In this paper, we will consider a concave-cost series production and inventory system with deterministic demands in which (i) backlogging at the final facility and/or (ii) demands at an intermediate facility is allowed_ A dynamic programming algorithm for (i) will be developed, which is a direct extension of the results obtained by W. Zangwill [3], [4] for a similar system but without backloggi...

An explicit description of the convex hull of solutions to the uncapacitated lot-sizing problem with backlogging, in its natural space of production, setup, inventory and backlogging variables, has been an open question for many years. In this paper, we identify valid inequalities that subsume all previously known valid inequalities for this problem. We show that these inequalities are enough t...

We develop the first algorithmic approach to compute provably good ordering policies for a multi-period, capacitated, stochastic inventory system facing stochastic non-stationary and correlated demands that evolve over time. Our approach is computationally efficient and guaranteed to produce a policy with total expected cost no more than twice that of an optimal policy. As part of our computati...

One of the basic assumptions of the classical dynamic lot-sizing model is that the aggregate demand of a given period must be satisfied in that period. Under this assumption, if backlogging is not allowed then the demand of a given period cannot be delivered earlier or later than the period. If backlogging is allowed, the demand of a given period cannot be delivered earlier than the period, but...

The Covid-19 epidemic has caused substantial obstacles to the supply network globally. Hence there is urgency and necessity build a model for cash flow in chain of demand system. This research suggests an inventory assist retailers determining optimal ordering quantity replenishment cycle reduce total cost different payment cases. current study looks toward partial advance delays system conside...

In this paper, we introduce a generalization of the continuous mixing set (which we refer to as the continuous n-mixing set) Qm,n := {(y, v, s) ∈ ( Z× Zn−1 + )m×Rm+1 + : ∑nt=1 αty t + vi + s ≥ βi, i = 1, . . . ,m}. This set is closely related to the feasible set of the multi-module capacitated lot-sizing (MML) problem with(out) backlogging. For each n′ ∈ {1, . . . , n}, we develop a class of va...