Ben A. Chaouch

A heuristic solution procedure for the dynamic lot sizing problem with remanufacturing and product recovery

Here we discuss the lot sizing problem of product returns and remanufacturing. Let us consider a forecast of demands and product returns over a finite planning horizon - the problem is to determine an optimal production plan. This consists of either manufacturing new products or remanufacturing returned units, and in this way meets both demands at minimum costs. The costs of course are the fixed set-up expenses associated with manufacturing and/or remanufacturing lots and also the inventory holding costs of stocks kept on hand. In addition to showing that a general instance of this problem is NP-Hard, we develop an alternative mixed-integer model formulation for this problem and contrast it to the formulation commonly used in the literature. We show that when integrality constraints are relaxed, our formulation obtains better bounds. Our formulation incorporates the fact that every optimal solution can be decomposed into a series of well-structured blocks with distinct patterns in the way in which set-ups for manufacturing and remanufacturing occur. We then construct a dynamic programming based heuristic that exploits the block structure of the optimal solution. We also propose some improvement schemes as well. Finally, our numerical testing shows that the heuristic performs very well as intended.

Minimizing Cost of Continuous Audit: Counting and Time Dependent Strategies

Why do we need to audit databases? The answer to this question depends on several factors, including the users and the applications that have accessed the data, the timing and the type of data modifications such as permissions or schema and so on. This paper examines certain strategies that have been suggested in the database auditing literature (see, e.g. Orman, 2001). Orman studied the counting, periodic and hybrid auditing strategies with the objective of minimizing the number of errors introduced during database access. Unlike Orman whose focus is on assessing the number of errors infilterating the system, we focus on the long run operating cost of running database audit. We use results from regenerative stochastic processes to derive expressions for the long run average cost under the counting and periodic auditing strategies. Future directions for research are also proposed.

Application of the cohort-intelligence optimization method to three selected combinatorial optimization problems

The real world problems in the supply-chain domain are generally constrained and combinatorial in nature. Several nature-/bio-/socio-inspired metaheuristic methods have been proposed so far solving such problems. An emerging metaheuristic methodology referred to as Cohort Intelligence (CI) in the socio-inspired optimization domain is applied in order to solve three selected combinatorial optimization problems. The problems considered include a new variant of the assignment problem which has applications in healthcare and inventory management, a sea-cargo mix problem and a cross-border shipper selection problem. In each case, we use two benchmarks for evaluating the effectiveness of the CI method in identifying optimal solutions. To assess the quality of solutions obtained by using CI, we do comparative testing of its performance against solutions generated by using CPLEX. Furthermore, we also compare the performance of the CI method to that of specialized multi-random-start local search optimization methods that can be used to find solutions to these problems. The results are robust with a reasonable computational time and accuracy.

Scheduling elective surgeries: the tradeoff among bed capacity, waiting patients and operating room utilization using goal programming

Scheduling of surgeries in the operating rooms under limited competing resources such as surgical and nursing staff, anesthesiologist, medical equipment, and recovery beds in surgical wards is a complicated process. A well-designed schedule should be concerned with the welfare of the entire system by allocating the available resources in an efficient and effective manner. In this paper, we develop an integer linear programming model in a manner useful for multiple goals for optimally scheduling elective surgeries based on the availability of surgeons and operating rooms over a time horizon. In particular, the model is concerned with the minimization of the following important goals: (1) the anticipated number of patients waiting for service; (2) the underutilization of operating room time; (3) the maximum expected number of patients in the recovery unit; and (4) the expected range (the difference between maximum and minimum expected number) of patients in the recovery unit. We develop two goal programming (GP) models: lexicographic GP model and weighted GP model. The lexicographic GP model schedules operating rooms when various preemptive priority levels are given to these four goals. A numerical study is conducted to illustrate the optimal master-surgery schedule obtained from the models. The numerical results demonstrate that when the available number of surgeons and operating rooms is known without error over the planning horizon, the proposed models can produce good schedules and priority levels and preference weights of four goals affect the resulting schedules. The results quantify the tradeoffs that must take place as the preemptive-weights of the four goals are changed.

A replenishment control system with uncertain returns and random opportunities for disposal

We consider a replenishment control system in which product returns play an important role in inventory planning. We focus on the inventory of an individual item that is stored at a single location to meet a constant demand over time. We assume that the total amount of returns accumulated over a period of time can be represented by a compound Poisson process. We further assume that opportunities for inventory disposals or relocation arise occasionally in accordance with a Poisson process. We not only seek to resolve the issues of when to order and how much to order, we also consider the question of when to dispose of excess inventory and by how much. Inventory reductions occur when the opportunity for a disposal arises and the inventory position is deemed too high. After each disposal the inventory position is restored to a specified base-stock level. We develop a cost model of this system and highlight its properties through an extensive numerical study.

Analysis of the stochastic cash balance problem using a level crossing technique

The simple cash management problem includes the following considerations: the opportunity cost of holding too much cash versus the penalty cost of not having enough cash to meet current needs; the cost incurred (or profit generated) when making changes to cash levels by increasing or decreasing them when necessary; the uncertainty in timing and magnitude of cash receipts and cash disbursements; and the type of control policy that should be used to minimize the required level of cash balances and related costs. In this paper, we study a version of this problem in which cash receipts and cash disbursements occur according to two independent compound Poisson processes. The cash balance is monitored continuously and an order-point, order-up-to-level, and keep-level

An EOQ model with random variations in demand

\left( {s, S, M} \right)

STOCK LEVELS AND DELIVERY RATES IN VENDORMANAGED INVENTORY PROGRAMS

s,S,M policy is used to monitor the content, where