Tales of a so(u)rcerer : optimal sourcing decisions under alternative capacitated suppliers and general cost structures

Most companies must procure items necessary for their businesses from out- side sources, where there are typically a number of competing suppliers with varying cost structures, price schemes, and capacities. This situation poses some interesting research questions from the outlook of different parties in the supply chain. We consider this problem from the perspective of (i) the party that needs to outsource, (ii) the party that is willing to serve as the source, and (iii) the party that has in-house capability to spare. We allow for stochastic demand, capacitated facilities (in-house and suppliers'), and general structures for all relevant cost components. Some simpler versions of this problem are shown to be NP-hard in the literature. We make use of a novel dynamic programming model with pseudo-polynomial complexity to address all three perspectives by solving the corresponding problems to optimality. Our modeling approach also lets us analyze different aspects of the problem environment such as pricing schemes and channel coordination issues. We derive several managerial insights, some of which are counter to collective intuition

Modeling a four-layer location-routing problem

Distribution is an indispensable component of logistics and supply chain management. Location-Routing Problem (LRP) is an NP-hard problem that simultaneously takes into consideration location, allocation, and vehicle routing decisions to design an optimal distribution network. Multi-layer and multi-product LRP is even more complex as it deals with the decisions at multiple layers of a distribution network where multiple products are transported within and between layers of the network. This paper focuses on modeling a complicated four-layer and multi-product LRP which has not been tackled yet. The distribution network consists of plants, central depots, regional depots, and customers. In this study, the structure, assumptions, and limitations of the distribution network are defined and the mathematical optimization programming model that can be used to obtain the optimal solution is developed. Presented by a mixed-integer programming model, the LRP considers the location problem at two layers, the allocation problem at three layers, the vehicle routing problem at three layers, and a transshipment problem. The mathematical model locates central and regional depots, allocates customers to plants, central depots, and regional depots, constructs tours from each plant or open depot to customers, and constructs transshipment paths from plants to depots and from depots to other depots. Considering realistic assumptions and limitations such as producing multiple products, limited production capacity, limited depot and vehicle capacity, and limited traveling distances enables the user to capture the real world situations

A Branch-Price-and-Cut Algorithm for the Capacitated Multiple Vehicle Traveling Purchaser Problem with Unitary Demand

The multiple vehicle traveling purchaser problem (MVTPP) consists of simultaneously selecting suppliers and routing a fleet of homogeneous vehicles to purchase different products at the selected suppliers so that all product demands are fulfilled and traveling and purchasing costs are minimized. We consider variants of the MVTPP in which the capacity of the vehicles can become binding and the demand for each product is one unit. Corresponding solution algorithms from the literature are either branch-and-cut or branch-and-price algorithms, where in the latter case the route-generation subproblem is solved on an expanded graph by applying standard dynamic-programming techniques. Our branch-price-and-cut algorithm employs a novel labeling algorithm that works directly on the original network and postpones the purchasing decisions until the route has been completely defined. Moreover, we define a new branching rule generally applicable in case of unitary product demands, introduce a new family of valid inequalities to apply when suppliers can be visited at most once, and show how product incompatibilities can be handled without considering additional resources in the pricing problem. In comprehensive computational experiments with standard benchmark sets we prove that the new branch-price-and-cut approach is highly competitive

Analysis of multi-attribute multi-unit procurement auctions and capacity-constrained sequential auctions

This dissertation examines an iterative multi-attribute auction for multi-unit procurement in the first part. A multi-unit allocation problem that allows order split among suppliers is formulated to improve the market efficiency. Suppliers are allowed to provide discriminative prices over units based on their marginal costs. A mechanism called Iterative Multiple-attribute Multiple-unit Reverse Auction (IMMRA) is proposed based on the assumption of the modified myopic best-response strategies. Numerical experiment results show that the IMMRA achieves market efficiency in most instances. The inefficiency occurs occasionally on the special cases when cost structures are significantly different among suppliers. Numerical results also show that the IMMRA results in lower buyer payments than the Vickrey-Clarke-Grove (VCG) payments in most cases. In the second part, two sequential auctions with the Vickrey-Clarke-Grove (VCG) mechanism are proposed for two buyers to purchase multiple units of an identical item. The invited suppliers are assumed to have capacity constraints of providing the required demands. Three research problems are raised for the analysis of the sequential auctions: the suppliers\u27 expected payoff functions, the suppliers\u27 bidding strategies in the first auction, and the buyers\u27 procurement costs. Because of the intrinsic complexity of the problems, we limit our study to a duopoly market environment with two suppliers. Both suppliers’ dominant bidding strategies are theoretically derived. With numerical experiments, suppliers’ expected profits and buyers’ expected procurement costs are empirically analyzed

