A coordinated production and shipment model in a supply chain (original) (raw)
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Stochastic models for the coordinated production and shipment problem in a supply chain
Computers & Industrial Engineering, 2013
In this study, we consider the coordination of transportation and production policies between a single supplier and a single retailer in a stochastic environment. The supplier controls the production, holds inventory and ships the products to the retailer to satisfy the external demand. We model the system as a Markov decision process, and show that the optimal production and transportation decisions are complex and non-monotonic. Therefore, we analyze two widely-used shipment policies in the industry as well, namely time-based and quantity-based shipment policies in addition to a hybrid time-and-quantity based shipment policy. We numerically compare the performances of these policies with respect to the optimal policy and analyze the effects of the parameters in the system.
Optimal capacity in a coordinated supply chain
Naval Research Logistics, 2008
We consider a supply chain in which a retailer faces a stochastic demand, incurs backorder and inventory holding costs and uses a periodic review system to place orders from a manufacturer. The manufacturer must fill the entire order. The manufacturer incurs costs of overtime and undertime if the order deviates from the planned production capacity. We determine the optimal capacity for the manufacturer in case there is no coordination with the retailer as well as in case there is full coordination with the retailer. When there is no coordination the optimal capacity for the manufacturer is found by solving a newsvendor problem. When there is coordination, we present a dynamic programming formulation and establish that the optimal ordering policy for the retailer is characterized by two parameters. The optimal coordinated capacity for the manufacturer can then be obtained by solving a nonlinear programming problem. We present an efficient exact algorithm and a heuristic algorithm for computing the manufacturer's capacity. We discuss the impact of coordination on the supply chain cost as well as on the manufacturer's capacity. We also identify the situations in which coordination is most beneficial.
COORDINATION ALTERNATIVES IN A MANUFACTURER/DEALER INVENTORY SYSTEM UNDER STOCHASTIC DEMAND
Production and Operations Management, 2009
This paper introduces a stochastic model of a distribution system where the stocking location is owned by a dealer (or retailer) and the product is supplied by a manufacturer. Inventory is managed by the dealer, and the manufacturer is responsible for delivery of the product through both regular replenishment and expedite shipment modes. The dealer and the manufacturer share the goal of providing a high level of customer service. Demand, moreover, is a function of the service level offered to the market by the dealer. We develop optimal stock control policies for the cases where each decision maker in turn is dominant and acts unilaterally while being constrained by the supply/demand linkages of the system. We also develop an optimum policy for the case where both levels are managed under centralized control (i.e., both levels cooperate). Results indicate that the expected profit for a dominant dealer (or dominant manufacturer) is higher under decentralized control than the optimal solution for either under centralized control. However, the centralized solution is a global-optimal solution and therefore will guarantee longterm stability. Differences between the various solutions are analyzed explicitly to estimate the cost of coordination.
Coordinated Replenishment and Shipping Strategies in Inventory/Distribution Systems
2005
In this paper, we study the impact of coordinated replenishment and shipment in inventory/distribution systems. We analyze a system with multiple retailers and one outside supplier. Random demand occurs at each retailer, and the supplier replenishes all the retailers. In traditional inventory models, each retailer orders directly from the supplier whenever the need arises. We present a new, centralized ordering policy that orders for all retailers simultaneously. The new policy is equivalent to the introduction of a warehouse with no inventory, which is in charge of the ordering, allocation, and distribution of inventory to the retailers. Under such a policy, orders for some retailers may be postponed or expedited so that they can be batched with other retailers' orders, which results in savings in ordering and shipping costs. In addition to the policy we propose for supplying inventory to the retailers, we also consider three other policies that are based on these well known policies in the literature: (a) Can-Order policy, (b) Echelon Inventory policy, and (c) Fixed Replenishment Interval policy. Furthermore, we create a framework for simultaneously making inventory and transportation decisions by incorporating the transportation costs (or limited truck capacities). We numerically compare the performance of our proposed policy with these policies to identify the settings where each policy would perform well.
Computers & Operations Research, 2011
This paper deals with a two-stage supply chain that consists of two distribution centers and two retailers. Each member of the supply chain uses a (Q,R) inventory policy, and incurs standard inventory holding and backlog costs, as well as ordering and transportation costs. The distribution centers replenish their inventory from an outside supplier, and the retailers replenish inventory from one of the two distribution centers. When a retailer is ready to replenish its inventory that retailer must decide whether it should replenish from the first or second distribution center. We develop a decision rule that minimizes the total expected cost associated with all outstanding orders at the time of order placement; the retailers then repeatedly use this decision rule as a heuristic. A simulation study which compares the proposed policy to three traditional ordering policies illustrates how the proposed policy performs under different conditions. The numerical analysis shows that, over a large set of scenarios, the proposed policy outperforms the other three policies on average.
