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a Variation of the joint total expected cost and order quantity with fill rate. b Variation of safety factor, lead time and number of shipments per production cycle with fill rate
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In this paper, we develop an integrated inventory model in a single-vendor single-buyer supply chain under an unknown demand distribution at the buyer. It is assumed that each lot delivered to the buyer contains a random fraction of defective items, and lead time can be reduced at an extra crashing cost. We also consider that the unmet demand at th...
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This paper presents a centralized production-inventory model for an infinite planning horizon of a two-echelon closed-loop supply chain (CLSC) consisting a retailer, manufacturer, and remanufacturer. The demand at the retailer is satisfied through the new and remanufactured products received from the manufacturer and remanufacturer, respectively. T...
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... However, these require the computation of penalty costs, which are challenging to quantify in practice due to the presence of intangible components, such as loss of customer goodwill and damage to future business. Hence, service models are more common in practice (Escalona et al., 2019;Gutgutia and Jha, 2018;Silver et al., 2017), and the performance of inventory systems is better understood by managers in terms of service levels. ...
... Service-level requirements commonly exist in practice because planners need to ensure that unsatisfied demand is similar across geographical areas (Shehadeh and Snyder, 2021). The fill rate is a widely used performance metric to measure the service level, being applied in various scenarios such as inventory management (Gutgutia and Jha, 2018;Tan et al., 2017), resource pooling system (Zhong et al., 2018), and location-transportation problem (Baron et al., 2011;Wang et al., 2021b). In particular, Baron et al. (2011) construct a RO model for locating facilities in a network facing uncertain demand over multiple periods. ...
In humanitarian logistics, the location and inventory pre-positioning problem (LIPP), making decisions on facility location, inventory pre-positioning, and allocation, is critical to post-disaster rescue efficiency. Since post-disaster conditions are complex and uncertain, it is challenging for planners to make LIPP decisions and perform rescue activities. To reduce operational costs while also guaranteeing service levels to customers, it is necessary to take uncertainties into account when making decisions. This study explores a service-oriented LIPP under two types of uncertainties, i.e., uncertain customer demand and third-party supply. We propose a two-stage robust optimization framework to solve the problem, considering the service-level constraints and minimizing the total cost. We develop two algorithms to solve the problem. Specifically, a column-and-constraint generation algorithm is utilized to solve the original two-stage robust model, and an improved row generation algorithm is developed to tackle the affinely adjustable robust counterpart model. Simulation results show that both algorithms can provide satisfying solutions. A case study based on a power grid company in China is conducted to perform sensitivity analysis and compare models, producing several managerial insights.
... The control parameters of inventory policies are devoted to determining these issues according to a specific objective, normally using a cost or a customer service criterion. Even though the cost approach often leads to less mathematical complexity, the use of the service criterion avoids the difficulty of accurately estimating the stockout cost due to the presence of intangible components such as the loss of customer goodwill and the diminishing of future business (Gutgutia and Jha 2018) opportunities. For that reason, this paper follows a customer service approach that introduces a control parameter known as the service level that becomes a constraint in determining the control parameters of the system (Silver et al. 2017;Escalona et al. 2019). ...
One of the most frequently used inventory policies is the order-point, order-up-to-level ( s , S ) system. In this system, the inventory is continuously reviewed and a replenishment request is placed whenever the inventory position drops to or below the order point, s . The variable replenishment order quantity and the variable replenishment cycle characterize the system by the use of complex mathematical computations. Different methodological approaches diminish the mathematical complexity by neglecting the undershoots, i.e., the quantity that the inventory position is below the order point when it is reached. In this paper, we conceptually and empirically analyse the bias that neglecting the undershoots introduces into the estimation of the fill rate. After that, we suggest a new methodology developed under a data-driven perspective that uses a state-dependent parameter algorithm to correct such a bias. As a result, we propose two new methods, one parametric and the other nonparametric, to enhance the fill rate estimate. Both methods, named analytics fill rate methods, remove the bias that neglecting the undershoots introduces and are used to illustrate the practical implications of this hypothesis on the performance and design of the ( s, S ) system. This research is developed in a lost sales context with simulated stochastic and i.i.d. discrete demands as well as actual sales data.
... However, these require the computation of penalty costs, which are challenging to quantify in practice due to the presence of intangible components, such as loss of customer goodwill and damage to future business. Hence, service models are more common in practice (Escalona et al., 2019;Gutgutia and Jha, 2018;Silver et al., 2017). Moreover, the performance of inventory systems is typically measured in terms of service levels. ...
