The inventory packing problem

We study the problem of finding the minimum number of identical storage areas required to hold n items for which demand is known and constant. The replenishments of the items within a single storage area may be time phased so as to minimize the maximum total storage capacity required at any time. This is the inventory-packing problem, which can be considered as a variant of the well-known bin-packing problem, where one constraint is nonlinear. We study the worst-case performance of six heuristics used for that earlier problem since the recognition version of the inventory-packing problem is shown to be NP complete. In addition, we describe several new heuristics developed specifically for the inventory-packing problem, and also study their worst-case performance. Any heuristic which only opens a bin when an item will not fit in any (respectively, the last) open bin needs, asymptotically, no more than 25/12 (resp., 9/4) times the optimal number of bins. Improved performance bounds are obtainable if the range from which item sizes are taken is known to be restricted. Extensive computational testing indicates that the solutions delivered by these heuristics are, for most problems, very close to optimal in value.     

A survey of preventive maintenance models for stochastically deteriorating single-unit systems

A survey of the research done on preventive maintenance is presented. The scope of the present survey is on the research published after the 1976 paper by Pierskalla and Voelker [98]. This article includes optimization models for repair, replacement, and inspection of systems subject to stochastic deterioration. A classification scheme is used that categorizes recent research into inspection models, minimal repair models, shock models, or miscellaneous replacement models.     

浅论维修科学理论体系

本文论述建立维修科学理论体系的意义和研究时应考虑的一些准则,并提出具体的体系结构模式。该体系由维修导论、维修技术、装备采办和维修管理4个学科分支组成。     

Multiproduct dynamic lot-sizing model with coordinated replenishments

In this article we consider a multiproduct dynamic lot-sizing model. In addition to a separate setup cost for each product ordered, a joint setup cost is incurred when at least one product is ordered. We formulate the model as a concave minimization problem over a compact polyhedral set and present a finite branch and bound algorithm for finding an optimal ordering schedule. Superiority of the branch and bound algorithm to the existing exact procedures is demonstrated. We report computational experience with problems whose dimensions render the existing procedures computationally infeasible.     

Approximating nonstationary two-priority non-preemptive queueing systems

An approximation for analyzing transient and nonstationary two-priority non-preemptive queueing systems is presented. This system has a three-dimensional state space, and through use of state-space partitioning in conjunction with use of conditional surrogate distributions with constant parameters an approximation is designed. Regardless of system capacity K, the approximation requires the numerical solution of only ten differential equations, compared to the K² + K+1 Kolmogorov-forward equations required for the classic solution. Time-dependent approximations of the mean number of entities of type i and of the probability of a type-i entity being in service are obtained. Empirical test results over a wide range of systems indicate the approximation is quite accurate.     

A discounted machine-replacement model with an expected future technological breakthrough

A machine-replacement problem is analyzed in a technological-development environment, in which a new-type machine (built by a new technology) may appear in the future. The solution of the replacement problem depends on purchasing, operating, and resale costs, and on the probability distribution of the market debut of the new technology, and it indicates whether to replace the existing machine now with an available similar type of machine, or to continue to operate the existing machine for at least one more period. A dynamic discounted cost model is presented, and a method is suggested for finding the optimal age for replacement of an existing machine (under rather general conditions of a technological environment). A solution procedure and a numerical example are given.     

A multi-item EOQ model with inventory cycle balancing

This article concerns a multi-item, infinite-horizon, lot-sizing problem, where the objective is to minimize a total cost function made up of reordering cost, holding cost, and a cost determined by peak inventory levels. By spreading inventory replenishments over the reordering cycle, the peak inventory level can be reduced. The model permits the derivation of simultaneously optimal solutions for the length of the cycle and the individual item replenishment times within the cycle. An alternative formulation, in which total storage capacity is modeled as a constraint, is also solved.