Managing demand uncertainty through fuzzy inference in supply chain planning

In this paper, we investigate methods for managing the irregular and uncertain demands involved in supply chain planning. We first build a supply chain planning model based on fuzzy linear programming, which defines demand as a fuzzy parameter. Next, we propose a fuzzy inference approach for converting fuzzy demand into crisp demand. In the proposed fuzzy inference-based approach, judgments of upcoming demand from both internal and external experts are used as input variables to reflect the expected demand irregularity. By adopting fuzzy inference, we can compensate for the limitations of the existing demand treatment approaches, which usually demonstrate poor forecasting performance in cases of irregular demand and thus reduce the accuracy of supply chain planning. To verify the feasibility of the proposed approach, we present an illustrative example of a Korean electronics company.     

Adjustable Robust Optimisation approach to optimise discounts for multi-period supply chain coordination under demand uncertainty

In this research, a problem of supply chain coordination with discounts under demand uncertainty is studied. To solve the problem, an Affinely Adjustable Robust Optimisation model is developed. At the time when decisions about order periods, ordering quantities and discounts to offer are made, only a forecasted value of demand is available to a decision-maker. The proposed model produces a discount schedule, which is robust against the demand uncertainty. The model is also able to utilise the information about the realised demand from the previous periods in order to make decisions for future stages in an adjustable way. We consider both box and budget uncertainty sets. Computational results show the necessity of accounting for uncertainty, as the total costs of the nominal solution increase significantly even when only a small percentage of uncertainty is in place. It is testified that the affinely adjustable model produces solutions, which perform significantly better than the nominal solutions, not only on average, but also in the worst case. The trade-off between reduction of the conservatism of the model and the uncertainty protection is investigated as well.     

考虑价格和时间敏感性需求的两周期供应链鲁棒优化模型

在不确定需求下,考虑需求的时间和价格敏感性,研究两周期供应链定价及订货联合决策问题。利用分段函数构建需求的价格和时间敏感性,并采用区间不确定集描述需求不确定性。根据制造商是否给予零售商回扣,分别建立主从对策鲁棒优化模型,并转化为可解的数学规划。结果表明,需求不确定性以及需求的时间和价格敏感性对双方的定价、订货和利润具有影响。具有回扣的主从策略使双方获得更高利润,需求的不确定性以及需求的时间和价格敏感性增加会降低双方利润。     

Robust interval linear programming for environmental decision making under uncertainty

In this study, a robust interval linear programming (RILP) method is developed for dealing with uncertainties expressed as intervals with deterministic boundaries. An enhanced two-step method (ETSM) is also advanced to solve the RILP model. The developed RILP improves upon the conventional interval linear programming (ILP) method since it can generate solution intervals within a larger feasible zone. The decision space based on ETSM contains all feasible solutions, such that no useful information is neglected. Moreover, the RILP can guarantee the stability of the optimization model due to no violation for the best-case constraints. The results also suggest that the RILP is effective for practical environmental and engineering problems that involve uncertainties.     

An integer linear programming model to support customer-driven material planning in synchronised,multi-tier supply chains

This paper describes an integer linear programming model conceived as an alternative to a traditional material requirements planning (MRP) system for extending the concept of supply chain synchronisation upstream in a multi-tier supply chain. In this model, we assume there is an incumbent application for transmitting original equipment manufacturer (OEM) requirements to first-, second- and third-tier suppliers. The proposed model is regarded as being embedded within a web-enabled, multi-tier, supply chain information system that provides the application for transmitting the production requirements. The principal motivation for having second- and third-tier suppliers that are synchronised with OEM and first-tier activity is the significant inventory, lead time and responsiveness gains that can potentially be achieved. Here, inventory is considered as a whole across a supply chain, and stock-outs are prohibited for the first-tier supplier. For illustration purposes, an example based on a real, automotive case study is provided. The model results proved better in terms of inventory and bullwhip reduction than those found in a previous simulation-based approach. Also, a comparison of the proposed case results with those of a conventional MRP application is provided.     

