Capacitated Supply Research Articles

Capacity restrictions and supply chain performance: Modelling and analysing load-dependent lead times

Several studies have reported that capacitated supply chains may benefit from an improved dynamic performance as compared to unconstrained ones. This occurs as a consequence of the capacity limit acting as a production smoothing filter. In this research, the relationship between capacity restrictions and the operational performance of supply chains is investigated from a novel perspective, i.e. we assume that the influence of capacity constraints on lead times depends on the supply chain's responsiveness. Under these circumstances, the experiments show that there is a negative effect of capacity constraints on supply chain performance, both in terms of process efficiency (internal) and customer satisfaction (external). Nonetheless, the magnitude of this impact greatly depends on the responsiveness of the firm, market conditions and adopted policies for inventory management. More specifically, the combination of tight capacity restrictions and low responsiveness significantly contributes to decrease supply chain performance, which may be very damaging for the dynamic behavior of the system. In this sense, efficient capacity planning proves to be essential to prevent the supply chain from entering into a vicious circle.

Simulation based optimization of a stochastic supply chain considering supplier disruption: An agent-based modeling and reinforcement learning

Many researchers and practitioners in the recent years have been attracted to investigate the role of uncertainties in the supply chain management concept. In this paper a multi-period stochastic supply chain with demand uncertainty and supplier disruption is modeled. In the model, two types of retailers including risk sensitive and risk neutral, with many capacitated suppliers are considered. Autonomous retailers have three choices to satisfy demands: ordering from primary suppliers, reserved suppliers and spot market. The goal is to find the best behavior of the risk sensitive retailer, regarding the forward and option contracts, during several contract periods based on the profit function. Hence, an agent-based simulation approach has been developed to simulate the supply chain and transactions between retailers and unreliable suppliers. In addition, a Q-learning approach (as a method of reinforcement learning) has been developed to optimize the simulation procedure. Furthermore, different configurations for simulation procedure are analyzed. The R-netlogo package is used to implement the algorithm. Also a numerical example has been solved using the proposed simulation-optimization approach. Several sensitivity analyzes are conducted regarding different parameters of the model. Comparison of the numerical results with a genetic algorithm shows a significant efficiency of the proposed Q-leaning approach.

The newsvendor problem with capacitated suppliers and quantity discounts

We consider a seller who stocks an item in anticipation of a single selling season in which demand for the item is uncertain. The seller may order stock of the item from multiple suppliers, each of which offers a quantity discount pricing structure and has production volume limits. The seller seeks to minimize its total procurement plus expected overstock and understock costs, resulting in an objective function that is neither convex nor concave in the decision variables in general. We provide an algorithmic approach that permits solving this non-convex problem in pseudopolynomial time by solving a set of 0–1 multiple choice knapsack subproblems. We also provide an efficient heuristic solution algorithm and demonstrate the algorithm’s asymptotic optimality in the number of suppliers under mild assumptions on the problem data and under certain quantity discount structures. The results of a set of computational tests demonstrate the superior performance of the knapsack-based algorithms when compared with a commercial solver.

Procurement mechanism for dual sourcing and emergency production under capacity constraint

Abstract This study investigates the optimal procurement mechanism of a buyer who faces two potential suppliers with capacity constraint and private information on costs. The buyer places regular orders to the capacitated suppliers before demand realization and has the option to place an expensive emergency order depending on remaining capacity after that. We observe that the buyer solely exercises emergency option when the virtual cost of the first supplier (with low cost) is greater than emergency production cost. When this virtual cost is not too large, the buyer chooses dual sourcing solely, dual sourcing with emergency option, and single sourcing with emergency option when the capacity is small, moderate, and large, respectively. Compared with symmetric information, information asymmetry weakens capacity constraint for the buyer in terms of order quantity in regular sourcing. However, in terms of order quantity in emergency sourcing, information asymmetry either strengthens capacity constraint when total capacity is greater than expected demand, or weakens capacity constraint when the opposite is the case. Furthermore, the capacity constraint of the first supplier causes a greater buyer’s profit loss than the second supplier (with high cost) does under symmetric information, and information asymmetry further amplifies this asymmetric effect. We also show that the dual sourcing mechanism can be extended to the case of multiple sourcing without loss of the main properties.

