a. Formulate and solve a binary integer programming problem to maximize the total number of kitchen sets

Question:

a. Formulate and solve a binary integer programming problem to maximize the total number of kitchen sets (and thus the number of customer orders) Furniture City stocks in the local warehouse. Assume that when a customer orders a kitchen set, all the particular items composing that kitchen set are replenished at the local warehouse immediately.

b. How many of each feature and style should Furniture City stock in the local warehouse? How many different kitchen sets are in stock?

c. Furniture City decides to discontinue carrying nursery sets, and the warehouse space previously allocated to the nursery department is divided between the existing departments at Furniture City. The kitchen department receives enough additional space to allow it to stock both styles of dishwashers and three of the four styles of ranges. How does the optimal inventory policy for the kitchen department change with this additional warehouse space?

d. Brenda convinces management that the kitchen department should serve as a testing ground for future inventory policies. To provide adequate space for testing, management decides

Wallpaper Cabinets Floor Tile Light Fixtures (T1) White textured tile (W1) Plain ivory paper (W2) Ivory paper with dark

to allocate all the space freed by the nursery department to the kitchen department. The extra space means that the kitchen department can store not only the dishwashers and ranges from part c, but also all sinks, all countertops, three of the four light fixtures, and three of the four cabinets. How much does the additional space help?
e. How would the inventory policy be affected if the items composing a kitchen set could not be replenished immediately? Under what conditions is the assumption of immediate replenishment nevertheless justified?

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Daniel Holbrook, an expediter at the local warehouse for Furniture City, sighed as he moved boxes and boxes of inventory to the side to reach the shelf where the particular item he needed was located.
He dropped to his hands and knees and squinted at the inventory numbers lining the bottom row of the shelf. He did not find the number he needed. He worked his way up the shelf until he found the number matching the number on the order slip. Just his luck! The item was on the top row of the shelf! Daniel walked back through the warehouse to find a ladder, stumbling over boxes of inventory littering his path. When he finally climbed the ladder to reach the top shelf, his face crinkled in frustration. Not again! The item he needed was not in stock! All he saw above the inventory number was an empty space covered with dust! Daniel trudged back through the warehouse to make the dreaded phone call. He dialed the number of Brenda Sims, the saleswoman on the kitchen showroom floor of Furniture City, and informed her that the particular light fixture the customer had requested was not in stock. He then asked her if she wanted him to look for the rest of the items in the kitchen set. Brenda told him that she would talk to the customer and call him back.
Brenda hung up the phone and frowned. Mr. Davidson, her customer, would not be happy. Ordering and receiving the correct light fixture from the regional warehouse would take at least two weeks.
Brenda then paused to reflect upon business during the last month and realized that over 80 percent of the orders for kitchen sets could not be filled because items needed to complete the sets were not in stock at the local warehouse. She also realized that Furniture City was losing customer goodwill and business because of stock outs. The furniture megastore was gaining a reputation for slow service and delayed deliveries, causing customers to turn to small competitors that sold furniture directly from the showroom floor.
Brenda decided to investigate the inventory situation at the local warehouse. She walked the short distance to the building next door and gasped when she stepped inside the warehouse.
What she saw could only be described as chaos. Spaces allocated for some items were overflowing into the aisles of the warehouse while other spaces were completely bare. She walked over to one of the spaces overflowing with inventory to determine what item was overstocked. She could not believe her eyes! The warehouse had at least 30 rolls of pea-green wallpaper! No customer had ordered pea-green wallpaper since 1973! Brenda marched over to Daniel demanding an explanation.
Daniel said that the warehouse had been in such a chaotic state since his arrival one year ago. He said the inventory problems occurred because management had a policy of stocking every furniture item on the showroom floor in the local warehouse.
Management only replenished inventory every three months, and when inventory was replenished, management ordered every item regardless of whether it had been sold. Daniel also said that he had tried to make management aware of the problems with overstocking unpopular items and under stocking popular items, but management would not listen to him because he was simply an expediter............

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