Backorder Penalty Cost Research Articles

Benefits of CPFR Collaboration Strategy under Different Inventory Holding and Backorder Penalty Costs

This study uses discrete event simulation to investigate the benefits of Collaborative Planning, Forecasting andReplenishment (CPFR) strategy over Traditional Supply Chain (TSC) under different inventory holding costsand backorder penalty costs for both the manufacturer and retailer. A two-echelon production-inventory systemwith a retailer and manufacturer in a variable demand environment is considered for this study. No information isshared in TSC, while sales, forecast and inventory level information is shared in CPFR between a retailer and amanufacturer. The order quantity for retailer and the production quantity for manufacturer during each period aredetermined using periodic review order-up-to inventory policy. Lot-for-lot production policy is used by themanufacturer with a lead time of one period. The results suggest that CPFR performs better than TSC for boththe manufacturer and retailer under all inventory holding costs. As inventory holding cost per unit per periodincreases, benefits of CPFR also increases for both the manufacturer and retailer. Also, when inventory holdingcost is high, maximum benefits of CPFR is achieved for both the manufacturer and the retailerin an environmentwithhigh demand variability, high backorder penalty cost and long delivery lead time.

Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing

In this paper, we develop a unified mixed integer linear modelling approach to compute near-optimal policy parameters for the non-stationary stochastic lot sizing problem under static–dynamic uncertainty strategy. The proposed approach applies to settings in which unmet demand is backordered or lost; and it can accommodate variants of the problem for which the quality of service is captured by means of backorder penalty costs, non-stockout probabilities, or fill rate constraints. This approach has a number of advantages with respect to existing methods in the literature: it enables seamless modelling of different variants of the stochastic lot sizing problem, some of which have been previously tackled via ad hoc solution methods and some others that have not yet been addressed in the literature; and it produces an accurate estimation of the expected total cost, expressed in terms of upper and lower bounds based on piecewise linearisation of the first order loss function. We illustrate the effectiveness and flexibility of the proposed approach by means of a computational study.

BENEFITS OF CPFR AND VMI COLLABORATION STRATEGIES: A SIMULATION STUDY

This study provides managerial insight to pursue Collaborative Planning Forecasting and Replenishment (CPFR) or Vendor Managed Inventory (VMI) strategy for both the retailer and manufacturer under different supply chain settings. Discrete event simulation is used to investigate the cost benefits of CPFR and VMI strategies over Traditional Supply Chain (TSC) in a variable demand environment. The conceptual model is a two-echelon production-inventory system with a manufacturer and a retailer. The results from this study suggest that when compared to TSC, both VMI and CPFR achieve cost benefits in inventory management for both the manufacturer and retailer. Under most supply chain settings, higher cost benefits are achieved in CPFR compared to VMI. Also, CPFR achieves higher cost benefits when demand variability is high, production capacity is low, backorder penalty cost is high and delivery lead time is long. However, when production capacity is high and delivery lead time is short, the cost benefits of CPFR and VMI are significantly lower.DOI: 10.12660/joscmv6n2p59-73URL: http://dx.doi.org/10.12660/joscmv6n2p59-73

Cross-docking centre operation optimization using simulation-based genetic algorithm

The operational improvement of cross-docking centres in the literature involves job scheduling, layout design and dock assignment. The mentioned research is mainly concerned with makespan, number of tardy jobs or travel distance. However, these measures may not fully represent the main advantages of cross-docking operations. Little has been done to optimize the major performance measures of a cross-docking centre, which substantiates the main advantages of cross-docking technology. In this paper, inventory holding cost, transportation cost and backorder penalty cost are aggregated into total cost and a solution framework has been developed by integrating simulation, genetic algorithm (GA) and smart computing budget allocation (SCBA) for a comprehensive total cost minimization problem. This problem has huge search space even for medium-sized problem scenarios. To address this difficulty, the framework employs simulation to estimate the total cost, GA to search for better design and SCBA to efficiently allocate the simulation budget. Numerical experiments show that the proposed framework operates effectively in cases of different problem scales.

ANALYSIS OF MANUFACTURING COST MISREPORTING BEHAVIOR OF MANUFACTURER UNDER CONSIGNMENT CONTRACT WITH REVENUE SHARING

The two-echelon supply chain under stochastic manufacturing demand has a single component supplier selling to a single manufacturer.The model with perpetual manufacturing demand and many replenishment opportunities is considered by analytic method. The problem can be modeled as a supplier-led Stackelberg dynamic game.Supply chain performances under consignment and non-consignment are considered respectively.The supplier, acting as a designer of supply chain,offers the manufacturer a backorder penalty cost share allocation,and then the manufacturer decides the optimal base stock level.In this paper the following conclusions are obtained.Under consignment,there is a unique equilibrium solution in the game,and the supply chain system is optimal.Under non-consignment,there is a unique equilibrium solution in the game,and the supply chain system is optimal.Supply chain performance under consignment is superior to that under non-consignment.

