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Preferences and needs of purchasers must be thoroughly defined and analysed when a supplier is establishing criteria upon which to evaluate distribution service within cost constraints. Historically, time and time‐related standards have served as primary, and often only measures of customer service. This temporal emphasis is understandable, given the characteristics of delivery schedules, inventory management, and goods handling systems; however, time‐based standards should not preclude consideration of other service measures. Research has indicated that the backorder may be a useful alternative or supplementary measure of customer service. Morgan concluded that the backorder is “an inverse measure of service achievement”. Perreault and Russ found that 25 % of the purchasing managers they surveyed cancelled more than one‐fourth of all orders which were backordered. Others have suggested that the backorder is a useful service criterion. In those cases where finished goods inventory is not ordinarily present in the system between the production line and the customer it becomes an extremely useful potential measure of performance.

The capacitated lot sizing problem (CLSP) is one of the most important production planning problems which has been widely studied in lot sizing literature. The CLSP is the extension of the Wagner-Whitin problem where there is one product and no capacity constraints. The CLSP involves determining lot sizes for multiple products on a single machine with limited capacity that may change for each planning period. Determining the right lot sizes has a critical importance on the productivity and success of organizations. The paper aims to discuss these issues.

This study focuses on the CLSP with setup carryover and backordering. The literature focusing on this problem is rather limited. To fill this gap, a number of problem-specific heuristics have been integrated with fix-and-optimize (FOPT) heuristic in this study. The authors have compared the performances of the proposed approaches to that of the commercial solver and recent results in literature. The obtained results have stated that the proposed approaches are efficient in solving this problem.

The computational experiments have shown that the proposed approaches are efficient in solving this problem.

To address the solution of the CLSP with setup carryover and backordering, a number of heuristic approaches consisting of FOPT heuristic are proposed in this paper.

To develop and test three different inventory management strategies as applied to the complex emergency in south Sudan.

Quantitative modeling, simulation, and statistics.

This research identified critical system factors that contributed most significantly to inventory system performance, and identified strengths and weaknesses of each inventory management strategy.

This research represents a first step in developing inventory management systems for humanitarian relief. Future work would include modeling correlation among relief items, multiple items, and considering the impact of information.

In a domain that has seen limited application of quantitative models, this work demonstrates the performance benefits of using quantitative methods to manage inventory in a relief setting.

This research has value for relief organizations by providing a real‐world application of quantitative inventory management strategies applied to a complex emergency, and demonstrated performance advantages of quantitative versus ad hoc methods. This research has value for researchers by providing a new application of simulation and mathematical modeling (humanitarian relief).

Pull production systems have received much attention in the supply chain management environment. The number of Kanbans is a key decision variable in the pull production system as it affects the finished goods inventory (FGI) and backorders of the system. The purpose of this study is to compare the performance of the fixed and dynamic Kanban systems in terms of operational metrics (FGI and backorders) under the demand uncertainty.

In this paper, the system dynamics (SD) approach was used to model the performance of fixed and dynamic Kanban based production systems. SD approach has enabled the feedback mechanism and is an appropriate tool to incorporate the dynamic control during the simulation. Initially, a simple Kanban based production system was developed and then compared the performance of production systems with fixed and dynamic controlled Kanbans at the various demand scenarios.

From the present study, it is observed that the dynamic Kanban system has advantages over the fixed Kanban system and also observed that the variation in the backorders with respect to the demand uncertainty under the dynamic Kanban system is negligible.

In a just-in-time production system, the number of Kanbans is a key decision variable. The number of Kanbans is mainly depended on the demand, cycle time, safety stock factor (SSF) and container size. However, this study considered only demand uncertainty to compare the fixed and dynamic Kanban systems. This paper further recommends researchers to consider other control variables which may influence the number of Kanbans such as cycle time, SSF and container size.

This study will be useful to decision-makers and production managers in the selection of the Kanban systems in uncertain demand applications.

