A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment

This paper models supply chain (SC) uncertainties by fuzzy sets and develops a fuzzy linear programming model for tactical supply chain planning in a multi-echelon, multi-product, multi-level, multi-period supply chain network. In this approach, the demand, process and supply uncertainties are jointly considered. The aim is to centralize multi-node decisions simultaneously to achieve the best use of the available resources along the time horizon so that customer demands are met at a minimum cost. This proposal is tested by using data from a real automobile SC. The fuzzy model provides the decision maker (DM) with alternative decision plans with different degrees of satisfaction.     

A fuzzy optimization approach for procurement transport operational planning in an automobile supply chain

We consider a real-world automobile supply chain in which a first-tier supplier serves an assembler and determines its procurement transport planning for a second-tier supplier by using the automobile assembler’s demand information, the available capacity of trucks and inventory levels. The proposed fuzzy multi-objective integer linear programming model (FMOILP) improves the transport planning process for material procurement at the first-tier supplier level, which is subject to product groups composed of items that must be ordered together, order lot sizes, fuzzy aspiration levels for inventory and used trucks and uncertain truck maximum available capacities and minimum percentages of demand in stock. Regarding the defuzzification process, we apply two existing methods based on the weighted average method to convert the FMOILP into a crisp MOILP to then apply two different aggregation functions, which we compare, to transform this crisp MOILP into a single objective MILP model. A sensitivity analysis is included to show the impact of the objectives weight vector on the final solutions. The model, based on the full truck load material pick method, provides the quantity of products and number of containers to be loaded per truck and period. An industrial automobile supply chain case study demonstrates the feasibility of applying the proposed model and the solution methodology to a realistic procurement transport planning problem. The results provide lower stock levels and higher occupation of the trucks used to fulfill both demand and minimum inventory requirements than those obtained by the manual spreadsheet-based method.     

Managing a dual-channel supply chain under price and delivery-time dependent stochastic demand

Several leading manufacturers recently combined the traditional retail channel with a direct online channel to reach a wider range of customers. We examine such a dual-channel supply chain under price and delivery-time dependent stochastic customer demand. We consider five decision variables, the price and order quantity for both the retail and the online channels and the delivery time for the online channel. Uncertainty frequently arises in both retail and online channels and so additional inventory management is required to control shortage or overstock and that has an effect on the optimal order quantity, price, and lead time. We developed mathematical models with the profit maximization motive. We analyze both centralized and decentralized systems for unknown distribution function of the random variables through a distribution-free approach and also for known distribution function. We examine the effect of delivery lead time and customers’ channel preference on the optimal operation. For supply chain coordination a hybrid all-unit quantity discount along a franchise fee contract is used. Moreover, we use the generalized asymmetric Nash bargaining for surplus profit distribution. A numerical example illustrates the findings of the model and the managerial insights are summarized for centralized, decentralized, and coordinated scenarios.     

Dynamic dairy facility location and supply chain planning under traffic congestion and demand uncertainty: A case study of Tehran

In this paper, dynamic dairy facility location and supply chain planning are studied through minimizing the costs of facility location, traffic congestion and transportation of raw/processed milk and dairy products under demand uncertainty. The proposed model dynamically incorporates possible changes in transportation network, facility investment costs, monetary value of time and changes in production process. In addition, the time variation and the demand uncertainty for dairy products in each period of the planning horizon is taken into account to determine the optimal facility location and the optimal production volumes. Computational results are presented for the model on a number of test problems. Also, an empirical case study is conducted in order to investigate the dynamic effects of traffic congestion and demand uncertainty on facility location design and total system costs.     

Design and planning of supply chains with integration of reverse logistics activities under demand uncertainty

In this paper, a mixed integer linear programming (MILP) formulation is developed for the design and planning of supply chains with reverse flows while considering simultaneously production, distribution and reverse logistics activities. It is also considered products’ demand uncertainty using a scenario tree approach. As main goal the model defines the maximization of the expected net present value and the results provide details on sizing and location of plants, warehouses and retailers, definition of processes to install, establishment of forward and reverse flows and inventory levels to attain. The model is applied to a representative European supply chain case study and its applicability is demonstrated.     