Two-stage stochastic master production scheduling under demand uncertainty in a rolling planning environment

This paper proposes a scenario-based two-stage stochastic programming model with recourse for master production scheduling under demand uncertainty. We integrate the model into a hierarchical production planning and control system that is common in industrial practice. To reduce the problem of the disaggregation of the master production schedule, we use a relatively low aggregation level (compared to other work on stochastic programming for production planning). Consequently, we must consider many more scenarios to model demand uncertainty. Additionally, we modify standard modelling approaches for stochastic programming because they lead to the occurrence of many infeasible problems due to rolling planning horizons and interdependencies between master production scheduling and successive planning levels. To evaluate the performance of the proposed models, we generate a customer order arrival process, execute production planning in a rolling horizon environment and simulate the realisation of the planning results. In our experiments, the tardiness of customer orders can be nearly eliminated by the use of the proposed stochastic programming model at the cost of increasing inventory levels and using additional capacity.     

Robust closed-loop global supply chain network design under uncertainty: the case of the medical device industry

Improving performance of global supply chains requires careful consideration of various factors including distance from markets, access to resources, exchange and tax rates, import tariffs, and trade regulations. In this paper, a comprehensive optimization model is proposed to maximise the after-tax profit of a closed-loop global supply chain for medical devices under uncertainty. The uncertainty of the decision-making environment is modelled using the budget of uncertainty concept in interval robust optimization. International financial issues due to the Economic Cooperation Organisation Trade Agreement as well as national regulations including transfer pricing limitations, exchange rates, tax rates, and import tariffs are considered. The proposed model considers various realistic assumptions pertaining to medical device supply chains such as multiple products, multiple periods, multiple echelons, and limited warehousing lifetime. In addition, reverse flows of perished and defective products are considered to address environmental concerns and customers’ requirements as well as to gain economic advantages. To tackle this problem, an efficient memetic algorithm is developed that incorporates adaptive variable neighbourhood search as its local search heuristic. Computational results demonstrate the efficiency of the proposed model in dealing with uncertainty in an agile manufacturing context. In addition, several managerial insights are discussed based on the results.     

A rolling horizon approach for material requirement planning under fuzzy lead times

This paper proposes a fuzzy multi-objective integer linear programming (FMOILP) approach to model a material requirement planning (MRP) problem with fuzzy lead times. The objective functions minimise the total costs, back-order quantities and idle times of productive resources. Capacity constraints are included by considering overtime resources. Into the crisp MRP multi-objective model, we incorporate the possibility of occurrence of each uncertain lead time using fuzzy numbers. Then FMOILP is transformed into an auxiliary crisp mixed-integer linear programming model by a fuzzy goal programming approach for each fuzzy lead time combination. In order to defuzzify the set of solutions associated with each fuzzy lead time combination, a solution method based on the centre of gravity concept is addressed. Model validation with a numerical example is carried out by a novel rolling horizon procedure where uncertain lead times are updated during each planning period according to the centre of gravity obtained. For illustration purposes, the proposed solution approach is satisfactorily compared to a rolling horizon approach in which lead times are allocated when the possibility of occurrence is established at one.     

A survey of semiconductor supply chain models Part II: demand planning,inventory management,and capacity planning

Part I of this three-part series described semiconductor supply chains from the decision-making and functional perspectives, using this as a framework to review the industrial engineering and operations research literature on the problems arising in these supply chains. Part I then reviewed the literature on Strategic Network Design, supply chain coordination, sustainability and simulation-based decision support. This paper, Part II, reviews the areas of Demand Planning, Inventory Management and Capacity Planning in semiconductor supply chains. Part III concludes the series by discussing models to support Master Planning, Production Planning and Demand Fulfilment in this industry.     

Blood supply chain network design considering blood group compatibility under uncertainty

This paper addresses the design of a blood supply chain (SC) network considering blood group compatibility. To this aim, a bi-objective mathematical programming model is developed which minimises the total cost as well as the maximum unsatisfied demand. Due to uncertain nature of some input parameters, two novel robust possibilistic programming models are proposed based on credibility measure. The data of a real case study are then used to illustrate the applicability and performance of the proposed models as well as validating the proposed robust possibilistic programming approach. The obtained results show the superiority of the developed models and significant cost savings compared to current existed blood SC network.     

