An EOQ model with multiple suppliers and random capacity (original) (raw)
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An EOQ lot sizing model with random supplier capacity
International Journal of Production Economics, 1999
This paper presents a general formulation of the inventory lot sizing model with random supplier capacity under the EOQ framework. For a general capacity distribution, we show that the expected cost per unit of time is a unimodal function and pseudo-convex in the ordering quantity. Moreover, we derive some simple data-dependent bounds for both optimal lot size and expected cost per unit of time. In order to illustrate the general model, three types of distributions for the random capacity are analyzed as special cases. These are the uniform, exponential, and truncated normal distributions. For each of these distributions, we find that the maximum cost penalty of using the EOQ lot size instead of the optimal one is almost negligible (not greater than 0.52%, 1.81%, and 0.91% for the uniform, exponential, and truncated normal distributions, respectively). In addition, we extend the general model to allow for the presence of defective units in the quantity received from the supplier. It is shown that this extra randomness does not affect the optimal ordering policy for the original model.
Inventory models of future supply uncertainty with single and multiple suppliers
Naval Research Logistics, 1996
We consider order-quantity / reorder-point inventory models where the availability of supply is subject to random fluctuations. We use concepts from renewal reward processes to develop average cost objective function models for single, two, and multiple suppliers. Identifying the regenerative cycle for each problem aids the development of the cost function. In the case of two suppliers, spectral theory is used to derive explicit expressions for the transient probabilities of a four-state continuous-time Markov chain representing the status of the system. These probabilities are used to compute the exact form of the average cost expression. For the multiple-supplier problem, assuming that all the suppliers have similar availability characteristics, we develop a simple model and show that as the number of suppliers becomes large, the model reduces to the classical EOQ model. 0
Inventory control in a multi-supplier system
International Journal of Production Economics, 2006
An enterprise network is analyzed from the viewpoint of an end-product manufacturer who receives customer orders and organises his production and supply policy so as to minimize the sum of his average holding cost and average stockout cost. For each main component to be ordered, the producer has several possible suppliers. The arrivals of customers' orders are random and delivery times from suppliers are also supposed random. This supply system is represented as a queuing network where the producer uses a base-stock inventory control policy that keeps constant the inventory position level (current inventory level+pending replenishment orders). The decision variables are the reference inventory position level and the percentages of orders sent to the different suppliers. In the queuing network model, the percentages of orders are implemented as Bernoulli branching parameters. A close-form expression of the expected cost criterion is obtained as a complex non-linear function of decision variables. A decomposed approach is proposed for solving the optimization problem in an approximate manner. The quality of the approximate solution is evaluated by comparison to the exact solution, which can be computed numerically in some simple cases, in particular in the two-supplier case. Numerical applications show the important economic advantage for the producer of sending orders to several suppliers rather than to a single one. r
An Integrated Model for a Two-supplier Supply Chain with Uncertainty in the Supply
Journal of Industrial and Systems Engineering, 2011
The objective of this paper is to study an integrated two-supplier supply chain whose suppliers are unreliable. An unreliable supplier is alternative between available (ON) and unavailable (OFF) states which are considered to be independent exponential variables. The suppliers apply a continuous review policy and the retailer uses an adapted continuous review base on an(R,Q) policy. Transportation times are constant and lead times are non-zero random variables. The retailer faces independent Poisson demands. Using the idea of the one-for-one ordering policy, we implicitly incorporate the distribution function of the random delay for obtaining the value of the expected costs of system. Finally, resorting to a dozen of sample problems, we show that the average cost reduction in our inventory system is at least 3.69% and at most 36.95% comparing to the one with only one supplier.
Sourcing Decisions with Stochastic Supplier Reliability and Stochastic Demand
Production and Operations Management, 2009
Supplier sourcing strategies are a crucial factor driving supply chain success. In particular, a firm's allocation decision for determining an appropriate supplier set and order allotment impacts all competitive dimensions for the delivery of finished goods to its customers. While many firms utilize a single supplier strategy, others diversify their supply risk by sourcing from multiple suppliers. In this paper, we investigate the implications of uncertain supplier reliability on a firm's sourcing decisions in an environment with stochastic demand. In particular, we characterize conditions under which a firm should choose a single versus multiple supplier sourcing strategy. We also show that a supplier's unit cost dominates any reliability considerations when determining whether a particular supplier receives an order. A counterintuitive result is that placing a single order with the lowest cost supplier is preferable when demand is highly uncertain. Based on numerical examples, we also illustrate the impact of minimum order quantities on supplier sourcing decisions.