A hybrid GA-TLBO algorithm for optimizing a capacitated three-stage supply chain network

A hybrid GA-TLBO algorithm for optimizing a capacitated three-stage supply chain network

Responsive contingency planning of capacitated supply networks under disruption risks

This paper prescribes an appropriate risk mitigation model for a capacitated supply chain subject to premeditated attacks on facilities. It presents a unified approach to responsive contingency planning and optimizing protection of supply facilities utilizing a game-theoretic framework of attack and defense which involves multi level optimization. Gradual capacity backups is proposed for the first time in the context of protection under intentional attacks in a capacitated supply system. A recursive tree search algorithm is proposed to solve the tri-level optimization problem. Computational efficiency of the algorithm is demonstrated and managerial insights are presented.

Inventory allocation models for a two-stage, two-product, capacitated supplier and retailer problem with random demand

The objective of this research is to develop an optimal inventory allocation methodology for a supply chain consisting of a capacitated retailer with limited shelf space, and two unreliable capacitated suppliers in an uncertain environment. We develop conceptual and analytical models that provide allocation preferences between shelf-space and warehouse in both deterministic and stochastic demand cases, and develop managerial insights based on them. For each case, we provide both a closed-form solution and a heuristic method, and illustrate the bounds on the optimal solution. Further, we show that the cost function is L⋄-convex in some cases. Finally, we prove that the expected profit decreases as the variance of demand increases.

Revisiting the Effects of Forecasting Method Selection and Information Sharing Under Volatile Demand in SCM Applications

Using a two-stage capacitated supply chain with four retailers and one supplier, this paper reveals that volatile demand and the supplier's own forecasting intelligence may limit the value of information sharing (IS). The results show that capacity tightness (CT) is the most important factor that affects the performance of the supply chain compared with the effects of forecasting methods and IS policies. When CT is low, order information sharing is not preferred, because the supplier's own forecasts are more beneficial. When CT is high, IS becomes valuable. In addition, this study demonstrates that advanced forecasting methods such as generalized autoregressive conditional heteroscedasticity (GARCH) and properly configured neural network models significantly reduce costs relative to the conventional forecasting methods under most scenarios examined. However, misspecified models often result in poor system performance. The findings also reveal significant interaction effects among forecasting method, IS, and CT. In order to achieve cost reduction, supply chain managers should jointly consider all the critical factors when selecting forecasting method and IS policy.

Competitiveversuscooperative performances of a Stackelberg game between two suppliers

We investigate the competitive and cooperative performances of a supply chain with two capacitated suppliers solicited by a customer who offers a new product procurement suggestion. Suppliers have the option to accept or reject the new product offer according to its profitability. In addition, suppliers have to decide on their base stock levels. We classify suppliers as principal and secondary. The customer usually addresses demand to the principal supplier at first. We consider two schemes: in the first scheme, the principal supplier informs the customer about the demand ratio he wants to be allocated. The customer allocates the remaining quantity to the secondary supplier. In the second scheme, the principal supplier decides to respond to the entire demand and to subcontract a part of it to the secondary supplier. In the competitive situation, we give conditions that allow principal supplier to select the best scheme. We show that the new product offer can be refused while it is accepted when suppliers cooperate. We present a profit allocation policy under which collaboration is beneficial for the two suppliers.

An integrated approach to solve a robust forward/reverse supply chain for short lifetime products

Supply chain management plays a key role in optimizing manufacturing costs in competitive markets. In this paper, a multi period, multi product, multi echelon and capacitated supply chain problem for short lifetime products was solved using both exact method and metaheuristic algorithms. The considered echelons in a forward/reverse supply chain network design include suppliers, hybrid production–inspection centers, hybrid warehouse-collection centers, retailers, disposal centers and recovery centers. To tackle both strategic and tactical nature of the problem and due to its complexity, the location problem is first solved using an exact method in which strategic decisions are made aiming to minimize the location costs. Then the allocation problem is solved using both exact and metaheuristic algorithms, namely Tabu Search and Differential Evolution, in which based on the results obtained from the location problem, the profit is maximized and tactical decisions are made. A cyclic feedback procedure is proposed in between the location and allocation models to obtain the best solution. The allocation model is linearized using a new method and to handle the uncertainty, a robust mixed integer programming model is developed which can retain the linearity of the model. The computational results confirm the effectiveness of the exact method for the location problem while testifies the proposed algorithms can obtain effective solutions compared with that of the exact solutions for the allocation problem in both deterministic and uncertain environment. In addition, the results show that in terms of preciseness and convergence, the proposed Differential Evolution algorithm outperforms the other algorithm.