Selection of contract suppliers under price and demand uncertainty in a dynamic market

In this paper, we consider a supply contracting problem in which the buyer firm faces non-stationary stochastic price and demand. First, we derive analytical results to compare two pure strategies: (i) periodically purchasing from the spot market; and (ii) signing a long-term contract with a single supplier. The results from the pure strategies show that the selection of suppliers can be complicated by many parameters, and is particularly affected by price uncertainty. We then develop a stochastic dynamic programming model to incorporate mixed strategies, purchasing commitments and contract cancellations. Computational results show that increases in price (demand) uncertainty favor long-term (short-term) suppliers. By examining the two-way interactions of contract factors (price, demand, purchasing bounds, learning and technology effect, salvage values and contract cancellation), both intuitive and non-intuitive managerial insights in outsourcing strategies are derived.     

Integrated supply chain planning under uncertainty using an improved stochastic approach

This paper proposes an integrated model and a modified solution method for solving supply chain network design problems under uncertainty. The stochastic supply chain network design model is provided as a two-stage stochastic program where the two stages in the decision-making process correspond to the strategic and tactical decisions. The uncertainties are mostly found in the tactical stage because most tactical parameters are not fully known when the strategic decisions have to be made. The main uncertain parameters are the operational costs, the customer demand and capacity of the facilities. In the improved solution method, the sample average approximation technique is integrated with the accelerated Benders’ decomposition approach to improvement of the mixed integer linear programming solution phase. The surrogate constraints method will be utilized to acceleration of the decomposition algorithm. A computational study on randomly generated data sets is presented to highlight the efficiency of the proposed solution method. The computational results show that the modified sample average approximation method effectively expedites the computational procedure in comparison with the original approach.     

A robust optimization model for multi-product two-stage capacitated production planning under uncertainty

Production planning (PP) is one of the most important issues carried out in manufacturing environments which seeks efficient planning, scheduling and coordination of all production activities that optimizes the company’s objectives. In this paper, we studied a two-stage real world capacitated production system with lead time and setup decisions in which some parameters such as production costs and customer demand are uncertain. A robust optimization model is developed to formulate the problem in which minimization of the total costs including the setup costs, production costs, labor costs, inventory costs, and workforce changing costs is considered as performance measure. The robust approach is used to reduce the effects of fluctuations of the uncertain parameters with regards to all the possible future scenarios. A mixed-integer programming (MIP) model is developed to formulate the related robust production planning problem. In fact the robust proposed model is presented to generate an initial robust schedule. The performance of this schedule could be improved against of any possible occurrences of uncertain parameters. A case from an Iran refrigerator factory is studied and the characteristics of factory and its products are discussed. The computational results display the robustness and effectiveness of the model and highlight the importance of using robust optimization approach in generating more robust production plans in the uncertain environments. The tradeoff between solution robustness and model robustness is also analyzed.     

Coordinating a supply chain with effort and price dependent stochastic demand

This paper investigates the issue of channel coordination for a supply chain facing stochastic demand that is sensitive to both sales effort and retail price. In the standard newsvendor setting, the returns policy and the revenue sharing contract have been shown to be able to align incentives of the supply chain’s members so that the decentralized supply chain behaves as well as the integrated one. When the demand is influenced by both retail price and retailer sales effort, none of the above traditional contracts can coordinate the supply chain. To resolve this issue, we explore a variety of other contract types including joint return policy with revenue sharing contract, return policy with sales rebate and penalty (SRP) contract, and revenue sharing contract with SRP. We find that only the properly designed returns policy with SRP contract is able to achieve channel coordination and lead to a Pareto improving win–win situation for supply chain members. We then provide analytical method to determine the contract parameters and finally we use a numerical example to illustrate the findings and gain more insights.     