Coordinated Replenishment Strategies in Inventory/Distribution Systems
Management Science, 2007
In this paper, we study the impact of coordinated replenishment and shipment in inventory/distribution systems. We analyze a system with multiple retailers and one outside supplier. Random demand occurs at each retailer, and the supplier replenishes all the retailers. In traditional inventory models, each retailer orders directly from the supplier whenever the need arises. We present a new, centralized ordering policy that orders for all retailers simultaneously. The new policy is equivalent to the introduction of a warehouse with no inventory, which is in charge of the ordering, allocation, and distribution of inventory to the retailers. Under such a policy, orders for some retailers may be postponed or expedited so that they can be batched with other retailers' orders, which results in savings in ordering and shipping costs. In addition to the policy we propose for supplying inventory to the retailers, we also consider three other policies that are based on these well known policies in the literature: (a) Can-Order policy, (b) Echelon Inventory policy, and (c) Fixed Replenishment Interval policy. Furthermore, we create a framework for simultaneously making inventory and transportation decisions by incorporating the transportation costs (or limited truck capacities). We numerically compare the performance of our proposed policy with these policies to identify the settings where each policy would perform well.
The consignment stock of inventories in coordinated model with generalized policy
Computers & Industrial Engineering, 2015
In this paper, coordination between a single vendor (or manufacturer) and a buyer (or retailer) via the delivery schedule in a production and distribution system is presented. A continuous deterministic model with centralized decision process is developed. To satisfy the buyer's demands, the product is delivered in discrete batches from the vendor's stock to the buyer's stock and all shipments are realized instantaneously. A more general type of consignment stock (CS) policies for the vendor-buyer integrated production-distribution model is analyzed. Our model does not require equal in size shipments. The inventory patterns and the cost structure of production distribution cycles (PDC) are described in different scenarios. A comparative study of the results shows that the generalized CS policies perform better. Considering CS-policies Braglia and Zavanella (2003) ask about a possibility of cost reduction by delaying a number of late deliveries. Unfortunately, a negative answer was given by Zanoni and Grubbström (2004). We verify this problem to obtain a positive answer in more general setting. A solution procedure is developed to find optimal generalized CS-policy for the problems with nonequal and equal in size deliveries. Optimal solutions are found and illustrated with numerical examples.
Materials Today: Proceedings, 2018
In this paper, a two echelon inventory system with a single-warehouse and single-retailer is considered. Mathematical model is developed for the retailer, warehouse and for the entire chain by incorporating the ordering/setup costs, carrying costs and transportation costs. Replenishment quantity at the retailer and the number of shipments from the warehouse to the retailer are considered as the decision variables. The objective of the proposed work is to demonstrate the optimality of centralised inventory & shipment decisions and total relevant costs at the respective entities and the chain. Numerical example is considered and the model is solved using the computer program written in MATLAB. From the research findings, it is concluded that the percentage variation in optimality of total transportation cost of the supply chain is in decreasing order with respect to the increased ordering cost of the retailer and setup cost of the manufacturer. Finally, few managerial implications are derived based on the sensitivity analysis.
Coordinated Logistics: Joint Replenishment with Capacitated Transportation for a Supply Chain
Production and Operations Management, 2013
I n this study, we consider the integrated inventory replenishment and transportation operations in a supply chain where the orders placed by the downstream retailer are dispatched by the upstream warehouse via an in-house fleet of limited size. We first consider the single-item single-echelon case where the retailer operates with a quantity based replenishment policy, (r,Q), and the warehouse is an ample supplier. We model the transportation operations as a queueing system and derive the operating characteristics of the system in exact terms. We extend this basic model to a two-echelon supply chain where the warehouse employs a base-stock policy. The departure process of the warehouse is characterized in distribution, which is then approximated by an Erlang arrival process by matching the first two moments for the analysis of the transportation queueing system. The operating characteristics and the expected cost rate are derived. An extension of this system to multiple retailers is also discussed. Numerical results are presented to illustrate the performance and the sensitivity of the models and the value of coordinating inventory and transportation operations.
M.: Analysis of a Decentralized Production-Inventory System
2003
We model an isolated portion of a competitive supply chain as a M/M/1 make-to-stock queue. The retailer carries finished goods inventory to service a Poisson demand process, and specifies a policy for replenishing his inventory from an upstream supplier. The supplier chooses the service rate, i.e., capacity, of his manufacturing facility, which behaves as a single-server queue with exponential service times. Demand is backlogged and both agents share the backorder cost. In addition, a linear inventory holding cost is charged to the retailer, and a linear cost for building production capacity is incurred by the supplier. The inventory level, demand rate and cost parameters are common knowledge to both agents. Under the continuous state approximation that the M/M/1 queue has an exponential rather than geometric steady-state distribution, we characterize the optimal centralized and Nash solutions, and show that a contract with linear transfer payments based on backorder, inventory and ...