An integrated supply chain configuration model and procurement management under uncertainty: A set-based robust optimization methodology

Supply chain configuration and supplier selection are two significant strategic decision making problems in supply chain management. In order to tackle the uncertain environment in these two problems, we propose an integrated mathematical programming model based on robust optimization theory. The framework of the proposed supply chain network involves a forward flow from heterogeneous capacitated suppliers offering price discounts to customers, and also a reverse flow from customer zones to disposal centers or production facilities. The objective function of the model is to minimize the total cost of the supply chain network by determining a set of best suppliers, order allocation to selected suppliers, the location of facilities in each layer and transportation quantities between them. Moreover, to measure the imprecise input parameters, according to three types of uncertainty sets, the robust counterparts of the model have been developed. Finally, to validate the robust model, the eventual optimal solutions are compared with the deterministic model, and numerical studies have been implemented along with sensitivity analysis.

Analysis of a Stackelberg game between a customer and several cooperating suppliers: stability and efficiency

ABSTRACTWe analyse the performances of a supply chain where multiple capacitated suppliers are solicited by a customer who offers a new product procurement suggestion. The customer allocates demand volume to suppliers in a way to maximise his own profit. On the other hand, suppliers can cooperate by forming coalitions. We study coalition structures’ stability and show that such cooperation improves the total supply chain performances. We show however that decentralisation of decisions may lead to the loss of the offer even when suppliers cooperate. We show also that total performances can be more improved if suppliers and the customer cooperate together.

Capacity constraints, demand uncertainty, and the value of supply information sharing

Economic globalisation in general and enhanced core competencies in particular have greatly increased supply chain complexity. Supply chain integration is essential for effective supply chain management, whereas information sharing is a necessary condition for integrated supply chain operations. Supply chain information sharing (SCIS) research is more on demand-side than on supply-side. This paper simulates operating activities with and without supply information sharing in a three-level capacitated supply chain by using a simulation model with mixed-integer programming. The simulation results indicate that supply information sharing can greatly improve supply chain performance in terms of cost and service level. The impacts of supply information sharing on the supply chain performance are heavily influenced by demand patterns and capacity tightness.

Managing Finite-Horizon Down-Side Risks of Stochastic and Capacitated Supply Chains

We consider minimizing the down-side risk of a supply chain with random demand and capacity. A base-stock inventory to be determined buffers the demand-capacity interaction. The Conditional Value-at-Risk of the finite-horizon holding and back-ordering cost measures down-side risk. We demonstrate the problem is intractable and derive an approximation of the optimal base-stock level. A simulation experiment indicates the approximation yields optimal or near-optimal solutions. We study the manager’s behavior regarding the optimal base-stock level as the supply chain parameters change.

Determining the retailer's replenishment policy considering multiple capacitated suppliers and price-sensitive demand

This article presents a mixed integer nonlinear programming model to find the optimal selling price and replenishment policy for a particular type of product in a supply chain defined by a single retailer and multiple potential suppliers. Each supplier offers all-unit quantity discounts as an incentive mechanism. Multiple orders are allowed to be submitted to the selected suppliers during a repeating order cycle. The demand rate is considered to be not constant but dependent upon the selling price. The model provides the optimal number of orders and corresponding order quantities for the selected suppliers, and the optimal demand rate and selling price that maximize the total profit per time unit under suppliers’ capacity and quality constraints. In addition, we provide sufficient conditions under which there exists an optimal solution where the retailer only orders from one supplier. We also apply the Karush–Kuhn–Tucker conditions to investigate the impact of supplier's capacity on the optimal sourcing strategy. The results show that, there may exist a range of capacity values for the dominating supplier, where the retailer's optimal sourcing strategy is to consider multiple suppliers without fully utilizing the dominating supplier's capacity. A numerical example is presented to illustrate the proposed model.

Optimal sourcing from alternative capacitated suppliers with general cost structures

Most manufacturers or retailers must procure items or services necessary for their businesses, in an environment that typically includes a number of competing suppliers with varying cost structures, price schemes, and capacities. In this paper, we consider the sourcing problem in which the buyer determines the sources that should be utilized and to what extent, in turn, dictating the total quantity available for the buyer to sell/utilize, subject to stochastic demand/requirement. Our approach advocates not to determine the quantity to be sourced a priori. We allow for capacitated sources and any cost structure in which fixed costs and quantity discounts are special cases. Some simpler versions of this problem are shown to be NP-hard in the literature. By proving that the order of the sources is irrelevant for the optimal solution, we devise a dynamic programming model with pseudo-polynomial complexity to solve the multiple supplier sourcing problem to optimality. We propose two extensions: one limits the number of suppliers, and the other allows multi-period sourcing.

