Operations and Supply Chain Management The Core

LOCATION, LOGISTICS, AND DISTRIBUTION chapter 14 471
LO14–3 SOLVED PROBLEM 2
Industrial Packaging Solutions (IPS) is a manufacturer of corrugated fiberboard shipping boxes used
by companies across the United States. It sells to wholesalers, who in turn sell to resellers or enduser
customers. Final products are consolidated on standard shipping pallets of uniform dimensions
and weight. Because of this, the cost to ship a pallet to a single destination is the same regardless of
the type of box loaded on the pallet. The standard unit for sales and operations planning at IPS is a
pallet load.
After recently opening a new factory to satisfy growing demand for its products, IPS is concerned
about allocating demand from its customers to the facilities in its production network. It wants to do
so in a way that minimizes the total cost of shipping final products to the wholesalers.
It currently has three factories that service a network of eight major wholesalers. Relevant data
for the next year are shown in the table below.
FACTORY
LOCATION
PRODUCTION
CAPACITY
(PALLETS × 1,000)
WHOLESALER
LOCATION
DEMAND
(PALLETS × 1,000)
Denver, CO 25 Spokane, WA 8.5
Chicago, IL 50 Los Angeles, CA 19.6
Baltimore, MD 35 Kansas City, MO 9.3
Minneapolis, MN 8.8
Indianapolis, IN 11.8
Atlanta, GA 13.6
New York City, NY 17.2
Orlando, FL 8.4
Based on contracts with its transportation suppliers, IPS is confident that the following transportation
rates will be valid over the next year. Rates provided are to transport one pallet of
product. There is no quantity discount given for volume shipments.
DESTINATION CITY AND TRANSPORTATION RATES
FACTORY LOCATION SPOKANE L.A. K.C. MINN. INDY ATLANTA NYC ORLANDO
Denver, CO $42 $49 $45 $54 $56 $65 $70 $72
Chicago, IL 65 69 49 38 32 45 50 55
Baltimore, MD 75 77 68 62 43 44 35 38
Use the transportation method of linear programming to develop a low-cost transportation plan
for IPS for the upcoming year.
Solution
The first step is to consolidate the capacity, demand, and cost data in a single table. This table is
shown below. Note that the capacity and demand numbers have been converted to single pallets
to match the transportation cost units. You could instead convert the transportation cost data into
1,000 pallet units. Either way is fine as long as you have consistent units for all data.
FACTORY
LOCATION
DESTINATION CITY AND TRANSPORTATION RATES
SPOKANE L.A. K.C. MINN. INDY ATLANTA NYC ORLANDO CAPACITY
Denver, CO $42 $49 $45 $54 $56 $465 $70 $72 25,000
Chicago, IL $65 $69 $49 $38 $32 $45 $50 $55 50,000
Baltimore, MD $75 $77 $68 $62 $43 $44 $35 $38 35,000
Demand: 8,500 19,600 9,300 8,800 11,800 13,600 17,200 8,400