A robust optimization model for multi-site production planning problem in an uncertain environment

This paper addresses the multi-site production planning problem for a multinational lingerie company in Hong Kong subject to production import/export quotas imposed by regulatory requirements of different nations, the use of manufacturing factories/locations with regard to customers’ preferences, as well as production capacity, workforce level, storage space and resource conditions at the factories. In this paper, a robust optimization model is developed to solve multi-site production planning problem with uncertainty data, in which the total costs consisting of production cost, labor cost, inventory cost, and workforce changing cost are minimized. By adjusting penalty parameters, production management can determine an optimal medium-term production strategy including the production loading plan and workforce level while considering different economic growth scenarios. The robustness and effectiveness of the developed model are demonstrated by numerical results. The trade-off between solution robustness and model robustness is also analyzed.     

Integrating deterioration and lifetime constraints in production and supply chain planning: A survey

Items with short lifetimes that are subject to deterioration are important in the business world. Research has a long tradition in integrating deterioration and value loss effects into mathematical models for inventory planning and control where such effects are understood as a general loss or shrinkage of inventory. However, there has been little work in the modeling of lifetime restrictions of items to prevent wastage and disposals, especially in a dynamic planning context. Globalization and other trends extend the consideration of single companies to whole supply chains, implying increased coordination and information needs. This is important as planning decisions impact lead times and thus the quality of items in the whole supply chain. Products that exceed their useful lifetime can impose high costs due to inventory loss or the need to rework them. This implies increased utilization of (scarce) resources, e.g., machine time, metals, and/or energy, thereby increasing CO₂${\text{CO}}_2$-levels. We survey the state-of-the-art regarding depreciation effects and the modeling of lifetime constraints as well as a classification of models following business planning functions of the value chain. A critical evaluation of approaches and their limitations is provided, highlighting directions for future research.     

Analysis of supply chain coordination under fuzzy demand in a two-stage supply chain

This paper considers a two-stage supply chain coordination problem and focuses on the fuzziness aspect of demand uncertainty. We use fuzzy numbers to depict customer demand, and investigate the optimization of the vertically integrated two-stage supply chain under perfect coordination and contrast with the non-coordination case. As in the traditional probabilistic analysis, we prove that the maximum expected supply chain profit in a coordination situation is greater than the total profit in a non-coordination situation.     

Closed-loop supply chain network equilibrium under legislation

This paper expands previous work dealing with oligopolistic supply chains to the field of closed-loop supply chains. The model presented has been formulated with the intent of examining issues surrounding the recent European Union directive regarding waste of electric and electronic equipment (WEEE). The network modelled consists of manufacturers and consumer markets engaged in a Cournot pricing game with perfect information. Closed-loop supply chain network equilibrium occurs when all players agree on volumes shipped and prices charged. Certain properties of the model are examined analytically. Numeric examples are included and have been solved using an extragradient method with constant step size. The equilibrium solution obtained provide interesting insights that lead into a number of areas for future research.     

A fuzzy newsvendor approach to supply chain coordination

In the absence of a clear command and control structure, a key challenge in supply chain management is the coordination and alignment of supply chain members who pursue divergent and often conflicting goals. The newsvendor model is typically used as a framework to quantify the cost of misalignment and to assess the impact of various coordination initiatives. The application of the newsvendor framework, however, requires the specification of some probability distribution for the sources of uncertainty, and in particular, for the market demand. The specification of an adequate demand distribution becomes difficult in the absence of statistical data. We therefore consider a fuzzy approach to the newsvendor problem. We use several fuzzy parameters in the model for the demand, the wholesale price, and the market sales price. We solve the fuzzy newsvendor problem to study three coordination policies: quantity discounts, profit sharing, and buyback. For each coordination policy, the optimal order quantity of the retailer is computed. The possible profits of the members in the supply chain are calculated with minimum sharing of private information. We further extend the fuzzy newsvendor model to a setting with a single manufacturer and multiple retailers under the assumption of ample capacity for the manufacturer. Detailed numerical examples are also provided.     

Coordinating order quantity decisions in the supply chain contract under random demand

In this paper, we are concerned with the coordinating quantity decision problem in a supply chain contract. The supply chain contract is composed of one manufacturer and one retailer to meet the random demand of a single product with a short lifecycle. Our analysis show that the retailer expects to obtain higher profit under proper ordering policies, which can also maximize the expected profit of the supply chain. The manufacturer may induce the retailer to order the coordinated quantity by adjusting the unit return price. As a result, the supply chain is expected to achieve the optimal expected profit.     

