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  • Forecasting
    • Moving Averages
    • Exponential Smoothing
    • Linear Trends
    • Seasonal Components

  • Statistical Process Control
    • Control Charts
    • X-bar, R-bar, p-bar, C-bar charts
    • Process Capability

  • Decision Theory
    • Maximax and Maximin
    • Minimax Regret
    • Expected Monetary Value
    • Expected Value of perfect information (EVPI)
    • Expected Value of sample information (EVSI)
    • Decision Trees
    • Utility

  • Location Stretegies
    • Factor Rating
    • Center of Gravity
    • Transportation Model

  • Layout Strategy
    • Fix-position layout
    • Processed Oriented layout
    • Office layout
    • Warehouse layout
    • Forecasting

  • Inventory Models
    • A-B-C analysis
    • Economic Order Quantity (EOQ)
    • Economic Production Quantity (EPQ)
    • Quantity Discount Models
    • One-Period Model
    • Just in Time systems (JIT)

  • PERT
    • Single Estimate
    • Triple Estimate
    • Cost Crashing
    • Critical Paths
    • Gantt-Charts

  • Aggregate Scheduling
    • Demand Chase
    • Mixed Strategy

  • Material Requirement Planning (MRP)
    • Bills of material
    • Lot-for-lot

  • Linear Programming
    • Linear Programming
    • Transportation Problems
    • Transshipment
    • Integer Programming
    • Assignment Problems
    • Network Problems

  • Waiting-Line models
    • Queues
    • Single-Channel and Multi-Channel models

  • Simulation
    • Simulations in Excel
    • Monte Carlo Methods




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Question: The costs of placing an order is $150. It is estimated that 1,000 units will be used in the next 12 months. The carrying cost per unit per month is $2.50.

a. Compute the optimum order size

b. Now suppose that the company could lower the ordering cost to $50; the cost of the effort to accomplish this change is $1,000. Assume the product will be sold only for the next two years. Compute the new optimal order quantity if the lower ordering cost were implemented, and determine if the company should invest $1,000 in the ordering-cost reduction program.

Solution: (a) The following is obtained:

Hence, the optimal order quantity is

\[EOQ=\sqrt{\frac{2DS}{H}}=\sqrt{\frac{2\times 1000\times 150}{2.5}}=346.41\]

The total inventory cost is TC = $866.03.

(b) IF the setup cost was reduced to $50, we would get

In this case, the optimal order quantity is EOQ = 200, and the total inventory cost is $500. The savings in cost for 2 years operation are (866.03 – 500)*2 =$732.06, which is less than $1000 (the cost of reducing the setup cost), and hence, the ordering-cost reduction program should not be pursued.

Question: A logistics specialist for Wiethoff Inc. must distribute cases of parts from 3 factories to 3 assembly plants. The monthly supplies and demands, along with the per-case transportation costs are:

What are the total monthly transportation costs for the optimal solution?

Solution: We have 9 variables \({{x}_{ij}}\), where \({{x}_{ij}}\) represents the amount that is sent from factoryto assembly plant. For convenience of notation, we name the factories A, B and C as 1, 2 and 3.

The problem is written as

\[\begin{align} & \text{Minimize }\sum\limits_{i,j=1}^{3}{{{C}_{ij}}{{X}_{ij}}} \\ & \text{subject to }{{X}_{11}}+{{X}_{12}}+{{X}_{13}}\le 200 \\ & \text{ }{{X}_{21}}+{{X}_{22}}+{{X}_{23}}\le 400 \\ & \text{ }{{X}_{31}}+{{X}_{32}}+{{X}_{33}}\le 200 \\ & \text{ }{{X}_{11}}+{{X}_{21}}+{{X}_{31}}=120 \\ & \text{ }{{X}_{12}}+{{X}_{22}}+{{X}_{32}}=620 \\ & \text{ }{{X}_{13}}+{{X}_{23}}+{{X}_{33}}=60 \\ & \text{ }{{X}_{ij}}\ge 0 \\ \end{align}\]

We know solve this problem using Excel’s solver. The output is shown below:

Plants

Variables

1

2

3

1

2

3

A

5

9

16

A

0

200

0

Factories

B

1

2

6

B

0

400

0

C

2

8

7

C

120

20

60

1

2

3

\({{\mathbf{c}}_{ij}}{{\mathbf{x}}_{ij}}\)

1

0

1800

0

2

0

800

0

Objective

3420

3

240

160

420

Restrictions

Supply

Slack 1

0

200

Slack 2

0

400

Slack 3

0

200

Demand

Slack 4

0

Slack 5

0

Slack 6

0

This means that 120 cases of parts are sent from factory C to Plant 1. The total monthly transportation costs are $3,420.