ISEN 315Spring 2011

Dr. Gary Gaukler

Review: Prototype LP Problem

• Desk manufacturer• Regular and rolltop desks, made of wood• Regular: 20 sqft pine, 16 sqft cedar, 10 sqft

maple• Rolltop: 10 sqft pine, 4 sqft cedar, 15 sqft

maple

Review: Prototype LP Problem

• Profits:– Regular = $90– Rolltop = $115

• Wood available:– 200 sqft pine, 128 sqft cedar, 220 sqft maple

• How much to produce of each type of desk?

Review: Prototype LP Problem

• Decision variables:

• Objective function:

• Constraints:

Review: Aggregate Planning LP

• Parameters:– cH, cF

– cI

– cR

– cO, cU, cS

Aggregate Planning LP

• Parameters:– nt

– K

– I0 ,W0

– Dt

Aggregate Planning LP

• Decision variables:– Wt

– Pt

– It

– Ht, Ft

Aggregate Planning LP

• Decision variables:– Ot

– Ut

– St

Aggregate Planning LP

Aggregate Planning LP

• Constraints:

Aggregate Planning LP

• Constraints:

Aggregate Planning LP

• Objective function:

Aggregate Planning LP

• Now: Implement and solve the problem on p.147 in Excel

Hierarchy of Planning • Forecast of aggregate demand over time horizon

• Aggregate Production Plan: determine aggregate production and workforce levels over time horizon

• Master Production Schedule: Disaggregate the aggregate plan and determine per-item production levels

• Materials Requirements Planning: Detailed schedule for production/replenishment activities

Inventory Control

• Deterministic inventory control• Stochastic inventory control• MRP / Lot sizing / JIT• Supply chain management

Reasons for Holding Inventories

Relevant Costs

• Holding Costs - Costs proportional to the quantity of inventory held.

Relevant Costs (continued)

• Ordering Cost (or Production Cost).

Can include both fixed and variable components.

slope = c

K

Relevant Costs (continued)

• Penalty or Shortage Costs. All costs that accrue when insufficient stock is available to meet demand.

Simple EOQ Model

• Assumptions:

1. Demand is fixed at l units per unit time.

2. Shortages are not allowed.

3. Orders are received instantaneously.

4. Order quantity is fixed at Q per cycle.

5. Cost structure:

a) Fixed and marginal order costs (K + cx)

b) Holding cost at h per unit held per unit time.

Inventory Levels for the EOQ Model

Cost Equation for the EOQ Model

The Average Annual Cost Function G(Q)

The Average Annual Cost Function G(Q)

The Optimal Q*

Properties of the EOQ Solution

Example

• Desk production rate = 200 per month• Each desk needs 40 screws• Screws cost $0.03• Fixed delivery charges are $100 per order• 25% interest rate for holding cost

• What is the optimal order size?

Example