Download Average-Cost Control of Stochastic Manufacturing Systems by Suresh P. Sethi PDF

By Suresh P. Sethi

Such a lot production platforms are huge, complicated, and function in an atmosphere of uncertainty. it's common perform to regulate such platforms in a hierarchical type. This booklet articulates a brand new thought that exhibits that hierarchical determination making can in reality result in a close to optimization of approach pursuits. the cloth within the booklet cuts throughout disciplines. it's going to entice graduate scholars and researchers in utilized arithmetic, operations administration, operations examine, and procedure and keep an eye on idea.

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Example text

The averm age capacity level k¯ = j=0 jνj > z. (A5) z ∈ M. 1. 4. From Assumption (A2) it is clear that c(u) and dc(u)/du are nondecreasing. This assumption is required in order for the optimal control policy to be written explicitly in a simple form. Assumption (A4) is necessary in the sense that if this were not true, then even if the system is always producing at its maximum capacity, it still would not meet the demand and the backlog would build up without bound over time, with the consequence that no optimal solution with a finite average cost would exist.

2. Let Assumptions (A1)–(A5) hold. 47) as the case may be, is optimal. Proof. 3, we need only to show that E[V (x∗ (t), k(t))] = 0. 2 and the fact that u∗ (·, ·) is a stable control policy. 1. , there is no production cost in the model, the optimal control policy can be chosen to be the hedging point policy, which has the following form: There are real numbers xk , k = 1, . . , m, such that ⎧ ⎪ ⎪ 0, x > xk , ⎪ ⎨ ∗ u (x, k) = k ∧ z, x = xk , ⎪ ⎪ ⎪ ⎩ k, x < xk . xk (k = 1, . . , m) are called turnpike levels or thresholds.

1. A control process (production rate) u(·) = {u(t) ∈ + : t ≥ 0} is called admissible with respect to the initial capacity k(0) = k, if: (i) u(·) is adapted to the filtration {Ft } with Ft = σ{k(s) : 0 ≤ s ≤ t}, the σ-field generated by k(·); and (ii) 0 ≤ u(t)(ω) ≤ k(t)(ω) for all t ≥ 0 and ω ∈ Ω. ✷ Let A(k) denote the set of admissible control processes with the initial 26 3. Optimal Control of Parallel-Machine Systems condition k(0) = k. For any u(·) ∈ A(k), the dynamics of the system is d x(t) = u(t) − z, dt x(0) = x, t ≥ 0.

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