Online pricing with bundling and coupon discounts

We propose an online pricing strategy by utilising product bundling and coupon discounts. Given customer’s purchase behaviour and preference for bundling and coupon, we propose a nonlinear mixed-integer programming model to determine the most appropriate bundle discount and instant coupon so as to maximise e-tailer’s profit. A fast heuristic algorithm is designed to implement the proposed model online in real time. We investigate the robustness of the proposed method by examining how uncertainties in system parameters affect performance. Through collaborative optimisation, we offer important insights and managerial implications, and show how marketers can attract more purchase and maximise profit by properly integrating marketing tools such as bundling and coupon.     

Optimal supply contract selection

Selection of supply contracts is a critical decision faced by manufacturing firms in a variety of industries. Manufacturing firms often have the option of selecting from several types of supply contracts that include long-term, medium-term, and short-term contracts. While extant literature has stressed the importance of such contracts, few methodologies have been proposed for optimally selecting contracts under various business conditions. To this end, this paper proposes a methodology for optimal contract selection based on a mixed-integer programming approach. We present specific insights to manufacturing managers on choosing the right contracts in the presence of market price uncertainty, supplier discounts, investment costs, and supplier capacity restrictions.     

A fuzzy technique for supply chain network design with quantity discounts

This paper proposes a hierarchical technique for Supply Chain Network (SCN) efficiency maximisation under uncertainty composed of three steps. The first step extends a previous fuzzy cross-efficiency Data Envelopment Analysis approach, originally intended for suppliers’ selection, in order to evaluate and rank all the actors in each SCN stage under conflicting nondeterministic criteria. Afterwards, a fuzzy linear integer programming model is stated and solved for each pair of subsequent SCN stages to determine the quantities required from each stakeholder to maximise the overall SCN efficiency while satisfying the estimated demand and respecting the nodes capacity. Finally, a heuristics is applied to limit the exchange of small quantities in the SCN, in which the trade is not economically convenient according to quantity discounts. An illustrative example from the literature shows the technique effectiveness.     

A stochastic lot-sizing model with multi-supplier and quantity discounts

This research considers a stochastic lot-sizing problem with multi-supplier and quantity discounts. The objectives are to minimise total costs, where the costs include ordering cost, holding cost, purchase cost and shortage cost, and to maximise service level of the system. In this paper, we first formulate the stochastic lot-sizing problem as a multi-objective programming (MOP) model. We then transform the model into a mixed integer programming (MIP) model. Finally, an efficient heuristic dynamic programming (HDP) model is constructed for solving large-scale stochastic lot-sizing problems. An illustrative example with two cases for a touch panel manufacturer is used to illustrate the practicality of these models, and a sensitivity analysis is applied to understand the impact of the changes in parameters to the outcomes. The results demonstrate that the proposed two models are effective and accurate tools for determining the replenishment of touch panels from multiple suppliers for multi-periods.     

Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques

This paper has as a major objective to present a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.     

On the robust decision-making in a supply chain under disruption risks

This paper considers a robust decision-making problem associated with supplies of parts and deliveries of finished products in a customer driven supply chain under disruption risks. The robustness refers to an equitably efficient performance of a supply chain in average-case as well as in the worst-case, which reflects the decision-makers common requirement to maintain an equally good performance of a supply chain under different conditions. Given a set of customer orders for products, the decision-maker needs to select suppliers of parts required to complete the orders, allocate the demand for parts among the selected suppliers and schedule the orders over the planning horizon, to equitably optimise average and worst-case performance of the supply chain. The supplies are subject to independent random local and regional disruptions. The obtained combinatorial stochastic optimisation problem is formulated as a mixed-integer program with conditional value-at-risk as a risk measure. The ordered weighted averaging aggregation of the expected value and the conditional value-at-risk of the selected optimality criterion is applied to obtain a robust solution. The risk-neutral, risk-averse and robust solutions that optimise, respectively average, worst-case and equitable average and worst-case performance of a supply chain are determined and compared for cost and customer service level objective functions. Numerical examples and computational results, in particular comparison with the mean-risk approach, are presented and some managerial insights are reported.     