Ordering policy and coordination of a supply chain with two-period demand uncertainty

We develop a two-period game model of a one-manufacturer and one-retailer supply chain to investigate the optimal decisions of the players, where stock-out and holding costs are incorporated into the model. The demand at each period is stochastic and price sharply drops in mid-life. We assume the retailer has a single order opportunity, and decides how much inventory to keep in the middle of selling season. We show that both the price-protection mid-life and end-of-life returns (PME) scheme and the only mid-life and end-of-life returns (ME) scheme may achieve channel coordination and access a ‘win-win’ situation under some conditions. The larger the lowest expected profit of the retailer, the lower the possibility of ‘win-win’ situation will be. Combined with the analysis of feasible regions for coordination policies, we find that PME scheme is not always better than ME scheme from the perspective of implementable mechanism. Finally, we find that adopting the dispose-down-to (DDT) policy can bring a larger improvement of the expected channel profit in the centralized setting, and it is interesting that by using DDT policy, double marginalization occurs only at Period 1, and however, does not plague the retailer in Period 2.     

Combined pricing and supply chain operations under price-dependent stochastic demand

In this study, we determined product prices and designed an integrated supply chain operations plan that maximized a manufacturer’s expected profit. The computational results of this study revealed that as the variance of the demand distribution increases, a manufacturer will increase its inventory to levels that are greater than the anticipated demand to prevent the potential loss of sales and will simultaneously raise product prices to obtain a greater profit. In the cost minimization approach, the manufacturer may earn the highest possible profits, as determined by the profit optimization approach, only if this firm precisely forecasts the mean market demand for its products. Greater inaccuracies in this forecast will produce lower levels of expected profit.     

Possibilistic linear-programming approach for supply chain networking decisions

Supply chain networking decisions are very important for the medium- and long-term planning success of manufacturing companies. The inputs to supply chain planning models are subject to environmental and system uncertainties. In this paper, a fuzzy set theory-based model is proposed to deal with those uncertainties. For this purpose, a possibilistic linear programming (PLP) model is used to make strategic resource-planning decisions using fuzzy demand forecasts and fuzzy yield rates as well as other inputs such as costs and capacities. The objective of the proposed PLP is to maximize the total profit of the enterprise. The model is applied to Mercedes–Benz Türk, one of the largest bus-manufacturing companies in the world, and conclusions and suggestions for further research are provided.     

Optimal inventory policy with supply uncertainty and demand cancellation

We consider a periodic review model where the firm manages its inventory under supply uncertainty and demand cancellation. We show that because of supply uncertainty, the optimal inventory policy has the structure of re-order point type. That is, we order if the initial inventory falls below this re-order point, otherwise we do not order. This is in contrast to the work of Yuan and Cheung (2003) who prove the optimality of an order up to policy in the absence of supply uncertainty. We also investigate the impact of supply uncertainty and demand cancellation on the performance of the supply chain. Using our model, we are able to quantify the importance of reducing the variance of either the distribution of yield or the distribution of demand cancellation. The single, multiple periods and the infinite horizon models are studied.     

Supply chain optimization of petroleum organization under uncertainty in market demands and prices

A multi-period stochastic planning model has been developed and implemented for a supply chain network of a petroleum organization operating in an oil producing country under uncertain market conditions. The proposed supply chain network consists of all activities related to crude oil production, processing and distribution. Uncertainties were introduced in market demands and prices. A deterministic optimization model was first developed and tested. The impact of uncertainty on the supply chain was studied by performing a sensitivity analysis in which ±20% deviations were introduced in market demands and prices of different commodities. A stochastic formulation was then proposed, which is based on the two-stage problem with finite number of realizations. The proposed stochastic programming approach proved to be quite effective in developing resilient production plans in light of high degree of uncertainty in market conditions. The anticipated production plans have a considerably lower expected value of perfect information (EVPI). The main conclusion of this study is that for an oil producing country with oil processing capabilities, the impact of economic uncertainties may be tolerated by an appropriate balance between crude exports and processing capacities.