Backorder penalty cost coefficient “b”: What could it be?

The classical economic order quantity (EOQ) model with planned penalized backorders (PB) relies on postulating a value for the backorder penalty cost coefficient, b, which is supposed to reflect the intangible adverse effect of the future loss of customer goodwill following a stockout. Recognizing that the effect of the future loss of customer goodwill should be not a direct penalty cost but a change in future demand, Schwartz [1966. A new approach to stockout penalties. Management Science 12(12), B538–B544] modified the classical EOQ-PB model by eliminating the backorder penalty cost term from the objective function and assuming that the long-run demand rate is a decreasing, strictly convex function of the customer's “disappointment factor” (defined as the complement of the demand fill rate) following a stockout, which in turn is an increasing, strictly convex function of the demand fill rate. He called the new model a perturbed demand (PD) model. Schwartz provided convincing justification for his PD model and presented several variations of it in a follow-up paper, but he did not solve any of these models. In this paper, we solve Schwartz's original PD model and its variations, and we discuss the implications of their solutions, thus filling a gap in the literature left by Schwartz. Moreover, having been convinced that Schwartz's approach is more valid than the classical approach for representing the effect of the loss of customer goodwill following a stockout, but also recognizing that the classical approach is far more popular than the PD approach, because of its simplicity and because of tradition, we use the solution of the PD model to infer the value of b in the classical model, thus providing one possible answer to the question, what could b be? A noteworthy implication of the solution of Schwartz's original PD model is that the optimal fill rate is always 0 or 1, rendering the inferred value of b in the classical model 0 or ∞, respectively. Suspecting that the property of the PD function which is most likely responsible for producing this “bang-bang” type of result is strict convexity, we show that for the case where the PD function is proportional to an integer power, say n, of the fill rate, the optimal fill rate is always 0 or 1, if and only if n>1, in which case the PD function is strictly convex in the fill rate.

Improving agility of supply chains using base stock model and computer based simulations

PurposeThe 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.Design/methodology/approachThe 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.FindingsComputer 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.Originality/valueThe paper offers a review of simulation work aiming to support improvement of agility in the supply chain.

ON THE STRUCTURE OF OPTIMAL ORDERING POLICIES FOR STOCHASTIC INVENTORY SYSTEMS WITH MINIMUM ORDER QUANTITY

We study a single-product periodic-review inventory model in which the ordering quantity is either zero or at least a minimum order size. The ordering cost is a linear function of the ordering quantity, and the demand in different time periods are independent random variables. The objective is to characterize the inventory policies that minimize the total discounted ordering, holding, and backorder penalty costs over a finite time horizon. We introduce the concept of an M-increasing function. These functions allow us to characterize the optimal inventory policies everywhere in the state space outside of an interval for each time period. Furthermore, we identify easily computable upper bounds and asymptotic lower bounds for these intervals. Finally, examples are given to demonstrate the complex structure of the optimal inventory policies.

A multi-agent reinforcement learning approach to obtaining dynamic control policies for stochastic lot scheduling problem

This paper presents a methodology that, for the problem of scheduling of a single server on multiple products, finds a dynamic control policy via intelligent agents. The dynamic (state dependent) policy optimizes a cost function based on the WIP inventory, the backorder penalty costs and the setup costs, while meeting the productivity constraints for the products. The methodology uses a simulation optimization technique called Reinforcement Learning (RL) and was tested on a stochastic lot-scheduling problem (SELSP) having a state–action space of size 1.8 × 10 7. The dynamic policies obtained through the RL-based approach outperformed various cyclic policies. The RL approach was implemented via a multi-agent control architecture where a decision agent was assigned to each of the products. A Neural Network based approach (least mean square (LMS) algorithm) was used to approximate the reinforcement value function during the implementation of the RL-based methodology. Finally, the dynamic control policy over the large state space was extracted from the reinforcement values using a commercially available tree classifier tool.

