Coordinated ordering decisions for products with short lifecycle and variable selling price

The supplier–buyer coordination is an important policy in the supply chain management. The buyer in the two-echelon inventory system with regular selling season has to face the uncertainty of customer demand, supplier’s delivery time and variable price change. At the same time, the supplier has to consider the inventory holding and delay cost. The objective of this study is to develop an integrated supply chain strategy for products with short lifecycle and variable selling price to entice cooperation. The strategy must provide a win–win situation for both the supplier and the buyer. A numerical case example, sensitivity analysis and compensation mechanism are given to illustrate the model.     

A quantity flexibility contract model for a system with heterogeneous suppliers

This paper focuses on a quantity flexibility contract through which two or more heterogeneous suppliers periodically deliver a single type of product to a buyer as promised in the contract. The buyer starts each period by informing each supplier of the order size for the period and the reservation quantity for all future periods within a planning horizon. The order size for the current period is finalized according to the amount previously reserved, although this amount can be increased or decreased by a predetermined percentage of the reservation amount.In this paper, a linear programming model including several key features of a quantity flexibility contract is developed from the buyer's perspective. A rolling-horizon implementation strategy is suggested for efficient implementation of the contract. Computational experiments demonstrate that the proposed method can be used to determine a cost effective solution for the buyer in a reasonable amount of time.     

Supplier selection and procurement decisions with uncertain demand,fixed selection costs and quantity discounts

In this paper, we study the supplier selection and procurement decision problem with uncertain demand, quantity discounts and fixed selection costs. In addition, a holding cost is incurred for the excess inventory if the buyer orders more than the realized demand and the shortage must be satisfied by an emergent purchase at a higher price otherwise. The objective is to select the suppliers and to allocate the ordering quantity among them to minimize the total cost (including selecting, procurement, holding and shortage costs, etc.). The problem is modeled as a Mixed Integer Programming (MIP) and is shown to be NP-hard. Some properties of the optimal policy are provided and an optimal algorithm is proposed based on the generalized Bender's decomposition. Numerical experiments are conducted to show the efficiency of the algorithm and to obtain some managerial insights.     

A supplier-selection model with classification and joint replenishment of inventory items

Since inventory costs are closely related to suppliers, many models in the literature have selected the suppliers and also allocated orders, simultaneously. Such models usually consider either a single inventory item or multiple inventory items which have independent holding and ordering costs. However, in practice, ordering multiple items from the same supplier leads to a reduction in ordering costs. This paper presents a model in capacity-constrained supplier-selection and order-allocation problem, which considers the joint replenishment of inventory items with a direct grouping approach. In such supplier-selection problems, the following items are considered: a fixed major ordering cost to each supplier, which is independent from the items in the order; a minor ordering cost for each item ordered to each supplier; and the inventory holding and purchasing costs. To solve the developed NP-hard problem, a simulated annealing algorithm was proposed and then compared to a modified genetic algorithm of the literature. The numerical example represented that the number of groups and selected suppliers were reduced when the major ordering cost increased in comparison to other costs. There were also more savings when the number of groups was determined by the model in comparison to predetermined number of groups or no grouping scenarios.     

A multi-objective quantity discount and joint optimization model for coordination of a single-buyer multi-vendor supply chain

Supply chain management is concerned with the coordination of different parts of the production system. Companies have realized that they must closely collaborate with the suppliers of their strategic components or products. Recently, developing integrated inventory models for the supplier selection problem has attracted a significant amount of attention amongst researchers. In these models some incentives are required from the vendors to motivate the buyer to change his (her) policies to the policy which is optimal for the entire system. Quantity discount policies are used as common incentives in the literature. However, the literature on this problem does not incorporate quantity discount into the coordination model. This paper develops a multi-objective mixed integer nonlinear programming model to coordinate the system of a single buyer and multiple vendors under an all-unit quantity discount policy for the vendors. Due to the complexity of the problem two well known meta-heuristic algorithms are proposed to solve the problem. An illustrative example is given to show the behavior of the model. Results obtained from solving the sample problems show good performance of the proposed algorithms in finding the optimal solutions.     