... Cheikhrouhou et al. (2018) investigated the supply chain model with quality inspection and defective products under an effective transportation process. Gutgutia and Jha (2018) studied the continuous review inventory model under a distribution-free approach with the arrival of defective items with rework. Hemapriya and Uthayakumar (2020) have analyzed an integrated manufacturing inventory model with probabilistic defective products under variable setup costs. ...
... (i) Several inventory models (Gutgutia & Jha 2018;Hemapriya & Uthayakumar 2020;Dey et al. 2019b;Chakraborty & Bhuiya 2017;Dey et al. 2019a) in the literature include only a single safety factor for all batches of inventories received from the manufacturer, although if the lead time is long, it leads to lost sales. As a result, the integrated inventory model with varying safety factors for the first and remaining batches must be examined. ...
This paper explores the issues involved in delivering an item from a manufacturer to a retailer in a closed-loop two-echelon supply chain model. Two types of safety factors are maintained in the hands of the retailer to avoid stock-outs during the lead time. This model considers carbon emission from material production and supply chain-related transportation. If products are found to be defective during the inspection or screening process, they are returned to the manufacturer, and the defective items are reworked for resale. Moreover, the transportation costs incurred during the return of such defective items found through the screening process are added to the manufacturer as a penalty. All essential inventory costs of the supply chain are considered uncertain. Furthermore, this uncertainty is handled with an intuitionistic triangular fuzzy number and the corresponding defuzzification process is dealt with the signed distance method. The main objective of this research is to maximize the total expected profit of the supply chain with realistic factors. Distinct from the existing literature, two different solution techniques are employed to provide the optimal solution for the decision variables. In addition, two special cases are specialized in this study. Three numerical experiments are considered to validate the proposed model. Finally, sensitivity analysis, managerial insights, and conclusions are provided.
... Finally, the manufacturer dispatches them to the retailer in equal-sized batches to meet the consumers' demand. We use the JELS policy that has attracted considerable attention during the last few decades among many academics and practitioners (Giri and Bardhan 2015;Gutgutia and Jha 2018;Sarkar and Giri 2020;Yang and Kim 2020) since it leads to inventory reductions and significant profit gains accompanied by improved customer service (Seifert 2000). This study develops an MINLP model that handles the JELS problem. ...
This research studies a production-recycling inventory model for postconsumer recycled content products made from a mix of virgin and recycled materials with specific proportions. The proportion is known as the postconsumer recycled content level. We study a closed-loop supply chain (CLSC) where a recycling facility and a supplier respectively ship the recycled and virgin raw materials to a manufacturer. The manufacturer mixes them based on the proportion to produce these products for a retailer. The recycling facility recycles the used products collected by a material recovery facility. The paper develops a joint economic lot-size model (JELS) to maximize the chain-wide total profit. A branch-and-bound algorithm is developed, along with the convex analysis to find the exact solution. To coordinate the CLSC, we present models called disproportionate profit-sharing (DPS) and proportional profit-sharing (PPS) operating under quantity discount. The DPS would give more powerful members, a higher proportion of the extra profits resulting from the JELS. However, the PPS guarantees equitable increases in the individual profits accruing to all members from the JELS. Whereas the DPS works properly in vertically integrated CLSCs and decentralized ones with dominant player(s), the PPS is appropriate for decentralized ones with no dominant players. Additionally, we prove the optimal level of postconsumer recycled content is often either at its maximum or minimum allowable. However, the zero-derivative points within the range can be optimum in a particular case. Consequently, we present decision trees for managers to determine the right profit-sharing method and the optimal postconsumer recycled content level.
... For this reason, the most common approach in practical environments is to find the optimal parameters of the inventory system that guarantee the achievement of a target service level. In addition, this approach is more attractive to practitioners as it is easier for them to interpret the fill rate they strive to offer their customers [26]. However, to implement the service approach it is first required to have appropriate expression to compute accurately the service level because small errors in the calculation of the service level might have an important impact on the determination of optimal parameters [27]. ...
In the continuous review reorder point, base-stock ( s , S ) policy, the replenishment order is launched when the inventory position reaches the reorder point, s . It is commonly assumed that the inventory position is exactly equal to the reorder point at the moment the order is launched, when actually it could be lower at that moment. This implies neglecting the possible undershoots at the reorder point, which has a direct impact on the calculation of the expected shortages per replenishment cycle. This article presents a method for an exact calculation of the fill rate (fraction of demand that is immediately satisfied from shelf) which takes explicit account of the existence of undershoots and is applicable to any discrete demand distribution function in a context of lost sales. This method is based on the determination of the stock probability vector at the moment the replenishment order is launched. Furthermore, neglecting the undershoots is shown to lead to an overestimation of the fill rate, particularly when we move farther away from the unitary demand assumption. From a practical point of view, this behaviour involves underestimating the base-stock level, S , when a target fill rate is set for its determination. The method proposed in this paper overcomes these shortcomings.