Stock Wars: Inventory Competition in a Two-Echelon Supply Chain with Multiple Retailers

This paper studies the competitive and cooperative selection of inventory policies in a two-echelon supply chain with one supplier and N retailers. Stochastic demand is monitored continuously. Retailers incur inventory holding and backorder penalty costs. The supplier incurs holding costs for its inventory and backorder penalty costs for backorders at the retailers. The latter cost reflects the supplier's desire to maintain adequate availability of its product to consumers. Previous research finds the supply chain cost minimizing reorder point policies, the cooperative solution. The competitive solution is a Nash equilibrium, a set of reorder points such that no firm can deviate from the equilibrium and lower its cost. It is shown that Nash equilibria exist and a method is presented to find all of them. In some settings the cooperative solution is a Nash equilibrium; competition does not necessarily lead to supply chain inefficiency. In other settings, competition leads to costs that are substantially higher than optimal. Usually (but not always), the competitive supply chain carries too little inventory. Three cooperation strategies are discussed: change incentives, change equilibrium, and change control. A set of contracts is provided that changes the firms' incentives so that the optimal policy is a Nash equilibrium. An equilibrium change can improve performance but does not guarantee optimal performance. To change control, the firms let the supplier choose all reorder points, a key component in vendor managed inventory. That change leads to optimal supply chain performance.

Managing a Retailer's Shelf Space, Inventory, and Transportation

Retailers must constantly strive for excellence in operations; extremely narrow profit margins leave little room for waste and inefficiency. This article reports a retailer's challenge to balance transportation, shelf space, and inventory costs. A retailer sells multiple products with stochastic demand. Trucks are dispatched from a warehouse and arrive at a store with a constant lead time. Each truck has a finite capacity and incurs a fixed shipping cost, no matter the number of units shipped. There is a per unit shelf-space cost as well as holding and backorder penalty costs. Three policies are considered for dispatching trucks: a minimum quantity continuous review policy, a full service periodic review policy, and a minimum quantity periodic review policy. The first policy ships a truck when demand since the previous shipment equals a fixed fraction of a truck's capacity, i.e., a minimum truck utilization. The exact analysis of that policy is the same as the analysis of reorder point policies for the multiechelon problem with one-warehouse, multiple retailers, and stochastic demand. That analysis is not computationally prohibitive, but the minimum quantity level can be chosen with a simple economic order quantity (EOQ) heuristic. An extensive numerical study finds the following: Either of the two periodic review policies may have substantially higher costs than the continuous review policy, in particular when the warehouse to store lead time is short; the EOQ heuristic performs quite well; the minimum quantity policy's total cost is relatively insensitive to the chosen transportation utilization, and its total cost is close to a lower bound developed for this problem.

Supply Chain Inventory Management and the Value of Shared Information

In traditional supply chain inventory management, orders are the only information firms exchange, but information technology now allows firms to share demand and inventory data quickly and inexpensively. We study the value of sharing these data in a model with one supplier, N identical retailers, and stationary stochastic consumer demand. There are inventory holding costs and back-order penalty costs. We compare a traditional information policy that does not use shared information with a full information policy that does exploit shared information. In a numerical study we find that supply chain costs are 2.2% lower on average with the full information policy than with the traditional information policy, and the maximum difference is 12.1%. We also develop a simulation-based lower bound over all feasible policies. The cost difference between the traditional information policy and the lower bound is an upper bound on the value of information sharing: In the same study, that difference is 3.4% on average, and no more than 13.8%. We contrast the value of information sharing with two other benefits of information technology, faster and cheaper order processing, which lead to shorter lead times and smaller batch sizes, respectively. In our sample, cutting lead times nearly in half reduces costs by 21% on average, and cutting batches in half reduces costs by 22% on average. For the settings we study, we conclude that implementing information technology to accelerate and smooth the physical flow of goods through a supply chain is significantly more valuable than using information technology to expand the flow of information.

Competitive and Cooperative Inventory Policies in a Two-Stage Supply Chain

We investigate a two-stage serial supply chain with stationary stochastic demand and fixed transportation times. Inventory holding costs are charged at each stage, and each stage may incur a consumer backorder penalty cost, e.g. the upper stage (the supplier) may dislike backorders at the lower stage (the retailer). We consider two games. In both, the stages independently choose base stock policies to minimize their costs. The games differ in how the firms track their inventory levels (in one, the firms are committed to tracking echelon inventory; in the other they track local inventory). We compare the policies chosen under this competitive regime to those selected to minimize total supply chain costs, i.e., the optimal solution. We show that the games (nearly always) have a unique Nash equilibrium, and it differs from the optimal solution. Hence, competition reduces efficiency. Furthermore, the two games' equilibria are different, so the tracking method influences strategic behavior. We show that the system optimal solution can be achieved as a Nash equilibrium using simple linear transfer payments. The value of cooperation is context specific: In some settings competition increases total cost by only a fraction of a percent, whereas in other settings the cost increase is enormous. We also discuss Stackelberg equilibria.