Capacity-constrained supplier selection model with lost sales under stochastic demand behaviour

In today’s market conditions, volume of demand is quite uncertain and thus it is hard to estimate. In many cases, buyer is prone to use supply chain flexibility rather than inventory holding strategy to withstand demand uncertainty. We assume that the buyer releases a replenishment order to the supplier for each cycle (or period) under the contract which is mainly composed of four parameters: (1) supply cost per unit, (2) minimum order quantity, (3) order quantity reduction penalty and (4) maximum capacity of the supplier. Based on these parameters, there are two flexibility options that buyer should evaluate in the order of cycle (1) issue an order smaller than the minimum order quantity and pay the related penalty and (2) place no order and lose the sales. Hence, Q _lost emerges as a critical buyer decision, the order quantity, below which no order is placed. Total expected supply cost plus lost sales, as a function of Q _lost is presented. We derive the optimal Q _lost that minimises the total cost function. Since capacity of each supplier is finite, we then develop a supplier selection model with total cost minimisation over the suppliers subject to capacity constraint that has a stochastic nature stemming from demand behaviour. Linearisation on the model is performed using chance-constrained programming approach. From a given set of supply bids from the potential supply chain partners, the buyer is able to make a quantifiable choice.     

A goal programming model for joint decision making of inventory lot-size,supplier selection and carrier selection

In this paper, we address a problem in which a storage space constrained buyer procures a single product in multiple periods from multiple suppliers. The production capacity constrained suppliers offer all-unit quantity discounts. The late deliveries and rejections are also incorporated in sourcing. In addition, we consider transportation cost explicitly in decision making which may vary because of freight quantity and distance of shipment between the buyer and a supplier. We propose a multi-objective integer linear programming model for joint decision making of inventory lot-sizing, supplier selection and carrier selection problem. In the multi-objective formulation, net rejected items, net costs and net late delivered items are considered as three objectives that have to be minimized simultaneously over the decision horizon. The intent of the model is to determine the timings, lot-size to be procured, and supplier and carrier to be chosen in each replenishment period. We solve the multi-objective optimization problem using three variants of goal programming (GP) approaches: preemptive GP, non-preemptive GP and weighted max–min fuzzy GP. The solution of these models is compared at different service-level requirements using value path approach.     

A supplier selection and order allocation problem with stochastic demands

We consider a system comprising a retailer and a set of candidate suppliers that operates within a finite planning horizon of multiple periods. The retailer replenishes its inventory from the suppliers and satisfies stochastic customer demands. At the beginning of each period, the retailer makes decisions on the replenishment quantity, supplier selection and order allocation among the selected suppliers. An optimisation problem is formulated to minimise the total expected system cost, which includes an outer level stochastic dynamic program for the optimal replenishment quantity and an inner level integer program for supplier selection and order allocation with a given replenishment quantity. For the inner level subproblem, we develop a polynomial algorithm to obtain optimal decisions. For the outer level subproblem, we propose an efficient heuristic for the system with integer-valued inventory, based on the structural properties of the system with real-valued inventory. We investigate the efficiency of the proposed solution approach, as well as the impact of parameters on the optimal replenishment decision with numerical experiments.     

Supplier behavior modeling and winner determination using parallel MDP

Behavioral uncertainty of a supplier is a major challenge to a buyer operating in e-procurement setting. Modeling suppliers’ behavior from past transactions, estimation of possible future performance and integrating this knowledge with the winner determination process can bring a new dimension to procurement process automation. We propose a states-space model to capture the uncertainty involved in long-term supplier behavior. The states represent the performance level of a supplier. This behavioral aspect is then integrated with the winner determination process of a multi-attribute reverse auction for efficient supplier selection using parallel MDP. We also propose an implementation framework to collect the feedback on supplier, generate an aggregate performance score and integrate it with the winner determination process. The performance aggregation and winner determination with help of Markov decision process effectively uses the past performance information. In addition, it updates performance information in regular invervals and allevates the problem of maintaining a long history. We compare the MDP-based selection with that of performance score-based selection through a simulation experiment. It is observed that our scheme gives better buyer utility, selects best suppliers and fetches better quality product. The benefits realized through these attributes to the buyer increases the efficiency of the MDP-based selection process.     