Robust topology optimization under load position uncertainty

The topology optimization problem of a continuum structure on the compliance minimization objective is investigated under consideration of the external load uncertainty in its application position with a nonprobabilistic approach. The load position is defined as the uncertain-but-bounded parameter and is represented by an interval variable with a nominal application point. The structural compliance due to the load position deviation is formulated with the quadratic Taylor series expansion. As a result, the objective gradient information to the topological variables can be evaluated efficiently in a quadratic expression. Based on the maximum design sensitivity value, which corresponds to the most sensitive compliance to the uncertain loading position, a single-level optimization approach is suggested by using a popular gradient-based optimality criteria method. The proposed optimization scheme is performed to gain the robust topology optimizations of three benchmark examples, and the final configuration designs are compared comprehensively with the conventional topology optimizations under the loading point fixation. It can be observed that the present method can provide remarkably different material layouts with auxiliary components to accommodate the load position disturbances. The numerical results of the representative examples also show that the structural performances of the robust topology optimizations appear less sensitive to the load position perturbations than the traditional designs.     

Supply chain flexibility and operations optimisation under demand uncertainty: a case in disaster relief

After a disaster happens, emergency response operations are critical to save humans’ lives and properties. The limited resources and time requirements call for coordinated supply chain operations. This paper studies supply chain operations for rescue kits in disaster reliefs, motivated by a real-world application. The objective is to minimise the total tardiness and peak tardiness of product delivery over the multi-period planning horizon. One major challenge is the lack of reliable prediction of customer demand in disasters. In order to cope with demand uncertainty while maintaining the tractability of the optimisation model, we decompose the demand into two components: a relatively stable base demand predicted by historical data and unpredictable demand surges. For the base demand, an optimisation model is developed to optimise the production and distribution operations, as well as the inventory replenishment policy for manufacturers and distribution centres, so as to minimise the total tardiness. For the demand surges, we propose to deploy supply chain flexibility to cope with the uncertainty. An empirical study shows the effectiveness of increasing supply chain flexibility and suggests some managerial insights on configuring such flexibility in emergency operations.     

Individuals and their interactions in demand planning processes: an agent-based,computational testbed

The demand planning process in semiconductor supply chains faces many challenges. In this process, individuals, their properties such as sensing capabilities and their interactions play a crucial role. This paper shows how agent-based modelling (ABM) can provide a computational testbed to investigate these aspects with respect to forecast accuracy. Based on the requirements of the demand planning context, we develop an empirically validated agent-based model of the demand planning process. In this model, we incorporate different concepts from behavioural science and the distributed cognition perspective. We show the usefulness of this agent-based computational testbed by using a case study from the semiconductor industry. Our model shows that demand planning accuracy does not depend on the planning capabilities of planners alone, but that the interactions of the individuals, emerging from the planning process design, may both positively and negatively affect accuracy.     

A robust optimisation model for production planning and pricing under demand uncertainty

The profitability of every manufacturing plant is dependent on its pricing strategy and a production plan to support the customers’ demand. In this paper, a new robust multi-product and multi-period model for planning and pricing is proposed. The demand is considered to be uncertain and price-dependent. Thus, for each price, a range of demands is possible. The unsatisfied demand is considered to be lost and hence, no backlogging is allowed. The objective is to maximise the profit over the planning horizon, which consists of a finite number of periods. To solve the proposed model, a modified unconscious search (US) algorithm is introduced. Several artificial test problems along with a real case implementation of the model in a textile manufacturing plant are used to show the applicability of the model and effectiveness of the US for tackling this problem. The results show that the proposed model can improve the profitability of the plant and the US is able to find high quality solutions in a very short time compared to exact methods.     

Forest harvesting planning under uncertainty: a cardinality-constrained approach

Harvesting planning (HP) is a key tactical decision in lumber supply chains. Harvesting areas in the forests are divided into different blocks with different types and quantities of raw materials (logs). Predicting the availability of raw materials in each block along with log demand is impossible in this industry. Hence, incorporating uncertainty into the HP problem is essential in order to obtain robust plans that do not drastically fluctuate in the presence of future perturbations in the forest and log market. In this paper, we propose a robust harvesting planning model formulated based on cardinality-constrained method. The latter provides some insights into the adjustment of the level of robustness of the harvesting plan over the planning horizon and protection against uncertainty. An extensive set of experiments based on Monte-Carlo simulation is also conducted in order to better validate the proposed robust optimisation approach.     