Multiperiod Models with Capacities in Competitive Supply Chain
Production and Operations Management, 2008
T his paper considers a supply chain setting where several capacitated suppliers compete for orders from a single retailer in a multiperiod environment. At each period, the retailer places orders to the suppliers in response to the prices they announce. Each supplier has a fixed capacity. We consider a make-to-stock setting where the retailer can carry inventory. The retailer faces exogenous, price-dependent demand. We study the problem using ideas from fluid models. In particular, we (i) analyze when there are pure equilibrium policies in this setting and characterize the structure of these policies; (ii) consider coordination mechanisms; and (iii) present some preliminary computational results. We also consider a modified model that uses option contracts to coordinate the supply chain.
Multi-Supplier Sourcing with Random Yields: A Newsvendor Approach
In today's globally competitive environment, decision makers in supply chains are faced with numerous challenges particularly regarding the selection of suppliers. To assist in this endeavor, we examine a double-layered supply chain where a buyer (vendor) facing the end users has the option of selecting among a cohort of suppliers. The available suppliers have different yield rates and unit costs. The vendor has to decide, given the stochastic nature of the problem's governing parameters, whether or not to order from each supplier, and if so the quantity to be ordered so as to maximize the expected profit. The newsvendor problem is extended to model the considered situation. We develop an analytical model for the problem, and propose two solution algorithms for it. Numerical studies are preformed to capture the performance nature of the developed algorithms. One of the algorithms exhibits efficient performance and utilizing it leads to many managerial insights regarding the ...
Optimal replenishment order for uncertain demand in three layer supply chain
Economic Modelling, 2012
The authors study the well-known order quantity model in a three-player context, using a framework of newsboy problem. An expected average cost function of the chain by trading off inventory cost and shortage costs is formulated which is minimized to obtain optimal order sizes of the supplier, manufacturer and retailer. Our theoretical analysis of both cases; (i) when demand per unit time of each member of the chain is uncertain, (ii) when uncertain demand is distributed uniformly over finite time horizon; suggests the determining of optimal order sizes of the members so that the expected average channel cost is minimum. Numerical examples for different distributions are illustrated to justify our model.
Decision Sciences, 2014
This research considers a supply chain under the following conditions: (i) two heterogeneous suppliers are in competition, (ii) supply capacity is random and pricing is endogenous, (iii) consumer demand, with and without an intermediate retailer, is price dependent. Specifically, we examine how uncertainty in supply capacity affects optimal ordering and pricing decisions, supplier and retailer profits, and the incentives to reduce such uncertainty. When two suppliers sell through a monopolistic retailer, supply uncertainty not only affects the retailer's diversification strategy for replenishment, but also changes the suppliers' wholesale price competition and the incentive for reducing capacity uncertainty. In this dual-sourcing model, we show that the benefit of reducing capacity uncertainty depends on the cost heterogeneity between the suppliers. In addition, we show that a supplier does not necessarily benefit from capacity variability reduction. We contrast this incentive misalignment with findings from the single-supplier case and a supplier-duopoly case where both suppliers sell directly to market without the monopolistic retailer. In the latter single-supplier and duopoly cases, we prove that the unreliable supplier always benefits from reducing capacity variability. These results highlight the role of the retailer's diversification strategy in distorting a supplier's incentive for reducing capacity uncertainty under supplier price competition. He has a B.Tech degree in mechanical engineering from the Indian Institute of Technology, Mumbai, and a PhD in operations research and industrial engineering from Cornell University. His research focuses on industry-motivated quantitative modeling and decision making under uncertainty applied to capacity planning, production and inventory control, supply chain configuration and coordination, telecom hub location, workforce staffing, and healthcare delivery improvement. His research has been published in
A procurement model using capacity reservation
In this paper we model a scenario where a buyer reserves capacity from one or more suppliers in the presence of demand uncertainty. We explicitly derive suppliers' capacity reservation price, which is a function of their capacity, amount of capacity reserved by the buyer and other parameters. The buyer operates in a ''built-to-order'' environment and needs to decide how much capacity to reserve and from how many suppliers. For a strategy of equal allocation of capacity among the selected suppliers we develop closed form solutions and show that the model is robust to the number of suppliers from whom capacity is procured through reservation. When the parameters of demand distribution changes the supply base is likely to remain more or less the same. Our analysis further shows that increasing the number of pre-qualified suppliers does not provide significant advantages to the buyer. On the other hand, a pre-qualified supply base with greater capacity heterogeneity will benefit the buyer.