Analysis of multi-attribute multi-unit procurement auctions and capacity-constrained sequential auctions

This dissertation examines an iterative multi-attribute auction for multi-unit procurement in the first part. A multi-unit allocation problem that allows order split among suppliers is formulated to improve the market efficiency. Suppliers are allowed to provide discriminative prices over units based on their marginal costs. A mechanism called Iterative Multiple-attribute Multiple-unit Reverse Auction (IMMRA) is proposed based on the assumption of the modified myopic best-response strategies. Numerical experiment results show that the IMMRA achieves market efficiency in most instances. The inefficiency occurs occasionally on the special cases when cost structures are significantly different among suppliers. Numerical results also show that the IMMRA results in lower buyer payments than the Vickrey-Clarke-Grove (VCG) payments in most cases. In the second part, two sequential auctions with the Vickrey-Clarke-Grove (VCG) mechanism are proposed for two buyers to purchase multiple units of an identical item. The invited suppliers are assumed to have capacity constraints of providing the required demands. Three research problems are raised for the analysis of the sequential auctions: the suppliers\u27 expected payoff functions, the suppliers\u27 bidding strategies in the first auction, and the buyers\u27 procurement costs. Because of the intrinsic complexity of the problems, we limit our study to a duopoly market environment with two suppliers. Both suppliers’ dominant bidding strategies are theoretically derived. With numerical experiments, suppliers’ expected profits and buyers’ expected procurement costs are empirically analyzed

Optimal Global Supply Chain and Warehouse Planning under Uncertainty

A manufacturing company\u27s inbound supply chain consists of various processes such as procurement, consolidation, and warehousing. Each of these processes is the focus of a different chapter in this dissertation. The manufacturer depends on its suppliers to provide the raw materials and parts required to manufacture a finished product. These suppliers can be located locally or overseas with respect to the manufacturer\u27s geographic location. The ordering and transportation lead times are shorter if the supplier is located locally. Just In Time (JIT) or Just In Sequence (JIS) inventory management methods could be practiced by the manufacturer to procure the raw materials and parts from the local supplier and control the inventory levels in the warehouse. In contrast, the lead time for the orders placed with an overseas supplier is usually long because sea-freight is often used as a primary mode of transportation. Therefore, the orders for the raw materials and parts (henceforth, we collectively refer to raw material and part by part) procured from overseas suppliers are usually placed using forecasted order quantities. In Chapter 2, we study the procurement process to reduce the overall expected cost and determine the optimal order quantities as well as the mode of transportation for procurement under forecast and inventory uncertainty. We formulate a two-stage stochastic integer programming model and solve it using the progressive hedging algorithm, a scenario-based decomposition method. Generally, the orders are placed with overseas suppliers using weekly or monthly forecasted demands, and the ordered part is delivered using sea-containers since sea-freight is the primary mode of transportation. However, the end manufacturing warehouse is usually designed to hold around one to two days of parts. To replenish the inventory levels, the manufacturer considered in this research unloads the sea-container that contains the part that needs to be restocked entirely. This may cause over-utilization of the manufacturer\u27s warehouse if an entire week\u27s supply of part is consolidated into a single sea-container. This problem is further aggravated if the manufacturer procures hundreds of different parts from overseas suppliers and stores them in its warehouse. In Chapter 3, we study the time-series forecasting models that help predict the manufacturing company\u27s daily demand quantities for parts with different characteristics. The manufacturer can use these forecasted daily demand quantities to consolidate the sea-containers instead of the weekly forecasted demand. In most cases, there is some discrepancy between the predicted and actual demands for parts, due to which the manufacturer can either have excess inventory or shortages. While excess inventory leads to higher inventory holding costs and warehouse utilization, shortages can result in substantially undesirable consequences, such as the total shutdown of production lines. Therefore, to avoid shortages, the manufacturer maintains predetermined safety stock levels of parts with the suppliers to fulfill the demands arising from shortages. We formulate a chance-constraint optimization model and solve it using the sample approximation approach to determine the daily safety stock levels at the supplier warehouse under forecast error uncertainty. Once the orders are placed with the local and overseas suppliers, they are consolidated into trailers (for local suppliers) and sea-containers (for overseas suppliers). The consolidated trailers and sea-containers are then delivered to the manufacturing plant, where they are stored in the yard until they are called upon for unloading. A detention penalty is incurred on a daily basis for holding a trailer or sea-container. Consolidating orders from different suppliers helps maximize trailer and sea-container space utilization and reduce transportation costs. Therefore, every sea-container and trailer potentially holds a mixture of parts. When a manufacturer needs to replenish the stocks of a given part, the entire sea-container or trailer that contains the required part is unloaded. Thus, some parts that are not imminently needed for production are also unloaded and stored inside the manufacturing warehouse along with the required parts. In Chapter 4, we study a multi-objective optimization model to determine the sea-containers and trailers to be unloaded on a given day to replenish stock levels such that the detention penalties and the manufacturing warehouse utilization are minimized. Once a sea-container or trailer is selected to replenish the warehouse inventory levels, its contents (i.e., pallets of parts) must be unloaded by the forklift operator and then processed by workers to update the stock levels and break down the pallets if needed. Finally, the unloaded and processed part is stored in the warehouse bins or shelves. In Chapter 5, we study the problem of determining the optimal team formation such that the total expected time required to unload, process, and store all the parts contained in the sea-containers and trailers selected for unloading on a given day is minimized