This paper aims to present a set of five models for the economic order quantity problem. Four models solve problems for a single product: incremental discounts with or without backorders and all-unit discounts with or without backorders, and the last model solves problems for the multiproduct case.

A basic integer non-linear model with binary variables is presented, and its flexible structure allows for all five models to be utilised with minor modifications for adaptation to individual situations. The multiproduct model takes into consideration the work of Chopra and Meindl (2012), who studied two types of product aggregations: full and adaptive. To find optimal or near-optimal solutions for the multiproduct case, the authors propose a simulated annealing metaheuristic application. Numerical examples are presented to improve the comprehension of each model, and the authors also present the efficiency of the simulated annealing algorithm through an example that aggregates 50 products, each one with different discount schemes and some allowing backorders.

Our model proved to be efficient at finding optimal or near optimal solutions even when confronted with mathematical complexities such as the allowance of backorders and incremental discounts.

Finally our model can process a mix of products with different discount schemes at the same time, and the simulated annealing metaheuristics could find optimal or near optimal solutions with very few iterations.

This research formulated to obtain the optimum ordered quantity and optimum inventory range of fish products under the conditions: (1) fully back ordered (lockdown) and (2) partial back ordered (normal geographical market). In both the cases, due to the deterioration nature and in quarantine situation some vendors are not able to satisfy the customers (retailers). So in this model, the cost of penalty is introduced in quarantine time to obtain the optimal total cost.

To find the total cost, holding cost, shortage cost and deterioration cost have to be considered. There are so many disadvantages in holding the deteriorating food products. Due to the demand and deterioration, the holding cost of the fish products is determined. The supply chain of fish marketing process to find the optimum total cost and optimum back ordered quantity in the two situations, namely, (1) normal backordering and (2) Quarantine period is explained.

The conclusion of this research is exhibited for the uncertain lockdown situation and the normal geographical markets. But in both the cases, the demand function is dependent on the backorder quantity. The expected total cost of the retailers of fish products increased at the least possible range with the increase in the shortage parameter, cost of penalty and variance. But the change in mean value leads to decreasing in the back ordered quantity, inventory level and the annual total cost of the retailers. This analysis contributes to the service of supply chain from wholesaler to retailer in high level.

Fish products are very essential for nourishment and economic spread in India. This study has spotlight the efficient method for reducing the total cost of the retailers of fish marketing. The cost of deterioration of fish is high because of its perishable nature. Due to lockdown situation, the holding cost of the fish products depends upon the backordered quantity of geographical market of fish.

This research formulated to obtain the optimum ordered quantity and optimum inventory range of fish products under the conditions: (1) fully back ordered (lockdown) and (2) partial back ordered (normal geographical market).

Due to lockdown situation, the holding cost of the fish products depends upon the backordered quantity of geographical market of fish. This research formulated to obtain the optimum ordered quantity and optimum inventory range of fish products.

This research formulated to obtain the optimum ordered quantity and optimum inventory range of fish products under the conditions: (1) fully back ordered (lockdown) and (2) partial back ordered (normal geographical market). In both the cases, due to the deterioration nature and in quarantine situation some vendors are not able to satisfy the customers (retailers). So in this model, the cost of penalty is introduced in quarantine time to obtain the optimal total cost. A few number of sensitivity analysis are carried out for deterioration rate, shortage parameter and cost of penalty to indicate the existence of total cost in the least possible range.

The purpose of this paper is to analyze the effects of supply chain coordination on inventory management while the retailer inventory cycle consists of a shortage period and the backorder rate linearly decreases as a function of shortage duration. It is intended to consider how on‐hand inventory and shortage durations are altered when the decisions are centralized.

Mathematical modelling of inventory costs for the retailer and the vendor is used to formulate objective functions. The vendor sets his inventory period as an integer multiple (n) of the retailer inventory cycle in which the integer multiple is a decision variable. Solution spaces of models are analyzed to determine two other decision variables including, on‐hand inventory duration and shortage length.