Multi-period dynamic supply contracts with cancellation

This paper considers a class of multi-period dynamic supply contracts in which a buyer orders a product from a supplier in each period and the supplier allows the buyer to cancel a portion of an outstanding order with penalty during a planning horizon. We assume that both the buyer and the supplier have common knowledge. We first characterize the buyer's ordering and canceling policy that minimizes his expected cost during the planning horizon. We also characterize the supplier's optimal production policy under a very mild assumption on the costs of production and storage. Based on this structure, we then use simulation to show how the supplier chooses cancellation costs that minimize her expected cost during the planning horizon. Our simulation shows that both the buyer and the supplier would benefit from the contract.     

Sourcing with random yields and stochastic demand: A newsvendor approach

We studied a supplier selection problem, where a buyer, while facing random demand, is to decide ordering quantities from a set of suppliers with different yields and prices. We provided the mathematical formulation for the buyer's profit maximization problem and proposed a solution method based on a combination of the active set method and the Newton search procedure. Our computational study shows that the proposed method can solve the problem efficiently, and is able to generate interesting and insightful results that lead us to various managerial implications.

Scope and purpose

In today's globally competitive environment, decision makers in supply chains face numerous challenges particularly regarding the selection of suppliers or outsourcing partners. To assist in this endeavor, we examined a double-layered supply chain where a buyer facing the end users has the option of selecting among a cohort of suppliers. The available suppliers may have different yield rates and unit costs. The buyer has to decide, given the stochastic nature of the problem's governing parameters, whether or not to order from each supplier, and if so how much. We developed a ‘newsvendor-style’ model for the problem, and proposed a solution algorithm for it. Numerical studies were performed to provide some insights for supplier selection and order quantity decisions.     

An integrated fuzzy-lp approach for a supplier selection problem in supply chain management

In supply chain management process, the firm select best supplier takes the competitive advantage to other companies. Thus, supplier selection is an important issue and with the multiple criteria decision-making approach, the supplier selection problem includes both tangible and intangible factors. This paper is aimed to present an integrated fuzzy and linear programming approach to the problem. Firstly, linguistic values expressed in trapezoidal fuzzy numbers are applied to assess weights and ratings of supplier selection criteria. Then a hierarchy multiple model based on fuzzy set theory is expressed and fuzzy positive and negative ideal solutions are used to find each supplier’s closeness coefficient. Finally, a linear programming model based on the coefficients of suppliers, buyer’s budgeting, suppliers’ quality and capacity constraints is developed and order quantities assigned to each supplier according to the linear programming model. The integrated model is illustrated by an example in a textile firm.     

The joint replenishment problem involving multiple suppliers offering quantity discounts

In this article, we deal with the problem of determining the economic operating policy when a number of items are to be procured from a number of suppliers offering different quantity discounts schedules. In such inventory problems, a fixed cost is incurred with each replenishment order, independent of the suppliers as well as the items involved in the order. Further, the item involves a minor fixed cost. In such a system, it includes the supplier selection problem when considering the quantity discounts as well as the general joint replenishment problem. We develop a hybrid genetic algorithm for this NP-hard decision problem and extend it to systems with resource restrictions.     

Optimal apparel supplier selection with forecast updates under carbon emission taxation scheme

Carbon emission tax is an important measure for sustainable supply chain management. This paper studies an optimal supplier selection problem in the fashion apparel supply chain in the presence of carbon emission tax. We consider the scenario in which there are multiple suppliers in the market. In the basic model, each supplier offers a supply lead time and a wholesale pricing contract to the fashion retail buyer. For the fashion retail buyer, the supplier which offers a shorter lead time allows it to postpone the ordering decision with updated and better forecast, and also a smaller carbon tax. However, the wholesale price is usually larger. We propose a two-phase optimal supplier selection scheme in which phase one filters the inferior suppliers and phase two helps to select the best supplier among the set of non-inferior suppliers by multi-stage stochastic dynamic programming. The impacts brought by different formats of carbon emission tax are explored. Finally, we examine an extended model in which there is a local supplier who offers a buyback contract and accepts product returns. Insights from the analysis are discussed.     

Integrated inventory control and inspection policies with deterministic demand

In this paper, we develop integrated inventory inspection models with and without replacement of nonconforming items. Inspection policies include no inspection, sampling inspection, and 100% inspection. We consider a buyer who places an order from a supplier. When a lot is received, the buyer uses some type of inspection policy. The fraction nonconforming is assumed to be a random variable following a beta distribution. Both the order quantity and the inspection policy are decision variables. In the inspection policy involving determining sampling plan parameters, constraints on the buyer and manufacturer risks are set in order to obtain a fair plan for both parties. A solution procedure for determining the operating policies for inventory and inspection consisting of order quantity, sample size, and acceptance number is proposed. Numerical examples are presented to conduct a sensitivity analysis for important model parameters and to illustrate important issues about the developed models.     