... To give an investigation for CLSC, Fang et al. (2016) established an integer linear programming model, and an optimal production planning is well provided. Gutgutia and Jha (2018) developed a modelling of inventory in a single-vendor single-buyer supply chain under an unknown demand distribution at the buyer. In order to optimize the order quantity, they derived closed-form functions for the model. ...
This paper is focused on a triopoly closed-loop supply chain (CLSC) game model, including triopoly oligopolies applying for circular economy development. In the CLSC model, manufacturers sell new products and re-collect waste products for maximizing their profits. This paper analyzes the game processing, the Nash equilibrium solutions, and the stability of the game model. Moreover, the influences of parameters on the system’s stability have been investigated, using the maximal Lyapunov exponent, bifurcation graph, and the stable domain. The results show that the system will be unstable when the adjustment speed of the manufacture is too high; unreasonable price strategies could easily cause system bifurcation; the critical point of system bifurcation is closely related to the collecting price.
... To retain an acceptable level of customer satisfaction, a proper matching of supply with demand is vital. Gutgutia and Jha (2016) proposed a way to capture customer satisfaction in a modeling framework, incorporating a service-level constraint (SLC) into their mathematical model. SLC requires that the actual fill rate is no less than the desired fill rate, where the actual fill rate measures the fraction of the actual demand that can be fulfilled from the on-hand inventory. ...
... They used geometric programming to tackle the problem. In supply chain management, Gutgutia and Jha (2016) developed an integrated inventory model in a single-vendor single-buyer supply chain under an unknown user's demand distribution. In particular, in transportation, LTP with stochastic demands has been investigated in several studies. ...
... Fill rate has been widely applied in the field of operations management; it is typically adopted to model the stock-out situations in an inventory system. Gutgutia and Jha (2016) formulated an integrated inventory model to minimize the total expected cost of the system and considered an exact expression of the service level constraint to ensure that a certain percentage of customer orders are filled by the buyer. Tan et al. (2017) demonstrated a common problem that afflicts SLAs, and then proposed a solution methodology to reduce inventory levels while achieving target service levels. ...
We study a target-oriented, multi-period location–transportation problem where customer demands are uncertain. This problem is to determine the facility locations, production quantities, capacities, and shipment quantities, where the objective is to achieve the desired profit and fill rate to the full extent when it is impossible to reach both. To achieve the goal, we propose a target-oriented framework for the location–transportation problem, where a service-level measure is constructed to guarantee the desired fill rate and a hard constraint on profit is imposed to ensure a decent profit. This framework gets rid of the issues arising from estimating the weights of different objectives in a multi-objective optimization approach. To capture the characteristics of a multi-period decision-making process, an affine decision rule is introduced. Our method not only ensures that the transportation decisions of each period can adapt to realized demands wisely, but also prevents the high complexity of the model resulting from uncertainty and adaptation. Specifically, to tackle challenges of problem intractability, we reformulate the robust counterpart of the problem into a conservative approximation in the form of a mixed-integer quadratic program and propose a Benders decomposition approach to produce effective solutions. Finally, the performance of the target-oriented framework is assessed through computational experiments based on realistic instances.
... Table 1 presents the contribution of this paper. Gallego and Moon [12] Moon and Choi [14] Ouyang and Wu [13] Ouyang et al. [4] Ma and Qiu [16] Tsao and Lu [36] Ouyang et al. [37] Jha and Shanker [38] Dey and Giri [6] Priyan and Uthayakumar [39] Tayyab and Sarkar [9] Ben-Daya and Hariga [5] Tang et al. [25] Shin et al. [34] Kim et al. [23] Gutgutia and Jha [40] This paper ...
The need for efficient electrical energy consumption has greatly expanded in the process industries. In this paper, efforts are made to recognize the electrical energy consumption in a two-echelon supply chain model with a stochastic lead-time demand and imperfect production, while considering the distribution free approach. The initial investments are made for quality improvement and setup cost reduction, which ultimately reduce electrical energy consumption. The inspection costs are considered in order to ensure the good qualities of the product. Centralized and decentralized strategies are used to analyze the proposed supply chain model. The main objective of this study is to reduce the overall cost through efficient electrical energy consumption in supply chain management by optimizing the lot size, the number of shipments, the setup cost, and the failure rate. A quantity-based transportation discount policy is applied to reduce the expected annual costs, and a service-level constraint is incorporated for the buyer to avoid a stockout situation. The impact of the decision variables on the expected total costs is analyzed, and sensitivity analysis is carried out. The results show a significant reduction in overall cost, with quality improvement and setup cost reduction ultimately reducing electrical energy consumption.