价格不确定供应链的多目标运作鲁棒模型

建立了由一个制造商和一个供应商构成的多产品、多阶段供应链在原材料和最终产品的市场价格均不确定情况下运作的鲁棒模型.采用区间不确定性描述价格的不确定性.供应链的运作模型为一个多目标规划问题,满足诸如供应链协调运作、所有供应链成员的目标利润尽可能最大、对应于不确定供求价格的决策的鲁棒性等多个相互冲突的目标.数值算例的结果表明,一定范围内的市场价格波动不改变供应链的运作策略,仅对其运作性能产生一定影响,即所提出的模型是鲁棒的.     

Optimal ordering policy for a price-setting newsvendor with option contracts under demand uncertainty

In this article, we investigate the newsvendor problem in a joint ordering and pricing setting in the presence of option contracts under demand uncertainty. At the beginning of a single selling season, the newsvendor who faces additive stochastic demand can obtain goods through two ways: ordering from a firm or purchasing and exercising call options. Single ordering (ordering from a firm only or purchasing and exercising call options only) and mixed ordering (ordering from a firm and purchasing and exercising call options simultaneously) cases are investigated. We find that the newsvendor’s optimal pricing and ordering strategies exist and are unique for both cases, respectively. In addition, when both cases are available, mixed ordering is the newsvendor’s optimal ordering policy. If only single ordering is available, the newsvendor prefers ordering from a firm when demand risk is low, while enjoys purchasing and exercising call options when demand risk is high. We also find that with option contracts, the newsvendor’s optimal order quantity and maximum expected profit are all decreasing in the option price and exercise price of product, while the optimal retail price in terms of option price and exercise price of product are intricate. Moreover, we show that, mixed ordering is more capable to deal with supply price volatility risk.     

Robust closed-loop supply chain network design for perishable goods in agile manufacturing under uncertainty

In this study, a general comprehensive model is proposed for strategic closed-loop supply chain network design under interval data uncertainty. The proposed model considers various assumptions such as multiple periods, multiple products, and multiple supply chain echelons as well as uncertain demand and purchasing cost. In addition, bill of materials for each product is considered via a new approach in management of forward and reverse flows of products for producing new products and reusing or disassembling returned products. Uncertainty of parameters in the proposed model is handled via an interval robust optimisation technique. The model assumptions are well matched with decision making environments of food and high-tech electronics manufacturing industries. The factors that make these two industries similar are time-dependent properties of products such as prices and warehousing lifetime period. The computational results of solving the proposed model via LINGO 8 demonstrate efficiency of the proposed model in dealing with uncertainty in an agile manufacturing context.     

Fuzzy goal programming for material requirements planning under uncertainty and integrity conditions

In this paper, we formulate the material requirements planning) problem of a first-tier supplier in an automobile supply chain through a fuzzy multi-objective decision model, which considers three conflictive objectives to optimise: minimisation of normal, overtime and subcontracted production costs of finished goods plus the inventory costs of finished goods, raw materials and components; minimisation of idle time; minimisation of backorder quantities. Lack of knowledge or epistemic uncertainty is considered in the demand, available and required capacity data. Integrity conditions for the main decision variables of the problem are also considered. For the solution methodology, we use a fuzzy goal programming approach where the importance of the relations among the goals is considered fuzzy instead of using a crisp definition of goal weights. For illustration purposes, an example based on modifications of real-world industrial problems is used.     

A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty

In this paper we introduce a robust optimization approach to solve the Vehicle Routing Problem (VRP) with demand uncertainty. This approach yields routes that minimize transportation costs while satisfying all demands in a given bounded uncertainty set. We show that for the Miller-Tucker-Zemlin formulation of the VRP and specific uncertainty sets, solving for the robust solution is no more difficult than solving a single deterministic VRP. Our computational results on benchmark instances and on families of clustered instances show that the robust solution can protect from unmet demand while incurring a small additional cost over deterministic optimal routes. This is most pronounced for clustered instances under moderate uncertainty, where remaining vehicle capacity is used to protect against variations within each cluster at a small additional cost. We compare the robust optimization model with classic stochastic VRP models for this problem to illustrate the differences and similarities between them. We also observe that the robust solution amounts to a clever management of the remaining vehicle capacity compared to uniformly and non-uniformly distributing this slack over the vehicles.