methods include exact methods (limited on solving large-size problems) and heuristics (no guarantee on solution quality). In order to avoid their weakness but to leverage their strength, we develop an improved MIP heuristic combining branch-and-bound, Lagrangian relaxation, and linear programming relaxation. In the heuristic, we generate a population of initial feasible solutions using the branch-and-bound and Lagrangian relaxation methods and create a linear-relaxed solution using the linear programming relaxation method. We combine these feasible and linear-relaxed solutions to fix a portion of hub location variables so as to create a number of restricted hub location subproblems. We then combine the branch-and-bound method to solve these restricted subproblems for iteratively improving solution quality. We discuss in detail the application of the method to the intermodal hub location problem. The discussion is followed by extensive statistical analysis and computational tests, where the analysis shows statistical significance of solutions for guiding the heuristic search and comparisons with other methods indicate that the proposed approach is computationally tractable and is able to obtain competitive results.     

Trip packing in petrol stations replenishment

This paper considers a generalized version of the trip packing problem that we encountered as a sub-problem of the petrol stations replenishment problem. In this version we have to assign a number of trips to a fleet composed of a limited number of non-identical tank-trucks. Each trip has a specific duration, working time of vehicles is limited and the net revenue of each trip depends on the truck used. The paper provides a mathematical formulation of the problem and proposes some construction, improvement and neighbourhood search solution heuristics. A set of benchmark problem instances is created in a way that reflects real-life situations and used to analyse the performance of the proposed heuristics. A real-life case is also used to further assess the proposed heuristics.     

Bi-objective multi-resource scheduling problem for emergency relief operations

Abstract

Resource scheduling for emergency relief operations is complex as it has many constraints. However, an effective allocation and sequencing of resources are crucial for the minimization of the completion times in emergency relief operations. Despite the importance of such decisions, only a few mathematical models of emergency relief operations have been studied. This article presents a bi-objective mixed integer programming (MIP) that helps to minimize both the total weighted time of completion of the demand points and the makespan of the total emergency relief operation. A two-phase method is developed to solve the bi-objective MIP problem. Additionally, a case study of hospital network in the Melbourne metropolitan area is used to evaluate the model. The results indicate that the model can successfully support the decisions required in the optimal resource scheduling of emergency relief operations.     

Comments on the Paper: Attacking the Market Split Problem with Lattice Point Enumeration

We present a few comments on the paper Attacking the market split problem with lattice point enumeration by A. Wasserman, published in Journal of Combinatorial Optimization, vol. 6, pp. 5–16, 2002.     

A goal programming model for paper recycling system

The conflict between economic optimization and environmental protection has received wide attention in recent research programs for waste management system planning. This has also resulted in a set of new waste management goals in reverse logistics system planning. The purpose of this analysis is to formulate a mixed integer goal programming (MIGP) model to assist in proper management of the paper recycling logistics system. The model studies the inter-relationship between multiple objectives (with changing priorities) of a recycled paper distribution network. The objectives considered are reduction in reverse logistics cost; product quality improvement through increased segregation at the source; and environmental benefits through increased wastepaper recovery. The proposed model also assists in determining the facility location, route and flow of different varieties of recyclable wastepaper in the multi-item, multi-echelon and multi-facility decision making framework. The use of the model has been illustrated through a problem of paper recycling in India.