Exploring the economic consequences of letting a supplier hold reserve storage

We consider a single-item, periodic review inventory control problem with discrete non-stationary stochastic demand. The time horizon is finite and all shortages at the downstream level are backordered. There are two modes of supply: a normal supplier and a reserve storage supply. The reserve storage is capacitated and the downstream buyer can only order the entire inventory in the reserve storage or nothing. If the reserve storage is empty, it takes a fixed time interval before it is replenished again. Provided that the reserve storage is fully replenished it can be used at any time period, whereas orders to the normal supplier can only be issued at specific time periods. The lead time from the reserve storage is shorter than from the normal supplier, but using the reserve storage is more expensive than using the normal supplier. We use stochastic dynamic programming to specify an exact model of the problem. We also develop an approximate model which is computationally faster than the first model. The models are then used to analyze numerically the sensitivity with respect to key parameters like the reserve storage size and unit purchase cost. This paper is motivated by a problem presented during contacts with a leading Danish provider of communications solutions.     

A mathematical model for order splitting in a multiple supplier single-item inventory system

In this paper we develop a mathematical model which considers multiple-supplier single-item inventory systems. The lead times of the suppliers and demand arrival rate are random variables. All shortages are backordered. Continuous review (s, Q) policy has been assumed. When the inventory level hits the reorder level, the total order is split among n suppliers. The problem is to determine the reorder level and order quantity for each supplier so that the expected total cost per time unit, including ordering cost, procurement cost, inventory holding cost and shortage cost is minimized. We also conduct extensive numerical experiments to show the advantages of our model compared to the relevant models in the literature. In addition, some managerial insights are observed.     

A new order splitting model with stochastic lead times for deterioration items

In unreliable supply environments, the strategy of pooling lead time risks by splitting replenishment orders among multiple suppliers simultaneously is an attractive sourcing policy that has captured the attention of academic researchers and corporate managers alike. While various assumptions are considered in the models developed, researchers tend to overlook an important inventory category in order splitting models: deteriorating items. In this paper, we study an order splitting policy for a retailer that sells a deteriorating product. The inventory system is modelled as a continuous review system (s, Q) under stochastic lead time. Demand rate per unit time is assumed to be constant over an infinite planning horizon and shortages are backordered completely. We develop two inventory models. In the first model, it is assumed that all the requirements are supplied by only one source, whereas in the second, two suppliers are available. We use sensitivity analysis to determine the situations in which each sourcing policy is the most economic. We then study a real case from the European pharmaceutical industry to demonstrate the applicability and effectiveness of the proposed models. Finally, more promising directions are suggested for future research.     

Inventory lot-sizing with supplier selection

This paper presents a multi-period inventory lot-sizing scenario, where there are multiple products and multiple suppliers. We consider a situation where the demand of multiple discrete products is known over a planning horizon. Each of these products can be sourced from a set of approved suppliers, a supplier-dependent transaction cost applying for each period in which an order is placed on a supplier. A product-dependent holding cost per period applies for each product in the inventory that is carried across a period in the planning horizon. The decision maker needs to decide what products to order in what quantities with which suppliers in which periods. An enumerative search algorithm and a heuristic are presented to address the problem.     

Optimal transfer,ordering and payment policies for joint supplier–buyer inventory model with price-sensitive trapezoidal demand and net credit

This study aims at formulating an integrated supplier–buyer inventory model when market demand is variable price-sensitive trapezoidal and the supplier offers a choice between discount in unit price and permissible delay period for settling the accounts due against the purchases made. This type of trade credit is termed as ‘net credit’. In this policy, if the buyer pays within offered time M₁, then the buyer is entitled for a cash discount; otherwise the full account must be settled by the time M₂; where M₂ > M₁ ? 0. The goal is to determine the optimal selling price, procurement quantity, number of transfers from the supplier to the buyer and payment time to maximise the joint profit per unit time. An algorithm is worked out to obtain the optimal solution. A numerical example is given to validate the proposed model. The managerial insights based on sensitivity analysis are deduced.