Optimal Design of Electronic Components by Mixed-Integer Nonlinear Programming

Computer-aided design optimization of electronic components is a powerful tool to reduce development costs on one hand and to improve the performance of the components on the other. In this paper, a mathematical model of an electronic filter is outlined. It depends on certain parameters, some of them of being continuous, others of integer type. The purpose of the paper is to introduce an extension of the well-known sequential quadratic programming (SQP) method to solve the mixed-integer programming problem (MINLP). It is assumed that the integer variables cannot be relaxed to real ones, that the integer range is sufficiently large, and that they possess some physical meaning so that they basically behave like continuous ones. The general idea is to combine an SQP step with a direct search cycle in the integer space. Hessian information is updated based on difference formulae at neighbored grid points. Numerical results are included to show the feasibility of the mixed-integer nonlinear programming code for academic test examples and in addition for the optimal design of an electronic filter.     

Decentralised planning coordination with quantity discount contract in a divergent supply chain

This paper proposes to solve a supply chain planning problem with realistic features. The problem consists of planning productions, transportations and storage activities in a supply chain at a tactical level on a finite horizon. The main features considered are decentralised decision making and iteration of the planning process on a rolling horizon basis. In each planning process, the actors optimise their local planning and coordinate to achieve a good overall planning. A multi-agent system is used to model such supply chain behaviour. The study is conducted in a divergent two-echelon supply chain with one manufacturer and multiple independent retailers. Coordination is achieved using a standard contract in practice, known as the ‘quantity discount’ contract. The planning framework on the supply chain structure is detailed. Lot-sizing models integrating the quantity discount are presented for the local planning problems. Experimental tests are conducted with three major parameters: quantity discount price, quantity discount breakpoint and rolling horizon length. They are used to determine the quantity discount parameters in achieving the best supply chain profit, and to analyse the increasing profit of the actors. A decision-making tool which is able to consider realistic features of supply chain planning is therefore resulted.     

Optimal production control policy in unreliable batch processing manufacturing systems with transportation delay

This paper considers the problem of production planning of unreliable batch processing manufacturing systems. The finished goods are produced in lots, and are then transported to a storage area in order to continuously meet a constant demand rate. The main objective of this work is to jointly determine the optimal lot sizing and optimal production control policy that minimise the total expected cost of inventory/backlog and transportation, over an infinite time horizon. The decision variables are the lot sizing and the production rate. The problem is formulated with a stochastic dynamic programming model and the impulse control theory is applied to establish the Hamilton–Jacobi–Bellman (HJB) equations. Based on a numerical resolution of the HJB equations, it is shown that the optimal control policy is governed by a base stock policy for production rate control and economic lot size for batch processing. A thorough analysis and practical issues are addressed with a simulation-based approach. Thus, a combined discrete–continuous simulation model is developed to determine the optimal parameters of the proposed policy when the failure and repair times follow general distributions. The results are illustrated with numerical examples and confirmed through sensitivity analysis.     

Supply chain optimisation with assembly line balancing

Supply chain management operates at three levels, strategic, tactical and operational. While the strategic approach generally pertains to the optimisation of network resources such as designing networks, location and determination of the number of facilities, etc., tactical decisions deal with the mid-term, including production levels at all plants, assembly policy, inventory levels and lot sizes, and operational decisions are related to how to make the tactical decisions happen in the short term, such as production planning and scheduling. This paper mainly discusses and explores how to realise the optimisation of strategic and tactical decisions together in the supply chain. Thus, a supply chain network (SCN) design problem is considered as a strategic decision and the assembly line balancing problem is handled as a tactical decision. The aim of this study is to optimise and design the SCN, including manufacturers, assemblers and customers, that minimises the transportation costs for determined periods while balancing the assembly lines in assemblers, which minimises the total fixed costs of stations, simultaneously. A nonlinear mixed-integer model is developed to minimise the total costs and the number of assembly stations while minimising the total fixed costs. For illustrative purposes, a numerical example is given, the results and the scenarios that are obtained under various conditions are discussed, and a sensitivity analysis is performed based on performance measures of the system, such as total cost, number of stations, cycle times and distribution amounts.     