The integrated model consists of a unique pseudo convex area when (n) is fixed and as a result, there is a unique minimum point. Based on numerical examples and sensitivity analysis, in most situations coordinated inventory management reduces total costs of the supply chain and cost reduction rate increase at larger production rates.

This paper is a combination between production‐inventory models in two‐stage supply chains and partial backordering, which has appeared in single inventory models. To the best of the authors' knowledge, no mathematical model has yet been proposed. Moreover, the benefits of synchronization are analyzed through numerical examples.

Logistics practitioners must continually improve inventory management processes as they daily respond to the twin drivers of customer satisfaction and cost efficiency. The purpose of this paper is to investigate the scenario of sourcing goods through lateral transshipments in a periodic-review policy setting, against a backdrop of cost optimization objectives.

The authors develop decision rules that make cost-optimized selection between backordering and combined reactive and proactive lateral transshipment options possible. This necessarily takes account of the trade-off between purchasing, holding and backorder cost components. In addition, the authors use simulation studies to illustrate the superior performance of the proposed decision options.

According to results of the simulation studies, the proposed two-step decision rule generates the lower inventory cost than the alternative decisions rules. The outperformance of proposed two-step decision rule is valid in different scenario.

This study develops the decision rules to assist wholesaler logistics practitioners to make optimized decisions with regard to whether they should proactively lateral transshipments and if selected, the optimum size of the extra lateral transshipment.

This study has made a significant contribution to the existing knowledge base as it develops decision rules for a combined proactive and reactive approach using lateral transhipments to meet both urgent demand and a part of the demand expected during the supplier lead time in a cost-efficient way.

This paper presents a study on the impacts of information sharing and ordering co‐ordination on the performance of a supply chain with one capacitated supplier and multiple retailers under demand uncertainty. In particular, a computer model is proposed to simulate inventory replenishment decisions by the retailers and production decisions by the supplier under different demand patterns and capacity tightness. It is found that information sharing and ordering co‐ordination significantly impact the supply chain performance in terms of both total cost and service level. It is also found that the value of sharing information and ordering co‐ordination is significantly affected by demand patterns and capacity tightness. Guidelines are developed for companies to share information and co‐ordinate orders under different conditions. These guidelines can help companies reduce costs and improve customer service levels in the supply chain.

The purpose of this paper is to deal with the application of the stochastic inventory model to the three‐tier supply chain and verify the values obtained by mathematical model in physical simulation.

The paper investigates three‐stage serial supply chain with stochastic demand and fixed replenishment lead‐time. Inventory holding costs are charged at each stage, and each stage may incur a consumer backorder penalty cost charged by primary supplier to secondary supplier. The customer‐demand follows Poisson distribution. The base stock model is implemented for inventory control at both suppliers. Physical simulation is then designed in such a way that it satisfies all the assumptions for mathematical model. Simulation is run to verify the values obtained from mathematical model.

Computer simulation is designed to include all the assumptions made by mathematical model. Hence, mathematical base stock model and computer simulation model are comparable. Demand follows Poisson distribution in both cases. The backorder cost and inventory holding cost are calculated in each phase of simulation and summarized. The paper infers that the total inventory cost is optimum in phase II, in which reorder point is same as that calculated by mathematical model. In phase I, total inventory cost is more than that of phase II because of backorders. In phase III, excess inventory increased the total cost. Thus, the values obtained from mathematical model produce optimal inventory cost. Base stock model is effective when the demand is not deterministic and service factor assumed in mathematical model is 0.9, which is quite acceptable. Base stock model assumes replenishment order quantity as 1 and the total inventory cost decreases with replenishment lead time. Base stock model is beneficial for supply chains having short replenishment lead time. Computer simulation results indicate that discrete event simulations can be used to model stochastic systems like organizational supply chains and to validate the results from mathematical models.

The paper offers a review of simulation work aiming to support improvement of agility in the supply chain.