Optimal control of decoupling point with deteriorating items

Purpose: The aim of this paper is to develop a dynamic model to simultaneously determine the optimal position of the decoupling point and the optimal path of the production rate as well as the inventory level in a supply chain. With the objective to minimize the total cost of the deviation from the target setting, the closed forms of the optimal solution are derived over a finite planning horizon with deterioration rate under time-varying demand rate. Design/methodology/approach: The Pontryagin's Maximum Principle is employed to explore the optimal position of decoupling point and the optimal production and inventory rate for the proposed dynamic models. The performances of parameters are illustrated through analytical and numerical approaches. Findings: The results denote that the optimal production rate and inventory level are closely related to the target setting which are highly dependent on production policy; meanwhile the optimal decoupling point is exist and unique with the fluctuating of deteriorating rate and product life cycle. The further analyses through both mathematic and numerical approaches indicate that the shorten of product life cycle shifts the optimal decoupling point forward to the end customer meanwhile a backward shifting appears when the deterioration rate increase. Research limitations/implications: There is no shortage allowed and the replacement policy is not taken into account. Practical implications: Solutions derived from this study of the optimal production-inventory plan and decoupling point are instructive for operation decision making. The obtained knowledge about the performance of different parameters is critical to deteriorating supply chains management. Originality/value: Many previous models of the production-inventory problem are only focused on the cost. The paper introduces the decoupling point control into the production and inventory problem such that a critical element-customer demand, can be taken into account. And the problem is solved as dynamic when the production rate, inventory level and the position of the decoupling point are all regarded as decision variables.Peer Reviewe

Optimal control of decoupling point with deteriorating items

Purpose: The aim of this paper is to develop a dynamic model to simultaneously determine the optimal position of the decoupling point and the optimal path of the production rate as well as the inventory level in a supply chain. With the objective to minimize the total cost of the deviation from the target setting, the closed forms of the optimal solution are derived over a finite planning horizon with deterioration rate under time-varying demand rate. Design/methodology/approach: The Pontryagin's Maximum Principle is employed to explore the optimal position of decoupling point and the optimal production and inventory rate for the proposed dynamic models. The performances of parameters are illustrated through analytical and numerical approaches. Findings: The results denote that the optimal production rate and inventory level are closely related to the target setting which are highly dependent on production policy; meanwhile the optimal decoupling point is exist and unique with the fluctuating of deteriorating rate and product life cycle. The further analyses through both mathematic and numerical approaches indicate that the shorten of product life cycle shifts the optimal decoupling point forward to the end customer meanwhile a backward shifting appears when the deterioration rate increase. Research limitations/implications: There is no shortage allowed and the replacement policy is not taken into account. Practical implications: Solutions derived from this study of the optimal production-inventory plan and decoupling point are instructive for operation decision making. The obtained knowledge about the performance of different parameters is critical to deteriorating supply chains management. Originality/value: Many previous models of the production-inventory problem are only focused on the cost. The paper introduces the decoupling point control into the production and inventory problem such that a critical element-customer demand, can be taken into account. And the problem is solved as dynamic when the production rate, inventory level and the position of the decoupling point are all regarded as decision variables.Peer Reviewe

An Inventory Model for Deteriorating Commodity under Stock Dependent Selling Rate

Economic order quantity (EOQ) is one of the most important inventory policy that have to be decided in managing an inventory system. The problem addressed in this paper concerns with the decision of the optimal replenishment time for ordering an EOQ to a supplier. This Model is captured the affect of stock dependent selling rate and varying price. We developed an inventory model under varying of demand-deterioration-price of commodity when the relationship of supplier-grocery-consumer at stochastic environment. The replenishment assumed instantaneous with zero lead time. The commodity will decay of quality according to the original condition with randomize characteristics. First, the model is addressed to solve a problem phenomenon how long is the optimum length of cycle time. Then, an EOQ of commodity to be ordered by will be determined by model. To solve this problem, the first step is developed a mathematical model based on reference’s model, and then solve the model analytically. Finally, an inventory model for deteriorating commodity under stock dependent selling rate and considering selling price was derived by this research. Keywords: deterioration commodity, expected profit, optimal replenishment time stock dependent selling rate

An integrated pricing and deteriorating model and a hybrid algorithm for a VMI (vendor-managed-inventory) supply chain