Decision support system for vendor managed inventory supply chain:a case study

Vendor-managed inventory (VMI) is a widely used collaborative inventory management policy in which manufacturers manages the inventory of retailers and takes responsibility for making decisions related to the timing and extent of inventory replenishment. VMI partnerships help organisations to reduce demand variability, inventory holding and distribution costs. This study provides empirical evidence that significant economic benefits can be achieved with the use of a genetic algorithm (GA)-based decision support system (DSS) in a VMI supply chain. A two-stage serial supply chain in which retailers and their supplier are operating VMI in an uncertain demand environment is studied. Performance was measured in terms of cost, profit, stockouts and service levels. The results generated from GA-based model were compared to traditional alternatives. The study found that the GA-based approach outperformed traditional methods and its use can be economically justified in small- and medium-sized enterprises (SMEs)

A production planning model considering uncertain demand using two-stage stochastic programming in a fresh vegetable supply chain context

Production planning models are achieving more interest for being used in the primary sector of the economy. The proposed model relies on the formulation of a location model representing a set of farms susceptible of being selected by a grocery shop brand to supply local fresh products under seasonal contracts. The main aim is to minimize overall procurement costs and meet future demand. This kind of problem is rather common in fresh vegetable supply chains where producers are located in proximity either to processing plants or retailers. The proposed two-stage stochastic model determines which suppliers should be selected for production contracts to ensure high quality products and minimal time from farm-to-table. Moreover, Lagrangian relaxation and parallel computing algorithms are proposed to solve these instances efficiently in a reasonable computational time. The results obtained show computational gains from our algorithmic proposals in front of the usage of plain CPLEX solver. Furthermore, the results ensure the competitive advantages of using the proposed model by purchase managers in the fresh vegetables industry.This work was supported by the MEyC under contracts TIN2011-28689-C02-02, TRA2013-48180-C3-P and TIN2014- 53234-C2-2-R. The authors are members of the research group 2014-SGR163 and 2014-SGR151, funded by the Generali- tat de Catalunya

Multi-echelon distribution systems in city logistics

In the last decades , the increasing quality of services requested by the cust omer, yields to the necessity of optimizing the whole distribution process. This goal may be achieved through a smart exploitation of existing resources other than a clever planning of the whole distribution process. For doing that, it is necessary to enha nce goods consolidation. One of the most efficient way to implement it is to adopt Multi - Echelon distribution systems which are very common in City Logistic context, in which they allow to keep large trucks from the city center, with strong environmental a dvantages . The aim of the paper is to review routing problems arising in City Logistics , in which multi - e chelon distribution systems are involved: the Two Echelon Location Routing Problem ( 2E - LRP) , the Two Echelon Vehicle Routing Problem (2E - VRP) and Truck and Trailer Routing Problem (TTRP), and to discuss literature on optimization methods, both exact and heuristic, developed to address these problems