A new two-party bargaining mechanism

If resources and facilities from different partners need to be engaged for a large-scale project with a huge number of tasks, any of which is indivisible, decision on the number of tasks assigned to any collaborating partner often requires a certain amount of coordination and bargaining among these partners so that the ultimate task allocation can be accepted by any partner in a business union for the project. In the current global financial crisis, such cases may appear frequently. In this paper, we first investigate the behavior of such a discrete bargaining model often faced by service-based organizations. In particular, we address the general situation of two partners, where the finite Pareto efficient (profit allocation) set does not possess any convenient assumption for deriving a bargaining solution, namely a final profit allocation (corresponding to a task assignment) acceptable to both partners. We show that it is not appropriate for our discrete bargaining model to offer the union only one profit allocation. Modifying the original optimization problem used to derive the Nash Bargaining Solution (NBS), we develop a bargaining mechanism and define a related bargaining solution set to fulfil one type of needs on balance between profit-earning efficiency and profit-earning fairness. We then show that our mechanism can also suit both Nash’s original concave bargaining model and its continuous extension without the concavity of Pareto efficient frontier on profit allocation.     

The topology aware file distribution problem

We present theoretical results for large-file distribution on general networks of known topology (known link bandwidths and router locations). We show that the problem of distributing a file in minimum time is NP-hard in this model, and we give an O(logn) approximation algorithm, where n is the number of workstations that require the file. We also characterize our method as optimal amongst the class of “no-link-sharing” algorithms.     

On the outer-connected domination in graphs

A set S of vertices of a graph G is an outer-connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraph induced by V?S is connected. The outer-connected domination number $\widetilde{\gamma}_{c}(G)$ is the minimum size of such a set. We prove that if δ(G)≥2 and diam?(G)≤2, then $\widetilde{\gamma}_{c}(G)\le (n+1)/2$ , and we study the behavior of $\widetilde{\gamma}_{c}(G)$ under an edge addition.     

Ensuring units invariant slack selection in radial data envelopment analysis models,and incorporating slacks into an overall efficiency score

This paper introduces a new methodology ensuring units invariant slack selection in radial DEA models and incorporating the slacks into an overall efficiency score. The CCR and BCC models are units invariant in their radial component, but not in their slack component, thus changing the units of measurement of one or more variables can change the models' solution. The proposed Full Proportional Slack (FPS) methodology improves the slack selections of the CCR and BCC models by producing slack selections that (a) are units invariant, thus producing fully units invariant models, (b) maximize the relative improvements represented by the slacks, and not their values, and (c) measure the full slacks that need to be removed from their corresponding variables. The FPS methodology is a fully oriented methodology first maximizing the improvements in the variables on the side of the orientation of the model. The Proportional Slack Adjusted (PSA) methodology incorporates the FPS slacks into an overall efficiency score, making it easier to interpret and use the results. The FPS and PSA methodologies are illustrated using an input oriented VRS Loan Quality DEA model with data from the retail branch network of one of Canada's largest banks.     

Single-machine batch delivery scheduling with an assignable common due window

This paper addresses a batch delivery single-machine scheduling problem in which jobs have an assignable common due window. Each job will incur an early (tardy) penalty if it is early (tardy) with respect to the common due window under a given schedule. There is no capacity limit on each delivery batch, and the cost per batch delivery is fixed and independent of the number of jobs in the batch. The objective is to find the optimal size and location of the window, the optimal dispatch date for each job, as well as an optimal job sequence to minimize a cost function based on earliness, tardiness, holding time, window location, window size, and batch delivery. We show that the problem can be optimally solved in O(n⁸)$O(n^8)$ time by a dynamic programming algorithm under a reasonable assumption on the relationships among the cost parameters. A computational experiment is also conducted to evaluate the performance of the proposed algorithm. We also show that some special cases of the problem can be optimally solved by lower order algorithms.     

Impact of product proliferation on the reverse supply chain

Product variety is one of the most important advantages in highly competitive markets. However, excessive product proliferation's reducing the profit margin has caused increased focus on developing a management method for maximal profit. In a closed-loop supply chain, product proliferation affects the reverse supply chain as well as the forward supply chain. Although increasing the number of product types can better satisfy diverse customer needs, complexity in the product recycling, remanufacturing, and resale processes may erode a firm's overall profits. In this study, we develop a mathematical model for analyzing a capacitated reverse supply chain consisting of a single manufacturer and multiple retailers. We reveal closed-form solutions for the optimal batch size and maximal profit, and discuss managerial insights into how the number of products and other factors can affect both batch size and profit. Finally, we investigate the relationship between product proliferation and the choice of logistics strategy.     

Setups and effective capacity: the impact of lot sizing techniques in an MRP environment

This study investigates how lot sizing techniques influence the profit performance, inventory level, and order lardiness of an assembly job shop controlled by MRP. Four single-level lot sizing techniques are compared by simulation analysis under two levels of master schedule instability and two levels of end item demand. A second analysis investigates the influence of a multilevel lot sizing technique, the generalized constrained-K (GCK) cost modification, on the four single-level techniques at low demand and low nervousness. The analyses reveal a previously unreported phenomenon. Given the same inventory costs, the single-level lot sizing techniques generate substantially different average batch sizes. The lot sizing techniques maintain the following order of increasing average batch size (and decreasing total setup time):

economic order quantity (EOQ)

period order quantity (POQ)

least total cost (LTC)

Silver-Meal heuristic (SML)

The causes for different average batch sizes among the lot sizing techniques are analysed and explained. Demand lumpiness, inherent in multilevel manufacturing systems controlled by MRP, is found to be a major factor. The number of setups each lot sizing technique generates is the primary determinant of profit performance, inventory level, and order tardiness. EOQ, a fixed order quantity technique, is less sensitive to nervousness than the discrete lot sizing techniques. EOQ_, however, generates the smallest average batch size, and, therefore, the most setups. Since setups consume capacity, EOQ, is more sensitive to higher demand. SML generates the largest average batch sizes, and is, therefore, less sensitive to increased demand. At low demand, the other lot sizing techniques perform better on all criteria. They generate smaller batches and, therefore, shorter actual lead times. The GCK cost modification increases the average batch size generated by each lot sizing technique. GCK improves the profit and customer service level of EOQ the lot sizing technique with the smallest batches. GCK causes the other lot sizing techniques to generate excessively large batches and, therefore, excessively long actual lead times.     

Hierarchical model to design manufacturing systems applied to a metal-mechanic company

This paper describes the application of a model to design and manage the manufacturing process through an integrated system, using a Hierarchical methodology-by means of different aggregation and disaggregation stages with an appropriate time horizon. The hierarchical model obtained allows interfacing between the master schedule and the schedule of the orders. At each level of the hierarchical model some decisions have to be made in order to design the manufacturing system, but having a model that also takes into consideration the management of the system. To do this it is necessary to use aggregated information concerned with the level at which decisions are made. It is obtained from the database, which contains the information at the highest level of aggregation. This model has been applied to a metal mechanic company, that makes final products such as car washers, etc. The benefits of this approach for the company are addressed in this paper.     

Multi-item EOQ inventory model with varying holding cost under two restrictions: A geometric programming approach

In this paper we provide a simple method to determine the inventory policy of multiple items having varying holding cost using a geometric programming approach. The varying holding cost is considered to be a continuous function of the order quantity. The EOQ inventory model with constant holding cost and the classical EOQ inventory model without constraints are derived.