Lot sizing and scheduling — Survey and extensions <s> The general lot sizing and scheduling problem <s> Abstract A mixed integer 0-1 programming formulation for the lot sizing and sequencing of packaging lines in process industries is presented. Results of tests of the model under a variety of operating conditions are listed and it is illustrated that the model may be useful for the solution of smaller practical problems. Implications are discussed for the development of heuristics that may be used to solve large problems. <s> BIB001 </s> Lot sizing and scheduling — Survey and extensions <s> The general lot sizing and scheduling problem <s> This paper treats a version of the Economic Lot Scheduling Problem (ELSP) in which items may be produced several times in different amounts during a cycle. We show how to compute the optimal lot sizes and cycle length, given the sequence of items in a cycle. This requires solving a parametric quadratic program, plus a few EOQ calculations. Our procedure is designed to be used along with a heuristic for selecting the sequence of items in a cycle, such as the one proposed in 1987 by G. Dobson. The two algorithms together comprise a simple, plausible heuristic for the ELSP as a whole. <s> BIB002 </s> Lot sizing and scheduling — Survey and extensions <s> The general lot sizing and scheduling problem <s> A new model is presented for capacitated lot-sizing with sequence dependent setup costs. The model is solved heuristically with a backward oriented method; the sequence and lot-size decisions are based on a priority rule which consists of a convex combination of setup and holding costs. A computational study is performed where the heuristic is compared with the Fleischmann approach for the discrete lot-sizing and scheduling problem with sequence dependent setup costs. <s> BIB003 </s> Lot sizing and scheduling — Survey and extensions <s> The general lot sizing and scheduling problem <s> Abstract This paper deals with lot sizing and scheduling for a single-stage, single-machine production system where setup costs and times are sequence dependent. A large-bucket mixed integer programming (MIP) model is formulated which considers only efficient sequences. A tailor-made enumeration method of the branch-and-bound type solves problem instances optimally and efficiently. The size of solvable cases ranges from 3 items and 15 periods to 10 items and 3 periods. Furthermore, it will become clear that rescheduling can neatly be done. <s> BIB004 </s> Lot sizing and scheduling — Survey and extensions <s> The general lot sizing and scheduling problem <s> Although there is a significant amount of literature on the capacitated lot sizing problem, there has been insufficient consideration of planning problems in which it is possible for a lot size, or production run, to continue over consecutive time periods without incurring multiple setups. While there are papers that consider this feature, they typically restrict production to at most one product in each period. We present a set of mixed integer linear programs for the capacitated lot sizing problem that incorporate setup carry-over without restricting the number of products produced in each time period. Efficient reformulations are developed for finding optimal solutions, and a Lagrangian decomposition heuristic is provided that quickly generates near-optimal solutions. The computational results demonstrate that incorporating setup carry-over has a significant effect on both cost and lot sizes. <s> BIB005 </s> Lot sizing and scheduling — Survey and extensions <s> The general lot sizing and scheduling problem <s> Industrial lotsizing and scheduling pose very difficult analytical problems. We propose an unconventional model that deals with sequence-dependent setup costs in a multiple-machine environment. The sequence-splitting model splits an entire schedule into subsequences, leading to tractable subproblems. An optimization approach based on a column generation/branch and bound methodology is developed, and heuristically adapted to test problems including five real-world problem instances gathered from industry. <s> BIB006
A critique against small bucket models is that for real world problem sizes the number of periods is prohibitively large. This argument may apply for mathematical programming approaches. For common sense heuristics it is definitely not true, because instances with hundreds of periods can nowadays be solved on personal computers with reasonable effort. Nevertheless, it is a valid point that imposing a restriction on the number of items which may be produced per period is primarily motivated by modeling concerns. Comparing the small bucket lot sizing and scheduling models with the CLSP model reveals that only little needs to be added in order to model sequence decisions. Recent research has thus returned to take large bucket models into account where in contrast to the CLSP lot sizing and scheduling is done simultaneously. A practical case of large bucket lot sizing and scheduling is described in BIB001 . In [50] and BIB005 , large bucket lot sizing models are presented, but only a partial rather than a total order among the production quantities is determined. Large bucket lot sizing and scheduling models and methods are given in BIB003 , BIB004 and BIB006 . In more detail we discuss here the so-called general lot sizing and scheduling problem (GLSP) [44] . The parameters are the same as for the DLSP. The underlying idea for the GLSP comes from lot sizing with stationary demand, where each lot is uniquely assigned to a position number in order to define a sequence BIB002 . The fundamental assumption for the GLSP is that a user-defined parameter restricts the number of lots per period (see Table 8 ). Straightforwardly, the position numbers are 1 ..... N1, Nl + 1 ..... Nr. As a short-hand notation, we will use 