Dynamic reorder point replenishment strategies for a capacitated supply chain with seasonal demand

Managing inventory and service levels in a capacitated supply chain environment with seasonal demand requires appropriate selection and readjustment of replenishment decision variables. This study focuses on the dynamic adjustment of decision variables within supply chains using continuous-review reorder point (ROP) replenishment. A framework is proposed to adjust reorder points and lot sizes based on optimal settings within different regions of a seasonal demand cycle. This framework also includes the optimal timing of adjustments defining these regions. A discrete-event simulation model of a simple, capacity-constrained supply chain is developed and simulation–optimization experiments are performed, the objective being to minimize the total supply chain inventory subject to a target delivery service level. The performance of ROP systems with optimal static and optimal dynamic decision variable settings are compared using two different seasonal demand patterns. The results confirm that performance with dynamic decision variable adjustment is better. For a given delivery service level, average work-in-process inventory levels are almost the same for both systems. However average finished goods inventory levels decrease significantly and are more stable under dynamic adjustment. The practical implication is that both finished goods holding costs and maximum storage capacity requirements are reduced.

A Metaheuristic-Based Approach for the Capacitated Supply Chain Network Design Problem Including Imperfect Quality and Rework

A growing number of organizations have realized the importance of quantifying costs associated to product quality and optimizing their supply chains based not only on operational and logistics costs but also on quality-related costs or Cost of Quality (COQ). This paper presents a novel capacitated Supply Chain Network Design (SCND) model, known as the SCND-COQ model, which quantifies the overall economic profit of the supply chain while accounting for quality-related costs. Quality-related costs are computed from analytical expressions for tracking the Supply Chain (SC) quality level and quantifying the prevention, inspection, rework, failure and opportunity costs, which, in turn, depend on the internal operational decisions within the manufacturing plants. Two metaheuristic solution procedures, based on the Simulated Annealing (SA) and the Genetic Algorithm (GA), with calls to a nonlinear solver are proposed for identifying near-optimal SCNDs since maximizing the output of the SCNDCOQ model can be classified as an NPO-complete problem. The effectiveness of the proposed solution procedures is demonstrated through comprehensive numerical experiments. Based on computational results, the GA-based procedure outperformed the SA-based procedure for all the tested instances in terms of solution quality. The results show that quality-related costs may account up to 11% of the overall profit and the selected business entities differ when including quality-related costs in the SCND decision-making process.

A CAPACITATED REPLENISHMENT-LIQUIDATION MODEL UNDER CONTRACTUAL AND SPOT MARKETS WITH STOCHASTIC DEMAND

Various large-scale suppliers frequently use web-based spot markets, along with discount stores and foreign distributors, for inventory liquidation. Recognizing the potential benefits of such practices, we consider a multi-period, integrated replenishment, and liquidation problem for a capacitated supplier facing stochastic demand from a spot market along with its primary market (with higher priority contractual customers). In each period, the supplier must decide: (i) how much to produce, and (ii) if there are excess units left after sales to the primary market, how many of these to liquidate. We show that the optimal policy is characterized by two quantities: the critical produce-up-to level and the critical retain-up-to level. We establish bounds for these two quantities. We identify two practical benchmark policies and establish thresholds on the unit revenue earned from the spot market such that one of the two benchmark policies is optimal. We provide closed form expressions to determine these thresholds for the infinite horizon problem under specific conditions on the available production capacity. In general, it is difficult, if not impossible, to theoretically determine these thresholds in closed form for the finite horizon problem. Hence, we report results of a computational study to gain insights regarding the behavior of the optimal policy with respect to the spot market revenue. Our computational results also quantify the benefits of the optimal policy relative to the benchmark policies and examine the effects of demand correlation.

Measuring the performance sensitivity of replenishment systems using tradeoff curves

There are a number of studies in the literature where replenishment systems have been compared on the basis of mean performance. However, little attention has focused on comparing systems on the basis of sensitivity to changes in the supply chain environment. This study compares the performance sensitivity of reorder point (ROP) and Kanban replenishment systems in a capacitated supply chain using an optimum-seeking simulation approach. Changes in the supply chain environment include transit time variability, transporter frequency, demand rates and lot setup times. Performance tradeoff curves, showing the interaction of inventory and delivery performance, are generated and an index based on the areas under the tradeoff curves is proposed to quantify the performance sensitivity. It is found that the Kanban system is generally less sensitive, in part because it operates optimally at a lower utilisation level. It is also observed that performance sensitivity depends on the environmental factor that is perturbed.