Multiproduct vendor selection with volume discounts as the fuzzy multi-objective programming problem

Vendor selection in supply chain is a multi-criteria problem that involves a number of quantitative and qualitative factors. This paper deals with a concrete problem of flour purchase by a company that manufactures bakery products. The selection process is driven by the price, reliability and quality objectives of the buyer and is subject to the capacity constraints of the vendors in the situation where all suppliers offer several kinds of flour (multiproduct situation). Vendors often offer quantity discounts, i.e. the purchasing price of flour depends on the quantity ordered. The multiproduct situation complicates the mathematical formulation of the problem and in this context it is much more convenient to consider the discounts of the money volume of business with every vendor. This problem has been solved using an integration of analytic hierarchy process (AHP), weighted sum model (WSM) and fuzzy multi-objective mixed-integer programming to define the optimum quantities among the selected suppliers.     

Optimal design of an oil pipeline with a large-slope section

One of the important issues in the operation of a long-distance oil pipeline in a large-slope area is pressure control, especially for the section after the turning point. In this study, a method to optimally design an oil pipeline with a large-slope section is proposed. The method is based on a stochastic mixed-integer linear programming model with minimal total cost as the objective function to determine the size of the pipeline, the location, the operational plan of pump stations and the location of pressure reduction stations. Hydraulic calculations and different types of oil product are considered. The uncertainty in flow rates of the pipeline is studied by the proposed stochastic programming approach. This method is applied to a real case of designing an oil product pipeline in a large-slope area.     

Two-level hedging point control of a manufacturing system with multiple product-types and uncertain demands

This research is motivated by the co-operative production process of networked manufacturing systems (NMS). Manufacturing resource sharing and flexible production scheduling are two features of NMS. For an individual manufacturing system in an NMS, ‘flexible production scheduling’ means that it can produce multiple product-types and the switching of products is quick enough to respond to the demand fluctuation. ‘Manufacturing resource sharing’ means the utilisation of extra production capacity from other manufacturing systems in the NMS. Of course, that will bring extra cost. This paper focuses on the optimal production control problem of such a situation: one manufacturing system, multiple product-types, and uncertain demands. Here, it is assumed that there are two demand-levels for each product-type: the lower one and the higher one. The total normal production capacity is larger than the total lower demands and smaller than the total higher demands. If the total demands cannot be satisfied and the work-in-process (WIP) of all product-types decrease to a certain level, e.g. zero WIP, the extra production capacity may be utilised. For such a system, a new two-level hedging point policy is proposed, in which two hedging points (a higher one and a lower one) are given for each product-type. Different from the prioritised hedging point (PHP) policy which is usually applied to one-machine and multiple part-type systems, our control policy considers all part-types at the same prioritised level and keeps the work-in-process states of all product-types on a straight line in the state space. Thus, the total costs for WIP inventory and the occupation of extra capacity can be obtained in a closed form, which is a function with respect to the hedging points. Then the method for optimising the hedging points is proposed and the special structure of the optimal hedging point is obtained. Numerical experiments verify the optimality and the special structure of the hedging point obtained by our method.     

Channel coordination with quantity discounts and/or cooperative advertising

We assess the interactive effects of two commonly used channel coordination mechanisms (quantity discounts (QDs) and cooperative advertising (CA)). We use a game-theoretic model and solve four non-cooperative games. In the first game, neither QDs nor CA is implemented. Cooperative advertising alone is offered in the second game, while quantity discounts alone are offered in the third game. In the fourth game, both QDs and CA are implemented. We obtain analytical solutions and compare equilibrium results across games to assess the effectiveness of CA (QDs) when implemented alone or jointly with QDs (CA). The main findings suggest that the profitability of each of these mechanisms is affected by whether the other is implemented or not in the channel. For example, while CA benefits the manufacturer when implemented alone, it can increase or decrease the manufacturer’s profit when added to QDs. Looking at which coordination mechanism is most effective when used alone, we find that both the manufacturer and the supply chain prefer QDs to CA. Finally, the retailer may not benefit from either one or both of these coordination mechanisms, especially if marketing efforts are not highly effective.     

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.     