This paper studies a vendor-managed-inventory (VMI) supply chain where a manufacturer, as a vendor, procures a type of nondeteriorating raw material to produce a deteriorating product, and distribute it to multiple retailers. The price of the product offered by one retailer is also influenced by the prices offered by other retailers because consumers can choose the product from any of the retailers. This paper is one of the first papers that propose an integrated model to study the influence of pricing and deterioration on the profit of such a VMI system. A hybrid approach combining genetic algorithms and an analytical method is developed for efficiently determining the optimal price of the product of each retailer, the inventory policies of the product and the raw material. Our results of a detailed numerical study show that parameters related to the market and deterioration have significant influences on the profit of the VMI system. However, different from common intuition, we find that an increase in the substitution elasticity of the product among different retailers can bring an increase in the retail prices of the product, while the increase of the market scale can reduce the retail prices. © 2011 IEEE.published_or_final_versio

Supply chain finance for ameliorating and deteriorating products: a systematic literature review

Ameliorating and deteriorating products, or, more generally, items that change value over time, present a high sensitiveness to the surrounding environment (e.g., temperature, humidity, and light intensity). For this reason, they should be properly stored along the supply chain to guarantee the desired quality to the consumers. Specifically, ameliorating items face an increase in value if there are stored for longer periods, which can lead to higher selling price. At the same time, the costumers’ demand is sensitive to the price (i.e., the higher the selling price the lower the final demand), sensitiveness that is related to the quality of the products (i.e., lower sensitiveness for high-quality products). On the contrary, deteriorating items lose quality and value over time which result in revenue losses due to lost sales or reduced selling price. Since these products need to be properly stored (i.e., usually in temperature- and humidity-controlled warehouses) the holding costs, which comprise also the energy costs, may be particularly relevant impacting on the economic, environmental, and social sustainability of the supply chain. Furthermore, due to the recent economic crisis, companies (especially, small and medium enterprises) face payment difficulties of customers and high volatility of resources prices. This increases the risk of insolvency and on the other hand the financing needs. In this context, supply chain finance emerged as a mean for efficiency by coordinating the financial flow and providing a set of financial schemes aiming at optimizing accounts payable and receivable along the supply chain. The aim of the present study is thus to investigate through a systematic literature review the two main themes presented (i.e., inventory management models for products that change value over time, and financial techniques and strategies to support companies in inventory management) to understand if any financial technique has been studied for supporting the management of this class of products and to verify the existing literature gap

Optimal Deteriorating Inventory Models for Varies Supply Life Cycles

Agriculture items, such as fruits and vegetables, have different supply and demand characteristics during a harvest period. Fruits supply in the first and end of harvest time are not reliable so sometimes supply are not available when needed. Fruits demand is different during harvest season. In the first harvest season, demand depends on price and at the end of harvest time, the demand depends on presentation of the items. In this study, inventory deteriorating items models for the first and the end of the harvest season are developed. Since closed-form solutions cannot be derived from the models, a Genetic Algorithm and a heuristic method are used to solve the problems. A numerical example and sensitivity analysis are conducted to illustrate the model and get insights. The sensitivity analysis shows that the supplier will increase his price when supply is not reliable at the early harvest period.  The results show that the unreliable supply is susceptible to the total cost at the end of the harvest period

Efficient inventory control for imperfect quality items

In this paper, we present a general EOQ model for items that are subject to inspection for imperfect quality. Each lot that is delivered to the sorting facility undertakes a 100 per cent screening and the percentage of defective items per lot reduces according to a learning curve. The generality of the model is viewed as important both from an academic and practitioner perspective. The mathematical formulation considers arbitrary functions of time that allow the decision maker to assess the consequences of a diverse range of strategies by employing a single inventory model. A rigorous methodology is utilised to show that the solution is a unique and global optimal and a general step-by-step solution procedure is presented for continuous intra-cycle periodic review applications. The value of the temperature history and flow time through the supply chain is also used to determine an efficient policy. Furthermore, coordination mechanisms that may affect the supplier and the retailer are explored to improve inventory control at both echelons. The paper provides illustrative examples that demonstrate the application of the theoretical model in different settings and lead to the generation of interesting managerial insights

A Two-Warehouse Model for Deteriorating Items with Holding Cost under Particle Swarm Optimization

A deterministic inventory model has been developed for deteriorating items and Particle Swarm Optimization (PSO) having a ramp type demands with the effects of inflation with two-warehouse facilities. The owned warehouse (OW) has a fixed capacity of W units; the rented warehouse (RW) has unlimited capacity. Here, we assumed that the inventory holding cost in RW is higher than those in OW. Shortages in inventory are allowed and partially backlogged and Particle Swarm Optimization (PSO) it is assumed that the inventory deteriorates over time at a variable deterioration rate. The effect of inflation has also been considered for various costs associated with the inventory system and Particle Swarm Optimization (PSO). Numerical example is also used to study the behaviour of the model. Cost minimization technique is used to get the expressions for total cost and other parameters