定量包装商品净含量计量检验方法的探讨

为保证定量包装商品净含量计量检验结果的统一性、有效性和准确性,依据JJF 1070-2005《定量包装商品净含量计量检验规则》,对影响定量包装商品净含量检验结果的不确定度的主要来源和检验的关键点进行分析,找出每种检验方法中影响净含量检验结果的测量不确定度,为今后科学地计量检验定量包装商品净含量奠定基础。     

Optimal acquisition decision in a remanufacturing system with partial random yield information

When making decisions to acquire used products or components (cores), a remanufacturer faces limited information on the quality or proportional yield of cores during the recovery process. In this paper, we propose and analyse a robust optimisation model for studying the remanufacturing decision problem with partial random yield information, that is, when the quality information of cores is partly unknown in a remanufacturing system. Regarding the impacts of unknown yield information, we only require the support and mean of the proportional yield rather than the true distributions. The closed-form solutions of acquisition quantities are derived based on the minimax regret approach. In addition, to validate the effectiveness of the analytical results, particularly the acquisition of yield information, numerical experiments are designed and implemented using (1) the support and mean of the proportional yield based on the manufacturer’s knowledge and (2) a sampling inspection to evaluate the performance of the robust optimisation approach, the benchmark, and the naïve approach. We observe that the minimax regret approach slightly underperforms compared to the benchmark but performs much better than the naïve approach. As an acceptable choice, this approach is less complicated and extremely easy to implement to meet the needs of practical situations based on its robust closed-form solutions.     

Optimal introduction time decision for holiday products with uncertain market demand

In this paper, we investigate how retailers with different risk preferences determine the optimal introduction time and order quantity for holiday products to maximise performance in environments characterised by uncertain market demand. Specifically, both the market demand and the accuracy of sales forecasts are assumed to be affected by the timing of the introduction, which in turn affects the order quantity and subsequent performance. The results suggest that as the level of uncertainty in the market demand increases, as the retailer’s power in the industry increases and as the coefficient of elasticity of the competitive demand over introduction time is larger, the retailer prefers to set a later introduction time and to order smaller quantities, to reduce the risk of overstocking. Moreover, a risk-averse retailer will set a later introduction time and order smaller quantities than a risk-neutral retailer. Indeed, the more risk-averse the retailer is, the later will be the introduction time and the smaller the quantity ordered. The managerial implications are presented for decision-makers with different risk preferences regarding the interconnections between important factors and introduction time and inventory decisions for holiday products in environments characterised by uncertain market demand.     

Optimal order quantity and product modularity for a two-echelon returnable supply chain

This study considers a supply chain consisting of a manufacturer, a retailer, customers and a returnable and modular product with uncertain demand, in which customers return the unsatisfactory products to the retailer, and the retailer returns the unsold products to the manufacturer. We investigate the effects of the manufacturer’s refund for the retailer’s unsold products and the product modularity under the decentralised and the centralised strategies. We confirm that the order quantity and customer’s return probability both affect the optimal modularity level of the product, and that the optimal modularity level is related to the refund policy. Also, a strategic alliance between the supply chain members is more advantageous to product innovation based on modularity for a returnable chain. Finally, managerial insights and remarks are offered.     

Robust stability analysis of structures with uncertain parameters using mathematical programming approach

This paper presents a novel mathematical programming approach for the static stability analysis of structures with uncertainties within the framework of FEM. The considered uncertain parameters are material properties, geometry of element cross section, and loading conditions, all of which are described by an interval model. The proposed method formulates the two cases of interest, namely, worst and best buckling load calculation, into a pair of mathematical programming problems. Two straightforward advantages are exhibited by such formulations. The first advantage is that the proposed formulation can overcome the interference on the sharpness of bounds of the buckling load due to the interval dependence issue. The second benefit is that the information of uncertain parameters causing the extremities of buckling load can always be retrieved as by‐products of the uncertain stability analysis. Some numerical examples are presented to illustrate the capability of the proposed method on various structures and the sharpness of the bounds of the buckling load factors. The efficiency and effectiveness of the proposed method are also demonstrated through comparison with the classical Monte Carlo simulation method. Copyright © 2014 John Wiley & Sons, Ltd.